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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(32^25) B)y/(3^225) C)y/(325^2) D)y/(5^32^2) E)y/(532) SOLUTION:Solution: As y and n are both integers so y is of the form of 3522K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)58 sec SOLUTION:Speed = 45 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec ANSWER:A #### A QUESTION:Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)326 B)372 C)375 D)381 E)312 SOLUTION:A+B+C = 1500 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1500 => 375 Answer: C #### C QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this? options: A)264 B)328 C)460 D)588 E)642 SOLUTION:(8c6)(7c5) [8!/(6!2!)][7!/(5!2!)] 2821 588 D #### D QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)1200 B)1300 C)1500 D)1800 E)1900 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 6:30:90 Initial soap:alcohol = 6/30 =6:30 after doubled soap:alcohol =2* 6/30 = 12/30=12:30 Initial soap:water = 6/90=6:90 after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360 After soap: alcohol:water --> 12:30:360 given alcohol 150 cubic centimeter. ratio is 60:150:1800 (12:30:360) For 150 cubic centimeter of Alcohol ---1800 cu cm water is required. Answer-D #### D QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product? options: A)12.5% B)13% C)13.15% D)14% E)15% SOLUTION:Quantity X Rate = Price 1 x 1 = 1 0.7 x 1.25 = 0.875 Decrease in price = (0.125/1) × 100 = 12.5% A) #### A QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195 = 495 m Required time = 495 * 2/55 = 18 sec Answer: B #### B QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: options: A)173 m B)200 m C)273 m D)300 m E)None of these SOLUTION:xplanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, <ACB = 30º and <ADB = 45º. AB/AC=tan30 Answer: C #### C QUESTION:How many multiples of 5 are there between 50 and 500 ? options: A)128 B)91 C)89 D)61 E)60 SOLUTION:It should be mentioned whether 50 and 500 are inclusive. If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91. If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89. Since OA is C, then we have NOT inclusive case. #### C QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =441=16/9==> Remainder=7 Answer: E #### E QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[24+(50-1)2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent? options: A)70% B)45% C)48% D)30% E)40% SOLUTION:Explanation: 840 ---- 380 100 ---- ? => 45% Answer: B #### B QUESTION:John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? options: A)6 days B)8 days C)10 days D)12 days E)14 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 × 40/50 = 8 days B) #### B QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)21 B)24 C)88 D)99 E)26 SOLUTION:(1618)/12 = 24 Answer: B #### B QUESTION:If \|x\| = 4x - 1, then x = ? options: A)3 B)1/2 C)1 and 1/2 D)-1/2 E)-1 SOLUTION:Answer: A Approach: Substituted option A i.e x=1. Inequality satisfied. #### A QUESTION:A train covers a distance of 100km in 1 hour. If its speed is decreased by 25km/hr, the time taken by the car to cover the same distance will be? options: A)1hr B)1hr 20min C)50min D)1hr 30min E)1hr 45min SOLUTION:Speed = 100/1 = 100km/hr New speed = 100-25 = 75 km/hr Time taken = 100/75 = 1hr 20min Answer is B #### B QUESTION:A reduction of 5% in the price of sugar enables a lady to obtain 5kgs more for Rs.500, find the original price per kg? options: A)5.26 B)5.0 C)5.52 D)6.2 E)5.8 SOLUTION:Answer: 500(5/100) = 25 --- 5 ? --- 1 => Rs.5 500 --- 475 ? --- 5 => Rs.5.26.Answer: A #### A QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? options: A)E982 B)27 C)12 D)14.6 E)28 SOLUTION:Explanation: T = 11/45 * 60 = 14.6 Answer: Option D #### D QUESTION:In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? options: A)70 B)52 C)62 D)59 E)50 SOLUTION:total number of players= 16+12+18+13= 59 Answer is D #### D QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2(44 + 124) = 2(16+48) = 128 Then, Finally Length (L) = 212 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2(22 + 242) = 2(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)100 /Initial Area i.e. % change in Area of four walls = (104-128)100 /128=- 18.75% (Decrease) Answer: Option D #### D QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Solution: 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. Answer C #### C QUESTION:3^b + 3^b + 3^b = options: A)7^b B)7^(b + 1) C)7^(7b) D)3^(b + 1) E)49^B SOLUTION:Easy one. 33^b = 3^(b+1) Ans. D #### D QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:How much is 80% of 40 is greater than 4/5 of 25? options: A)15 B)57 C)16 D)12 E)73 SOLUTION:(80/100) * 40 – (4/5) * 25 32 - 20 = 12 Answer: D #### D QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/72/61/5=1/35. Ans E #### E QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent? options: A)25% B)5% C)10% D)15% E)20% SOLUTION:3000 --- 600 100 --- ? => 20% Answer: E #### E QUESTION:A cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is? options: A)24 B)48 C)64 D)2744 E)100 SOLUTION:Volume = 343 = side^3 i.e. Side of Cube = 7 New Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube Volume = 141414 = 2744 square feet Answer: option D #### D QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6 SOLUTION:Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1. ANSWER IS A #### A QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 66 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)(3/7)(4/6)(3/5) [4!/(2!2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 18/5 km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Option B #### B QUESTION:Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)s.10 B)s.2 C)s.5 D)s.3 E)s.4 SOLUTION:2500 = D(100/4)2 D = 4 ANSWER:E #### E QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? options: A)30 B)39 C)87 D)27 E)91 SOLUTION:Let the side of the square(ABCD) be x meters. Then, AB + BC = 2x metres. AC = = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = = 30% (approx) Answer:A #### A QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? options: A)12 years B)13 years C)15 years D)14 years E)18 years SOLUTION:Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) => 2x = 28 => x = 14 years. D #### D QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:x =1 2 3 y= 4 5 18 then what is the relation between x and y options: A)1X)^1 B)1X)^6 C)1X)^7 D)1X)^4 E)1X)^2 SOLUTION:Y=(1X)^2 4=(12)^2 4=4 ANSWER:E #### E QUESTION:9, 35, 91, 189, 341, ? options: A)502 B)521 C)559 D)611 E)712 SOLUTION:Explanation : 13 + 23 = 9 23 + 33 = 35 33 + 43 = 91 43 + 53 = 189 53 + 63 = 341 63 + 73 = 559 Answer : Option C #### C QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:How many integers between 263,205and 658,805 have tens digit 1 and units digit 3? options: A)3,955 B)3,925 C)3,956 D)3,926 E)3,915 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ... The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956 Answer:C. #### C QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench? options: A)700 B)710 C)720 D)800 E)820 SOLUTION:npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) #### C QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C #### C QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is? options: A)30 B)45 C)50 D)60 E)75 SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2 1^3+2^3+3^3+-----+5^3 = (56/2)^2 = 225 Required average is = 225/5 = 45 Answer is B #### B QUESTION:Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? options: A)1/6 B)1/4 C)5/9 D)1/3 E)1/2 SOLUTION:Group 1: 2 Men and 1 Woman Group 2: 1 Men and 2 Woman Need: 2 Men and 2 women Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C22C2 = 1 ways Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2112 = 4 ways Total Favorable cases = 1+4 = 5 Total Possible ways of selecting students 2 from each group = 3C23C2 = 33 = 9 Probability = 5/9 Answer : Option C #### C QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)5/18 = 45 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 34t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? options: A)1500 B)1600 C)1750 D)1900 E)2000 SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. #### C QUESTION:The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers? options: A)87 B)42 C)78 D)76 E)26 SOLUTION:5x 6x 2x 50 25 100 250x + 150x + 200x = 4200 600x = 4200 x = 7 => 6x =42 Answer: B #### B QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/4 %, then the amount invested at 11% was? options: A)12500 B)37500 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100) (9x + 1100000 - 11x) = 37000/4 = 925000 x = 87500 Sum invested at 9% = Rs. 87500 Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500. Answer: A #### A QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:Two trains are moving in opposite directions with speed of 210 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds options: A)56 B)48 C)47 D)26 E)24 SOLUTION:Explanation: Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds Answer: Option E #### E QUESTION:If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following? options: A)12x B)13x C)14x D)16x E)20x SOLUTION:1 + x^4 + x^3 + x^2 + x = 81 i.e. 1 +x+ x^2+ x^3+ x^4 = 81 x+ x^2+ x^3+ x^4 = 80 x(1 +x+ x^2+ x^3) = 80 x(81-x^4) = 80 81x - x^5 = 80 x^5 = 81x -80 Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x Average of R{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x AnswerD #### D QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)22 B)73 C)99 D)42 E)11 SOLUTION:Explanation: Just go in reverse order. Check the options with th subtracting 18 from each option for getting reverse number. 42 – 18 = 24 (which is in reverse). So answer is 42. Answer D #### D QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)13.9 sec B)12.1 sec C)17.9 sec D)61.9 sec E)47.98 sec SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec. Answer:B #### B QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? options: A)4328 B)5382 C)6174 D)7690 E)8436 SOLUTION:The number of ways for the ships to go to the ports is 3! = 6. At Port A, the number of ways to choose two winners is 7C2 = 21. At Port B, the number of ways to choose one winner is 7. At Port C, the number of ways to choose one winner is 7. The total number of ways to give out gift certificates is 62177 = 6174 The answer is C. #### C QUESTION:After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article? options: A)1400 B)1300 C)1200 D)1100 E)None of these SOLUTION:Explanation: CP (76/100) = 912 CP= 12 * 100 => CP = 1200 Answer is C #### C QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5? options: A)32 B)20 C)28 D)11 E)18 SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5 = 100/5 = 20. Answer: B #### B QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? options: A)2880. B)4860. C)5780 D)4320 E)6380. SOLUTION:Normal Day = 600 kw/h Stormy Day = 6001.2=720 kw/h 3 windmills for 2 hours on stormy day 72032=4320 Answer: D #### D QUESTION:If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = n 5a2 + 7b2 = n 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:60, 67, 63, 15, 61, 10, 15 Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list? options: A)25 B)36 C)53 D)60 E)62 SOLUTION:Yes, it can be solved with observation even without approximation in 30 sec. Just observe given numbers: 10, 15 ,15, 60, 61, 63, 67 Median is very easy to tell - its 60. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 60 DE are already out. Now, we have 25, 36 and 53 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 53. (Notice, if 25 is more than mean then 53 is also. If 36 is more than mean, 53 is also. ) Hence C it is! #### C QUESTION:If Juan takes 16 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)16x/y B)16y/x C)x/(16y) D)16/(xy) E)xy/16 SOLUTION:This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate. Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate. We can find Juan’s rate as follows: Rate = Distance/Time = y yards/16 seconds Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have: Time = Distance/Rate Time = x yards/(y yards/16 seconds) Time = (x yards) x (16seconds/y yards) Time = 16x/y seconds Answer A. #### A QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 12 =420 Answer: D #### D QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 344 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 26th September was a Wednesday. The answer is C. #### C QUESTION:A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room? options: A)10:00am B)10:45am C)12:00pm D)12:30pm E)1:30pm SOLUTION:In 6 hours the entrance door is opened to fill the room equal to 61/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours. Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm. Answer: D. #### D QUESTION:What is the sum of the different positive prime factors of 1092? options: A)5 B)12 C)20 D)25 E)27 SOLUTION:First, we make a prime factorization by dividing 1096 by 2 then 3, etc. 1096=2^23713 22+3+7+13=27 Answer (E) #### E QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed? options: A)720 B)625 C)30 D)960 E)255 SOLUTION:Potential combinations of 4 numbers that will yield positive product ++++ 4C6 ---- 4C6 ++-- 2C62C6 4C6 + 4C6 + 2C62C6 F=15 +15 + 1515 = 255=E #### E QUESTION:If c is 14% of a and 40% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 250% SOLUTION:Answer = D 14a/100 = 40b/100 b = 14a/40 = 35a/100 = 35% #### D QUESTION:A group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary. options: A)24 B)36 C)48 D)60 E)64 SOLUTION:The number of ways to choose three cities is 4C3=4. The number of itineraries for each group of 3 cities is 3!. So the number of itineraries to three cities is 43!=24. The number of ways to choose four cities is 4C4=1. The number of itineraries for the group of 4 cities is 4!. So the number of itineraries to four cities is 4!=24. The total number of itineraries is 24+24=48. The answer is C. #### C QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:When 4 dice are thrown, what is the probability that the same number appears on each of them? options: A)1/36 B)1/18 C)1/216 D)1/5 E)1/4 SOLUTION:Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296. Event (Numerator): The chances that all the dice show same number (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6. Probability = Event/ Sample space = 6/64 = 1/63 = 1/216. ANSWER:C #### C QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=? options: A)2515 B)2525 C)2535 D)2545 E)2555 SOLUTION:given,(x+ 1/x) = 5 x^2 + 1/x^2 = (x+ 1/x)^2 - 2x1/x = 5^2 - 2 = 23 -------(1) x^3 + 1/x^3 = (x+ 1/x)^3 - 3x1/x(x+ 1/x) = 5^3 - 35 = 110 -------(2) multiplying (1)& (2), we get =>(x^2+ 1/x^2)(x^3+ 1/x^3) = 23110 => x^5 + 1/x + x + 1/x^5 = 2530 => x^5 + 1/x^5 + (x+ 1/x)= 2530 => x^5 + 1/x^5 + 5 = 2530 => (x^5+ 1/x^5)= 2525 ANSWER:B #### B QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? options: A)1245 B)1567 C)1678 D)1335 E)1635 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Large number = 270+1365 = 1635 E #### E QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled? options: A)600 B)700 C)800 D)850 E)None of these SOLUTION:Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 280 (406 = 240) 100% -----> 600 (1006 = 600) Answer: Option A #### A QUESTION:A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share. options: A)Rs. 3240 B)Rs. 2520 C)Rs. 2880 D)Rs. 3360 E)None of these SOLUTION:Explanation: Let C's investment = Rs. x B's investment = Rs. (x - 3000) A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000) Now, (A + B + C)'s investment = Rs. 72000 => x + (x - 3000) + (x + 3000) = 72000 => 3x = 72000 => x = 24000 Hence, A's investment = Rs. 27000 B's investment = Rs. 21000 C's investment = Rs. 24000 Ratio of the capitals of A, B and C = 27000 : 21000 : 24000 = 9 : 7 : 8 A's share = Rs. [(8/24) Ã— 8640] = Rs. 2880 Answer: Option C #### C QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C QUESTION:A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet? options: A)6 B)3 C)2 D)4 E)5 SOLUTION:Total fleet--20 End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new). End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new). Answer is C--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet. #### C QUESTION:If 50 percent of the members of a certain organization are women and 5/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)I B)II C)III D)I,II & III E)I,II SOLUTION:5/10 (50%) of the members are women and 5/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 5/1080 = 40 women; 80 - 40 = 40 men; 5/840 = 25 married men; 40 - 25 = 15 unmarried men. So, option I,II is true. Answer: E #### E QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die. options: A)1/2 B)1/6 C)0 D)5/6 E)1 SOLUTION:Determine if E and F are independent. P(E\|F) = the probability of event E occurring given that event F has already occurred P(E\|F) ≠ P(E) as P(E) is changed if it is given that F occurs. Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F) We must use the more complex formula for finding the intersection of E and F: P(E∩F) = P(F)P(E\|F) P(F) = the probability of event F occurring The probability of rolling a 1, 2, or 3 is 3/6 = 1/2 P(E\|F) = the probability of event E occurring given that event F has already occurred If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E\|F) = 1/3 P(E∩F) = P(F)P(E\|F) = (1/2) * (1/3) = 1/6 Answer B #### B QUESTION:Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)6 B)40 C)50 D)10 E)20 SOLUTION:Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E #### E QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:Ed throws a blue die and a red die. How many combinations are there in which the two dice do not yield the same result and the sum of the results is not 9? options: A)10 B)24 C)26 D)30 E)36 SOLUTION:Total number of combination is 66 = 36.. Condition 1: we shouldn't get the same number... (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) - 6 combinations. condition 2: We shouldn't get the 9 as the sum (4,5)(5,4)(3,6)(6,3) - 4 combinations... Total = 36 - 10 = 26. ANS option C. #### C QUESTION:Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 6 and the product of the given number and the sum of its digits is equal to 136. options: A)82 B)93 C)39 D)28 E)17 SOLUTION:Using the elimination method the option that fits this description is 17 7-1 = 3 (unit's digit that exceeds its ten's digit by 3) 178 = 136 (the product of the given number and the sum of its digits is equal to 175) answer :E #### E QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y? options: A)1/7 B)14 C)15 D)52/7 E)60/7 SOLUTION:3x-y=6 ...equation 1 x+2y=8 ...equation 2 adding both the equations 4x+y=14 correct answer option B #### B QUESTION:Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? options: A)648 B)1800 C)2700 D)10800 E)948 SOLUTION:Let the required number of bottles be x. More machines, More bottles (Direct Proportion) More minutes, More bottles (Direct Proportion) Machines 6 : 10 :: 270 : x Time (in minutes) 1 : 4 Therefore, 6 x 1 x x = 10 x 4 x 270 => x =(10 x 4 x 270) / (6) => x = 1800. Correct answer is B. #### B QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:A box contains 8 pairs of shoes (16 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/19 D)1/10 E)1/15 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 16, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/11/15(as after taking one at random there are 15 shoes left and only one is the pair of the first one)=1/15 Answer: E. #### E QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:A bag contains 3 white balls, 3 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)0.25 B)0.15 C)0.35 D)0.45 E)0.4 SOLUTION:Each ball has an equal probability of being the third ball drawn. P(3rd ball is red) = 4/10 = 0.4 The answer is E. #### E QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:he average of 15 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)14 D)19 E)8 SOLUTION:Average of 15 numbers = 0. Sum of 15 numbers (0 x 15) = 0. It is quite possible that 14 of these numbers may be positive and if their sum is a the 15th number is (-a). Answer: Option C #### C QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!22= 480 The answer is C. #### C QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours * 1 choices = 1C11C1 = 11=1=D #### D QUESTION:A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business? options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500 SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. 15000 x 3/10 = Rs. 4,500. B #### B QUESTION:A coin is tossed six times. What is the probability that there is at the least one tail? options: A)63/64 B)31/64 C)31/67 D)31/64 E)63/31 SOLUTION:Let P(T) be the probability of getting least one tail when the coin is tossed six times. = There is not even a single tail. i.e. all the outcomes are heads. = 1/64 ; P(T) = 1 - 1/64 = 63/64 Answer: A #### A QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:Which of the number is the odd one out? options: A)21165 B)17642 C)81002 D)52832 E)72927 SOLUTION:D 52832 All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27. Answer is D #### D QUESTION:The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher. options: A)40 yrs B)42 yrs C)45 yrs D)46 yrs E)47 yrs SOLUTION:The average age of 30 boys of a class is equal to 14 yrs: i.e Sum of all boys:3014 include class teacher:31 candidates in a class & avg age is:15 yr i.e. sum of all:3115(include class teacher)=465 so,the age of the class teacher:465-420=45yr answer will be 45 yrs ANSWER:C #### C QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.) options: A)1/5 B)1/2 C)2/3 D)4/5 E)6/5 SOLUTION:Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B FOR THE FIRST BUCKET ... Red color - 2 Blue color - 2 FOR THE SECOND BUCKET Red color - 3 Blue color -2 In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios : Scenario I - He picks Red color from List A and Blue color from List B Scenario II - He picks Blue color from List A and Red color from List B Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5 Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ... Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ... We get 1/5 + 3/10 = 2/3 (C) #### C QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D <<<Examples ends QUESTION:What is the maximum number of points that 10 circles of different radii intersect? options: A)24 B)26 C)33 D)90 E)100 SOLUTION:the maximum number of points that two circles intersect is two. therefore, each of these 10 circles intersect two point with each of the other 9 circles. as a consequence, the number of these points is equal to two times the number of combination of the 10 circles. 2∗(10!)/(2!∗10!)=90 Answer: D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively options: A)19 B)17 C)13 D)22 E)21 SOLUTION:Explanation: Answer will be HCF of (48-4, 210-12, 136-4) HCF of (44, 198, 132) = 22 Option D #### D QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1245 B)1345 C)1455 D)1577 E)1671 SOLUTION:Let the smaller number be x. Then larger number = (x + 1395). x + 1395 = 6x + 15 5x = 1380 x = 276 Large number = 276+1395 = 1671 E #### E QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train? options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes SOLUTION:we don't need to assume here the direction.we need to find which will take less time so there are 2 cases 1)both moving in same direction...then time would be 2 minutes 2)both moving in opp direction then time would be 0.8 minutes as we need the shortest time it would be the second case Answer:E #### E QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is options: A)11 B)12 C)15 D)13 E)17 SOLUTION:Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D #### D QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue? options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17 SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/189/17 = 12/17. Answer: E. #### E QUESTION:The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour? options: A)60 B)61.2 C)3240 D)3,600 E)3,672 SOLUTION:moon revolves around the earth at a speed of 1.02kilometers per second. one hour equal to 60 minutes. one minute equals to 60 seconds. so one hour equals to 3600seconds. so one hour, speed= 0.93600=3240kilometers per hour. Option C is correct #### C QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)1/4 C)3/8 D)7/8 E)None of these SOLUTION:Explanation: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E) = n(E) / n(S) =7/8. ANSWER IS D #### D QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:What is the sum of all the even numbers between 31 and 99, inclusive? options: A)3,000 B)2,562 C)2,500 D)2,180 E)2,766 SOLUTION:To figure this problem out, you just have to add all the even numbers, starting with 32. 32+34+36+38 and so on, all the way up to 98. You'll get 2,180, so Final Answer: D #### D QUESTION:During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year? options: A)$2.5 B)$2.55 C)$1.51 D)$3.25 E)$3.0 SOLUTION:finding the Harmonic mean here. HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1 C #### C QUESTION:If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer? . options: A)√n + 1 B)n + 1 C)n^2 + 1 D)n + 2√n + 1 E)n^2 + 2n + 1 SOLUTION:Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a and a=n^(1/2) Therefore , (a+1)^2=n+1+2n^(1/2) Answer D #### D QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50 9/10 x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:If you roll one fair six-sided die, what is the probability that the number is even or less than 4? options: A)1/6 B)1/3 C)2/ 3 D)3/4 E)5/6 SOLUTION:Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5 Total possible outcome= 6 Probability=5/6. Answer: Option E #### E QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set? options: A) 87 B) 89 C) 90 D) 92 E) 95 SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97} Set Y = {10, 20, 30,..............., 70, 80, 90} Combining two sets, say Set Z Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97} Range = Max Value - Min Value Range (Z) = 97 - 10 = 87 OA A is the answer. #### A QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? options: A)12 days B)18 days C)15 days D)21 days E)22 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/10 work in 1 day B alone can do (1/6 -1/10) =1/15 work in 1 day => complete work can be done in 15 days by B Answer: Option C #### C QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work? options: A)10 B)12 C)22 D)28 E)20 SOLUTION:A can do the work in 60/4 i.e., 15 days. A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12 So A and B together can do the work in 12 days. Answer: B #### B QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)35 B)45 C)25 D)15 E)55 SOLUTION:A : B : C =10×7:12×5:15×3 =2×7:12×1:3×3 =14:12:9 Amount that C should pay =175×9/35=5×9=45 Answer is B. #### B QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? options: A)50 % B)60 % C)70 % D)80 % E)40 % SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:B #### B QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:The middle number is 40. Let the smallest number be x. Then the largest number is 2x+20. To make x as small as possible, let's make the remaining numbers as large as possible. So the second largest = the largest = 2x+20. The second smallest should be equal to the median. The numbers are x, 40, 40, 2x+20, 2x+20. x + 40 + 40 + 2x + 20 + 2x + 20 = 540 = 200 5x = 80 x = 16 The answer is B. #### B QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ? options: A)6000 B)5400 C)6200 D)7200 E)8200 SOLUTION:Investment Ratio = Profit Sharing Ratio. Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6. Giri share = 13200 × 6 / 11 = Rs.7200 Hari share = 13200 × 5 / 11 = Rs.6000 Option A #### A QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)100 =66 2/3% Ans C #### C QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:If pq = p^3 + q^2 – 2pq, for what value of q is pq equal to p^3 for all values of p? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:C p3 + q2 â€“ 2pq = p3 => q2 - 2pq = 0 => q (q - 2p) = 0 => q = 0 or q = 2p im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI C #### C QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100 P1’s income = Rs 51100 = Rs.5500 ANSWER:D #### D QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) 1 + 1 = 15 1 + 1 = 16. 3rd term = (2nd term) 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) 3 + 3 = 34 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is? options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3 SOLUTION:Correct sum = (36 * 50 + 48 - 23) = 1825. Correct mean = 1825/50 = 36.5 Answer:C #### C QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days SOLUTION:A 6.4 days 1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300 So, all three together will complete the work in 300/47 = 6.4 days.- #### A QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x? options: A)125 B)150 C)225 D)250 E)500 SOLUTION:90 = (x/100)(# boys) # boys = .4x substitute and solve: 90 = (x/100)(.4x) 9000 = .4(x^2) 25000 = x^2 x=150 Answer: B #### B QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is : options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5 SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 495 99c - 99a = 99(c - a) = 495 495 = 995 = 99(c - a) So c - a = 5 Answer (E) #### E QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)(1/5) So it takes 25 men to complete this job = 25 * (1/25) = 1 Answer: C #### C QUESTION:A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ? options: A)30 days B)15 days C)45 days D)24 days E)None of these SOLUTION:Let C completes the work in x days. Work done by (A + B) in 1 day = 1⁄10 Work done by (B + C) in 1 day = 1⁄18 A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1 or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1 or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days Answer C #### C QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately). options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48% SOLUTION:Let the total money=300 A's part=100 B's part=200 After 2 years A's part=73.46 (As it depreciates by 14.29% per annum) After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where P=200,r=0.2,n=1,t=2) So, After 2 years total amount=361.46 Therefore % increase in money=(361.46-300)100/300=20.48% ANSWER:B #### B QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = prt/100 = 100000043/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: options: A)12 B)24 C)34 D)48 E)54 SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.Answer: Option D #### D QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:A man can row upstream at 10 kmph and downstream at 20 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)25 D)88 E)34 SOLUTION:US = 20 DS = 30 M = (30 + 20)/2 = 25 Answer:C #### C QUESTION:If xy not equal 0 and x^2y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:If n = 2.0767 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0047 E) 0.0033 SOLUTION:n=2.08 n-n=2.08-2.0767 0.0033 Answer: E #### E QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x? I. 6/x II. -4/x III. 1/x options: A)I only B)II only C)I and II only D)I and III E)II and III SOLUTION:(x^2)(y^2) –2xy - 24 = 0 (xy – 6)(xy + 4) = 0 xy – 6 = 0 or xy + 4 = 0 xy = 6 or xy = -4 Since we need y in terms of x, we can isolate y in both of our equations. y = 6/x or y = -4/x Answer: C #### C QUESTION:Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey? options: A)432 miles B)651 miles C)387 miles D)954 miles E)556 miles SOLUTION:The number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer A #### A QUESTION:How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 4? options: A)a. 220 B)b. 249 C)c. 432 D)d. 216 E)e. 288 SOLUTION:Taking Question with it's same language as given To make number divisible by 5, the unit digit should be either 0 or 5 only Case 1: If unit digit is fixed as zero With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15 With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120 Total Such cases = 120+15 = 135 Case 2: If unit digit is fixed as Five With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065] With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12 With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40 With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60 Total Such cases = 2+12+40+60 = 114 Total numbers = 135+114 = 216 ANSWER OPTION D #### D QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:what is the radius of a circle that has a circumference of 3.14 meters? options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr. 2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? options: A)90 min B)100 min C)110 min D)120 min E)None SOLUTION:Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C #### C QUESTION:When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true? options: A)2 B)3 C)4 D)7 E)8 SOLUTION:When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2. It also means that 18 is completely divisible by k. Factors of 18 are 1, 2, 3, 6, 9, 18 Out of these, k can be 3, 6, 9 and 18. Answer (C) #### C QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Sol. By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6. Answer C #### C QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)12:30 B)1:00 C)1:30 D)2:00 E)2:30 SOLUTION:In thirty minutes the first train travels 35 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 35/10 = 3.5 hours, so at 1:00 pm. The answer is B. #### B QUESTION:The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages. options: A)30% B)32.50% C)33 1/3% D)40% E)50% SOLUTION:Explanation: The gain is 4 out of 12 articles. Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3% Answer: Option C #### C QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000? options: A)8275 B)1879 C)2779 D)2672 E)2782 SOLUTION:A = 25000(11/10)^3 = 33275 = 25000 ---------- 8275 Answer: A #### A QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? options: A)A)100 B)B)102 C)C)108 D)D)110 E)E)120 SOLUTION:The girl can select one jeans in 10 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 10 * 12 = 120 ways. E #### E QUESTION:Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 72 kmph and 90 kmph. In how much time will the trains cross each other? options: A)80/8 B)80/9 C)80/5 D)80/3 E)80/1 SOLUTION:Relative speed = (72 + 90)* 5/18 = 9* 5 = 45 mps. The time required = d/s = (100 + 100 + 200)/45 = 400/45 = 80/9 sec. Answer: B #### B QUESTION:Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in options: A)1 13/17 hours B)2 8/11 hours C)3 9/17 hours D)5 5/11 hours E)None SOLUTION:Solution Net part filled in 1 hour = (1/10 + 1/6 -1/12) = 11/60. Therefore, the tank will be full in 60/11 hrs. â€¹=â€º 5 5/11 hrs. Answer D #### D QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)50 SOLUTION:Relative speed of the train=63-3=60kmph=605/18=50/3 m/sec t=5003/50=30sec ANSWER:B #### B QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C QUESTION:Fourthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? options: A) 60 B) 70 C) 100 D) 120 E) 140 SOLUTION:40% of the members have passed the test, thus 60% have not passed the test. We also know that 30+12=42 members have not passed the test, thus 0.6Total=42 --> Total=70. Answer: B. #### B QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+10)=4/5 20x=4(3x+10) 8x=40 x=5 Quantity of alcohol = (4 x 5) litres = 20 litres. Answer is D. #### D QUESTION:How many 0's are there in the binary form of 61024 + 464 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:61024 + 464 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:If N = 2^0.15 and N^b = 8, b must equal options: A)3/80 B)3/5 C)20 D)5/3 E)80/3 SOLUTION:15/100 = 3/20 N = 2 ^ 3/20 N^b = 2^3 (2^3/20)^b = 2^3 b = 20 Answer: C #### C QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:If there are 10 apples and 20 oranges, what is the ratio of apples to oranges? options: A)10:20 B)2:4 C)1:2 D)4:8 E)It cannot be determined from the information given SOLUTION:A ratio should be reduced to the lowest common denominator. 10:20 means 10x:20x which can be written as 1(10):2(10)... ANSWER:C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1 options: A)I,III only B)III only C)I only D)II only E)II,III only SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+36=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1; I. y<3x --> is not always true. Answer: E #### E QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus? options: A)52 B)92 C)95 D)88 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 11 Total People can seat= 81+11=92 ANSWER:B #### B QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 7 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 14. D #### D QUESTION:Agatha has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have? options: A) 32 B) 30 C) 29 D) 28 E) 27 SOLUTION:5n + 10m = 460 n > m Pick an easy number to work with. suppose n=30. Then you have 150. You need another 310 and that means you need m=31 which is greater than n. Therefore, n > 30. The only answer choice where n> 30 is if n = 32. A is the answer. #### A QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $140 B) $160 C) $220 D) $240 E) $264 SOLUTION:12$ per week! An year has 52 weeks. Annual charges per year = 52* 12 = 624$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 30 = 360$ 624 - 360 = 264 Ans E #### E QUESTION:If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element? options: A)27 grams B)28 grams C)29 grams D)42 grams E)32 grams SOLUTION:Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 25 grams 25/7 = 3.571... C. 29 grams 29/7 = 4.142....... D. 42 grams 42/7 = 6 E. 32 grams 32/7 = 4.571.... Hence our answer will be (D) #### D QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 560/60 = 51/1 = 5 New time in minutes to cross 5 miles stretch = 560/40 = 53/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is options: A)22 kg B)21.6 kg C)22.4 kg D)10 kg E)None of these SOLUTION:Exp . The total weight of 29 students = 29* 28 The total weight of 30 students = 30* 27.4 Weight of the new student = ( 3027.4 – 2928) = 822 - 812 = 10 Answer:D #### D QUESTION:A bowl was filled with 10 ounces of water, and 0.004 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? options: A)0.004% B)0.04% C)0.40% D)2% E)40% SOLUTION:Total amount of water evaporated each day during a 50-day period = .004 * 50 =.004 * 100/2 = .4/2 = .2 percent of the original amount of water evaporated during this period = (.2/10) * 100% = 2 % Answer D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speedâˆ—Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, A receives : options: A)14700 B)24703 C)29400 D)33777 E)34778 SOLUTION:Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=> x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. A's share = Rs. (70000 * 21/50 ) = Rs. 29,400. Answer: C) #### C QUESTION:Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year. options: A)18% B)30% C)52% D)63% E)85.71% SOLUTION:Let Profit be x and cars sold be y Originally Profit/Car = x/y Now it is 1.3x / 0.7 y = 13/7 (x/y) Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71% Answer = E #### E QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident? options: A)35 B)30 C)25 D)20 E)None of these SOLUTION:Let the truth spoken by A and B be pl and p2 respectively, i.e., pl = 3⁄4 and p2 = 4⁄5 They will contradict each other only when one speaks truth and the other is lying. i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35% Answer A #### A QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x + y ? options: A)810 B)811 C)830 D)850 E)851 SOLUTION:21 integers from 30 to 50 inclusive so 11th integer is mean, it is 40 2140=840 from 21 integers 11 ones is even 840+11=851 ANSWER:E #### E QUESTION:If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil? options: A)5 B)3 C)1 D)4 E)2 SOLUTION:Blue is 1/2 but can also be written as 4/8 Red is 1/8 White is 3/8 4/8+1/8+3/8= 8/8=1 Answer is C) 1 #### C QUESTION:30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there? options: A)800 B)1000 C)1200 D)1500 E)1800 SOLUTION:800score Official Solution: People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers. Fishermen = (300 / 30) × 100 pers. = 1000 pers. The correct answer is choice (B). #### B QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 1/3 = 810 Option B #### B QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount. options: A)680 B)700 C)720 D)730 E)750 SOLUTION:From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal. As the annual Interest is to be calculated, the time period T =1. Plugging these values in the simple Interest formula, I = P x T x R = 8,000 x 1 x 0.09 = 720.00 Annual Interest to be paid = $720 answer :C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 12 = 84 Answer is A #### A QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32900+83000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? options: A)22 km B)40 km C)65 km D)18 km E)16 km SOLUTION:Distance = Relative Speed Time = (7 + 3) * 4 = 40 km [ They are travelling in the opposite direction, relative speed = sum of the speeds]. Answer: B #### B QUESTION:Which of the statements can be dispensed with while answering the above question? options: A)A only B)B only C)A or C only D)B or C only E)C or D only SOLUTION:Explanation: Justification: We can find the code for 'home' from the second and third statements. For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data. Clearly, statement A is not necessary. Answer: A #### A QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)115 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 25 : x => x = {\color{Blue} \frac{25\times 1}{0.128}} => x = 195.31 So time will be approx 195 seconds Answer: B #### B QUESTION:9823 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)3377 E)None of these SOLUTION:Answer x = 13200 - 9823 = 3377 Option: D #### D QUESTION:The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability W that exactly two visitors will buy a pack of candy? options: A)0.343 B)0.147 C)0.189 D)0.063 E)0.027 SOLUTION:3C2 * (3/10)^2 * 7/10 = 3 * 9/100 * 7/10 = 189/1000 = 0.189=W Answer - C #### C QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km options: A)200 Km B)222 Km C)224 Km D)248 Km E)None of these SOLUTION:Explanation: Let time taken to travel the first half = x hr Then time taken to travel the second half = (10 - x) hr Distance covered in the the first half = 21x [because, distance = timespeed] Distance covered in the the second half = 24(10 - x) Distance covered in the the first half = Distance covered in the the second half So, 21x = 24(10 - x) => 45x = 240 => x = 16/3 Total Distance = 221(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way] Option C #### C QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3 SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4x. Point (r, r+1) lies on line n means that (r+1)=1/4r --> r=-4/3. Answer: A. #### A QUESTION:Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...) options: A)31 B)42 C)46 D)56 E)68 SOLUTION:Explanation : We have two series here 34, 37, 40, 43, ... (Increase by 3) 7, 14, 28, ... (Multiply by 2) Hence, next term is 28 × 2 = 56 Answer : Option D #### D QUESTION:Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x? options: A)Three B)Four C)Five D)Six E)Seven SOLUTION:Since the number is positive and even and contains only 3 and 4 as digits, then its numbers digit is 4 and is fixed. As there are not many possibilities for x, I found the most simple method to just start plug in numbers starting from the first and least value of x, which is answer key A. three If x would have 3 digits, then we have 4 possibilities (since 4 is always the number digit for an even number): 334: is divisible by 4 but not by 3 344: is divisible by 4 but not by 3 434: is not divisible by 4 nor by 3 444: is divisible by 4 AND by 3 - then CORRECT ANSWER A #### A QUESTION:Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March? options: A)5% B)10% C)20% D)25% E)50% SOLUTION:Let J,F,M be the values of the stock in Jan,Feb and March. Thus, per the question, J = 0.9F = 1.2M ----> M =0.75F Thus the % decrease from F to M = (F-M)/(F) 100 = (F-0.75F)/F 100 = 0.25100 = 25 %, D is the correct answer. #### D QUESTION:If y > 0, (8y)/20 + (3y)/10 is what percent of y? options: A)40% B)50% C)60% D)70% E)80% SOLUTION:can be reduced to 4y/10+3y/10 =7y/10=70% Answer D #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:What will be in unit's place digit of 3 to the power 34. options: A)1 B)6 C)3 D)0 E)9 SOLUTION:as the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9.. ANSWER:E #### E QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4* and 5). Make the 4 number as large as possible and make the 5 number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6 and 7). Make the 6 number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:385, 462, 572, 396, 429, 671, 264 options: A)385 B)429 C)671 D)264 E)None of these SOLUTION:Solution In each number except 429,the middle digit is the sum of the other two. Answer B #### B QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B <<<Examples ends QUESTION:If c is 14% of a and 40% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 250% SOLUTION:Answer = D 14a/100 = 40b/100 b = 14a/40 = 35a/100 = 35% #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:Health insurance Plan Q requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$600 B)$1000 C)$3800 D)$5300 E)$6200 SOLUTION:0.5 * 600 = 300 where Q = B #### B QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C? options: A)2250 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 75/247 7410 = 2250 Answer: A #### A QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots? options: A)-12 B)-6 C)12 D)6 E)24 SOLUTION:Explanation: The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a). Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12. we get, sum of the roots = 1 / a = 1 a = 1 Product of the roots = -12 / 1 =-12 ANSWER: A #### A QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’? options: A)25% B)50% C)23% D)28% E)None of these SOLUTION:Cost price = 240×100/120= 200 S.P. at no discount = 240×100/80 = 300 ∴ % profit = 100×100/200 = 50 % Answer B #### B QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (2010.5 + 3012) = 0 Answer : A #### A QUESTION:1.14 expressed as a per cent of 1.9 is: options: A)6% B)10% C)60% D)90% E)None SOLUTION:Solution: Required percentage = (1.14100)/1.9 = 60%. Answer: Option C #### C QUESTION:The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 50% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 75 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:No of people from 10 - 11 is x No of people from 11 - 12 is 3x/4 No of people from 12 to 1 is (3/2)(3x/4) Given that 3x/4 + (3/2)(3x/4) = (3x/4)(5/2) = 75 Then x = 40 D #### D QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 6 minutes. How much time will be take to cover a distance of 6 kilometres? options: A)48 min. B)50 min. C)66 min. D)55 min. E)None of these SOLUTION:Rest time = Number of rest Ã— Time for each rest = 5 Ã— 6 = 30 minutes Total time to cover 6 km = (6â„10 Ã— 60)minutes + 30 minutes = 66 minutes Answer C #### C QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight? options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb SOLUTION:Sol. 66÷6 = 11. Answer : B #### B QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:A train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? options: A)229 B)288 C)600 D)888 E)1400 SOLUTION:D = 35 * 5 = 175 RS = 40 – 35 = 5 T = 175/5 = 35 D = 40 * 35 = 1400 km Answer: E #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 9 = 150 meter Answer:A #### A QUESTION:Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)40 m B)72 m C)80 m D)82 m E)84 m SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 44 - 36 = 8 km/hr. = 8 * 5/18 = 20/9 m/sec. 2x/36 = 20/9 => x = 40. ANSWER:A #### A QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (12523+16225)/125+162 = 24 years Answer is D #### D QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10 SOLUTION:The total possible choices are 12C3 = 220 The ways to choose 3 apples: 6C3 = 20 The ways to choose 2 apples: 6C2 * 6C1 = 90 P(at least 2 apples) = 110/220 = 1/2 The answer is A. #### A QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used. The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost? options: A)981 B)1000 C)1011 D)1101 E)1110 SOLUTION:The number of codes possible if leading zero is allowed = 10101010=10^4 The number of codes possible if leading zero is NOT allowed = 9101010=910^3 The difference = 10^4 - 910^3 = 10^3(10-9) = 10^3.=1000 Answer: B. #### B QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:28=16.Answer is A. #### A QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? options: A)720 B)760 C)680 D)780 E)880 SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is 10 x 9 x 8 = 720 ANSWER:A #### A QUESTION:If Jane takes 12 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/12 B)12x/(60y) C)60xy/12 D)xy/720 E)720x/y SOLUTION:The answer is B. She runs x yards in 12x/y seconds =12x/60y minutes. #### B QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:If p/q = 5/4 , then 2p+q= ? options: A)12 B)14 C)13 D)15 E)16 SOLUTION:let p=5, q=4 then 25+4=14 so 2p+q=14. ANSWER:B #### B QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 344 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used options: A)12 months B)10 months C)14 months D)16 months E)None of these SOLUTION:Explanation : B received 2/3 of the profit => A : B = 1 : 2 Let the total capital = x Then A's capital = x/4 B's capital = x – x/4 = 3x/4 Assume B's money was used for b months Then A:B = (x/4)15 : (3x/4)b = 1 : 2 => 15/4 : 3b/4 = 1 : 2 => 15 : 3b = 1 : 2 => 5 : b = 1 : 2 => 5/b = 1/ 2 => b = 52 = 10. Answer : Option B #### B QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)8 D)5 E)12 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 50 = 20 + 30 + 30 - (20) - 2x x = 5 So, answer will be D #### D QUESTION:A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is? options: A)4 kmph B)2 kmph C)7 kmph D)8 kmph E)3 kmph SOLUTION:DS = 19 US = 11 S = ? S = (19 - 11)/2 = 4 kmph Answer:A #### A QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)16 sec B)13 sec C)17 sec D)21 sec E)23 sec SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/20 = 6 m/sec. Relative speed = 12 + 6 = 18 m/sec. Required time = (120 + 120)/18 = 13 sec. Answer: B #### B QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x 100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:A company pays 20.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares? options: A)25 B)66 C)18 D)19 E)41 SOLUTION:Explanation: Dividend on 1 share = (20.5 * 50)/100 = Rs.10.25 Rs.25 is income on an investment of Rs.100 Rs.10.25 is income on an investment of Rs. (10.25 * 100)/25 = Rs.41 ANSWER: E #### E QUESTION:A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The speed at which the train must run to reduce the time of journey to 40min will be. options: A)60kmph B)63kmph C)57kmph D)70kmph E)61kmph SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=ST=485/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph Answer is A. #### A QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 Ã— 16 = 368 m2 Area of the inner rectangle = 19 Ã— 12 = 228 m2 Required area = (368 â€“ 228) = 140 m2 Answer B #### B QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)20 kmph B)30 kmph C)87 kmph D)99 kmph E)77 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. Answer:A #### A QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of shelves. 11x - 30 = 7(x-1) + 5 4x = 28 x = 7 The answer is C. #### C QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:1 percent for 3 years= 63 1 percent for 1 year = 21 => 100 percent = 2100 ANSWER:B #### B QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:200 is what percent of 40? . options: A)0.2% B)2% C)5% D)20% E)500% SOLUTION:200= x40/100 x = 500% Ans; E #### E QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2SDtomean + 2SD, thus from 50-250.5=51 to 50+250.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? options: A)87 B)89 C)90 D)93 E)95 SOLUTION:Total score on 3 tests = 813 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 834 = 332 Score required on the fourth test = 332 - 243 = 89 Option B #### B QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (11) = 2. 2(result) + (22) = 6. 6(result) + (33) = 15. 15(result) + (44) = 31. 31(result) + (55) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:John found that the average of 15 numbers is 40. If 12 is added to each number then the mean of number is? options: A)52 B)45 C)65 D)78 E)64 SOLUTION:(x+x1+...x14)/15 = 40 52 Option A #### A QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 144 metres, what is its area? options: A)1320 sq.metres B)1260 sq.metres C)1280 sq.metres D)1380 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 144 ⇒ x = 6 Area = 7 × 6 × 5 × 6 = 1260 sq.m. Answer B #### B QUESTION:A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest? options: A)5% p.a. B)7.5% p.a. C)10% p.a. D)12.5% p.a. E)None of these SOLUTION:Explanation: Given: 800 = (P R * 2) / 100 S.I. For 1 year = Rs. 400 Thus, (840 – 800) = S.I. on Rs. 400 for 1 year 40 = (400 * R * 1) / 100 R = 10% p.a. ANSWER C #### C QUESTION:A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.? options: A)50 kmph B)58 kmph C)62 kmph D)65 kmph E)75 kmph SOLUTION:Relative speed = 280/9 m / sec = ((280/9)(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph. Answer : C. #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years, The age of the 15th student is options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Explanation: Age of the 15th student = [15 15 - (14 * 7 + 16 * 7)] = 15 years. Answer: E #### E QUESTION:What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ? options: A)17/36 B)36/17 C)17/6 D)85/2 E)51/4 SOLUTION:2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12 1/5 - 1/6 = (6-5)/30 = 1/30 So 17/12/1/30 = 17/12 * 30 = 85/2 Answer - D #### D QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 25001.5/1.4= 2478 Answer:- D #### D QUESTION:The perimeter of one square is 48 cm and that of another is 36 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined? options: A)13√4 B)13√2 C)23√2 D)12√4 E)15√2 SOLUTION:4a = 48 4a = 36 a = 12 a = 9 a2 = 144 a2 = 81 Combined area = a2 = 225 => a = 15 d = 15√2 Answer: E #### E QUESTION:A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase? options: A)$18 B)$20 C)$22 D)$24 E)$25 SOLUTION:Let x be the daily wage before the increase. 1.4x = $28 x = $20 The answer is B. #### B QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7. options: A)18 B)20 C)17.5 D)30 E)32 SOLUTION:Solution Average = (7+14+21+28)/4) = 70 / 4 = 17.5. Answer C #### C QUESTION:The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class. options: A)A)48.55 B)B)49 C)C)51 D)D)61 E)E)62 SOLUTION:Required average = (50.25 x 16 + 45.15 x 8)/(16 + 8) = (804 + 361.20)/24 = 1165.20/24 = 48.55kg Answer is A #### A QUESTION:Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums? options: A)30 B)36 C)70 D)80 E)150 SOLUTION:Method I: the rates solution “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time: T = A/R = 15/(5/12) = 15(12/5) = (15/5)12 = 312 = 36 BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums. Answer = B. #### B QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature T in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median T will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is options: A)17.2 km B)7.2 km C)7.6 km D)17.6 km E)27.2 km SOLUTION:speed of a boat in still water = 15 km/hr Speed of the current = 3 km/hr Speed downstream = (15+3) = 18 km/hr Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km Answer is B #### B QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(32^25) B)y/(3^225) C)y/(325^2) D)y/(5^32^2) E)y/(532) SOLUTION:Solution: As y and n are both integers so y is of the form of 3522K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A QUESTION:A room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles. What will be the least number of square tiles required to cover the floor? options: A)176 B)124 C)224 D)186 E)190 SOLUTION:LENGTH = 5 M 44 CM = 544 CM BREADTH = 3 M 74 CM = 374 CM AREA = 544 374 HCF = 34 AREA OF SQUARE = 34 * 34 CM2 NO OF TILES REQ = 544* 374/3434 = 16 11 =176 ANSWER A #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick? options: A)5, 12, and 8 kg B)6, 12, and 8 kg C)7, 12, and 8 kg D)8, 12, and 8 kg E)None SOLUTION:Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x+2, respectively. So x+2x+x+2=26 4x=24 x=6 Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively. Answer B #### B QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ? options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these SOLUTION:Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 ANSWER:C #### C QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? options: A)8 B)9 C)9.5 D)10 E)11 SOLUTION:So, she works 30 hours in 3 days So, she works 16 hours in 2 days So in a week she works 46 hours ( 30 + 16 ) and earns $460 So, Hourly wage is 460/46 => 10 Hence answer will be (D) 10 #### D QUESTION:A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball is white? options: A)1 B)1/6 C)1/3 D)1/2 E)None of these SOLUTION:Explanation: Total cases = 50 + 10 = 60 Favourable cases = 10 So probability = 10/60 = 1/6 Answer: B #### B QUESTION:How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? options: A)48 B)12 C)72 D)100 E)720 SOLUTION:So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 24!=48. Answer A. #### A QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:If x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y? options: A)4 B)12 C)2 D)7 E)6 SOLUTION:For any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards So answer = 6 = E #### E QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is: options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in one years is: 5,870,000,000,000 = 587 10 ^10 The distance of the light travels in 1000 years is: = 587 * 10^10 x 10 ^3 = 587 x 10^13 miles Answer :A #### A QUESTION:X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : options: A)34 B)43.2 C)40 D)38 E)29 SOLUTION:Solution: Average speed = 2XY / X+Y = 25436 / 54+36 = 43.2 Answer : B #### B QUESTION:The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour? options: A)60 B)61.2 C)3240 D)3,600 E)3,672 SOLUTION:moon revolves around the earth at a speed of 1.02kilometers per second. one hour equal to 60 minutes. one minute equals to 60 seconds. so one hour equals to 3600seconds. so one hour, speed= 0.93600=3240kilometers per hour. Option C is correct #### C QUESTION:Which of the following numbers is not prime? options: A)50+70 B)150 -23 C)100+67 D)156-7 E)103+36 SOLUTION:10 can be factored out of both 50 and 70. -->50+70= 10(5+7). The correct answer is A. #### A QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)3 B)4 C)5 D)8 E)2 SOLUTION:M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: A #### A QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent J of the distribution is less than m +d ? options: A)16% B)32% C)48% D)84% E)92% SOLUTION:D The prompt says that 68% of the population lies between m-d and m+d. Thus, 32% of the population is less than m-d or greater than m+d. Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d. Thus,J= (68+16)% or (100-16)% of the population is less than m+d.D #### D QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z? I. 9 II. 10 III. 11 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:Average gives us an idea that 3 nos. are close to 10. so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations. Let us see options. If 9 has to be median W. 1st term has to less than 9 or equal to 9. (also maintain z-x = 3) 9 9 12 --> satisfies all conditions so 9 can be a median value. If 11 has to be a median 3rd term has to be 11 or more than 11. (also maintain z-x = 3) 8 11 11 -->satisfies all conditions so 9 can be a median value. Now for 10 to be median. z+ x = 20 and z-x = 3, we wont have integer values of z. 10 cannot be a median E is the answer. #### E QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum. options: A)500 B)600 C)700 D)800 E)900 SOLUTION:Difference in S.I. = P×T/100(R1−R2) ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2) ⇒ P = 144×100/6×4=600 Answer B #### B QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:The height of the wall is 4 times its width and length of the wall is 3 times its height .if the volume of the wall be 10368 cu.m.its width is options: A)4m B)5m C)6m D)7m E)8m SOLUTION:Explanation: Let width = x Then, height=4x and length=12x 12x Ã— 4x Ã— x = 10368 x = 6 Answer: C #### C QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:Evaluate 30!/28! options: A)720 B)600 C)870 D)910 E)650 SOLUTION:we have 30!/28! = 302928!/28! = 3029 = 870 Answer is C #### C QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 2) = 30 years. (A+B), now = (30+52)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A QUESTION:What least number must be subtracted from 7538 so that remaining no.is divisible by 14 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 7538 by 14 we get the remainder 6, so 6 should be subtracted Option C #### C QUESTION:Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Tuesday, how many croissants will Marina eat on the 24th of that month? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:She eat as follow Mon - 1 Tue - 2 Wed - 3 Thr - 5 Fri - 1(since she had more than 4 previous day) sat - 6 sunday - 1 (since she had more than 4 previous day) so 24th day of month she will have 5. Answer is D #### D QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it? options: A)78 kg B)60 kg C)64 kg D)70 kg E)None SOLUTION:Sol. For 9 kg Zinc, mixture melted = (9+11) kg. For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg = 78 kg. Answer A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 312=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 109/2 = 45 ANSWER:B #### B QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)37.5 B)40 C)50 D)48 E)52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 ANSWER B #### B QUESTION:If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. options: A)2/7 B)3/11 C)4/15 D)5/21 E)6/25 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 4 bottles of apple juice is 5C45C2 = 510 = 50 P(selling 4 bottles of apple juice) = 50/210 = 5/21 The answer is D. #### D QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? options: A)x B)(85/12)x C)(85/24)x D)(85/36)x E)(85/48)x SOLUTION:Let Q be the number of homework questions. Q = 4Q/5 + (5/17)(Q/5) + x Q = 68Q/85 + 5Q/85 + x 12Q/85 = x Q = (85/12)x The answer is B. #### B QUESTION:If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in how many ways can the 5 digits be arranged? options: A)6 B)24 C)72 D)96 E)120 SOLUTION:Use the slot method for all the possible arrangements: we have 5 options for the 1st slot, 4 for the 2nd, 3 for 3rd , 2 for 4th and 1 for the 5th, giving the total number of arrangements = 54321 = 120, E is the correct answer. #### E QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 2600 = Rs.1200 Answer: A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)16 B)18 C)24 D)22 E)26 SOLUTION:C 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### C QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 1410 = 140 sq cmV Answer: A #### A QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(620053)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E <<<Examples ends QUESTION:A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? options: A)A)$200 B)B)$1000 C)C)$819 D)D)$1200 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 55X+44X+1X=8600 25X+16X+X=8600 42X=8600, X=204.76. Daughter receives four times of nephew so 4 * 204.76= 819. So Each Daughter receives $800. answer is option C) $819. #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard? options: A) 1/6 and 1/4 only B) 1/4 and 1/3 only C) 1/6, 1/4, and 1/3 D) 1/12, 1/6 and 1/4 E) 1/12, 1/6, and 1/3 SOLUTION:Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4. In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length). Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces. Answer: A. #### A QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 22 = 4 Share of all women = (104000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2 options: A)I only B)I,II only C)II only D)I,III only E)III only SOLUTION:12=223 16=2222 GCF =22=4 Answer : C #### C QUESTION:3x^2 + 5x - 2 = options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above SOLUTION:3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x (x + 2) - (x+2) = (3x-1) (x+2) Option A #### A QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum? options: A)20 B)22 C)25 D)27 E)29 SOLUTION:(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131 a + b + c = √625 = 25 C #### C QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46 options: A)16 B)46 C)24 D)11 E)7 SOLUTION:Explanation : 7 is the only odd number in the given series Answer : Option E #### E QUESTION:The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − 2)...3.2.1 is not divisible by n is options: A)5 B)7 C)13 D)14 E)16 SOLUTION:Explanation : (n-1)! is always divisible by n unless and untill n is a prime number e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number Therefore, find all prime numbers in the range of 12 to 40 i.e 13, 17, 19, 23, 29, 31 and 37 Hence, the number of positive integers n is 7. Answer : B #### B QUESTION:Solve for x: 2x – y = (3/4)x + 6. options: A)(y + 6)/5 B)4(y + 6)/5 C)(y + 6) D)4(y - 6)/5 E)6(y-4)/5 SOLUTION:2x – y = (3/4)x + 6. or, 2x - (3/4)x = y + 6. or, (8x -3x)/4 = y + 6. or, 5x/4 = y + 6. or, 5x = 4(y + 6). or, 5x = 4y + 24. or, x = (4y + 24)/5. Therefore, x = 4(y + 6)/5 correct answer B #### B QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: . options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720 SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C QUESTION:The ratio 25:50 expressed as percent equals to options: A)50 % B)85 % C)25 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 25 is what percent of 50, which can be calculated as, (25/50)100 = 25 2 = 50 Answer: Option A #### A QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 2460 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5) Answer - C #### C QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish? options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84 SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.150.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40. Answer: D. #### D QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? options: A)9 B)8 C)10 D)8.5 E)21 SOLUTION:63/3=21 Answer : E #### E QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3\|X^3-3 options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1 SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t\|(t+3)^2-3, which is equivalent to the condition t\|3^3-3, or t\|24. Therefore, it is necessary and sufficient for t to be an integer divisor of 24, hence t must be equal to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7, 9, 11, 15, and 27. Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B QUESTION:Ram works in a bakery. He made cookies that cost $1.75 and made $325. How many customer did he have? options: A)200 customers B)186 customers C)250 customers D)100customers E)170 customers SOLUTION:A cookie costs $1.75 adding another one is $3.5. 325 divided by 3.5 is 92.86 x 2 is 186. He had 186 customers. The correct answer is B. #### B QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:A student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:xC1 * (x-1)C1=42 x^2 -x -42 =0 (X-7 (X+6) = 0 X= 7 , -6 -6 can't possible. Hence 7 should be the answer A #### A QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N? options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N). Answer: B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 9/3 m = 150 m. ANSWER : OPTION D #### D QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps. options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s SOLUTION:Explanation: Distance = Speed x Time Speed = (1080/10) = 108 kmph Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps. Answer: Option E #### E QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 851 is 0. The answer is A. #### A QUESTION:1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? options: A)10.5 B)12.5 C)13.5 D)11.5 E)11 SOLUTION:100015 = 1200x x = 12.5 ANSWER B #### B QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack? options: A)106 B)301 C)309 D)400 E)450 SOLUTION:Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301. Answer: B) 301 #### B QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:What is the remainder when 3990990900032 is divided by 32 ? options: A)0 B)8 C)4 D)2 E)3 SOLUTION:Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans A #### A QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is: options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %. SOLUTION:Explanation : Let sum = x. Then, S.I. = x/3 Let N =3R [x * 3R * R / 100] = x/3? R^2 = 100/9 R = 10/3 = 3 1/3%. Hence, Rate = 3 1/3 %. Answer : C #### C QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/21/5+x/21/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years? options: A)5:8 B)7:5 C)3:8 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8 Answer A #### A QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions. = 1500 * 2 * 22/7 * 22.4 = 211200 cm = 2112 m Answer: A #### A QUESTION:What is greatest positive integer n such that 2^n is a factor of 12^11? options: A)a)10 B)b)12 C)c)22 D)d)20 E)e)60 SOLUTION:The given number is 12^11 =(223)^11 =(2^22)(3^11) So the greatest possible value for n such that 2^n can be factor of given number is 22. Answer C #### C QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is? options: A)$440 B)$450 C)$460 D)$470 E)$480 SOLUTION:avg = sum of observations/number of observations avg income=(250+400+750+400+500)/5 = 460 Answer is C #### C QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? options: A)72 B)83 C)45 D)53 E)64 SOLUTION:Sum of all the 13 numbers = 13 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Answer:A #### A QUESTION:By selling an article at Rs.600, a profit of 30% is made. Find its cost price? options: A)400 B)267 C)287 D)480 E)811 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+50)] = 600 * [100/150] = Rs.400 Answer: A #### A QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr. SOLUTION:Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=24 or x=12. Rate upstream=12 km/hr,rate downstream=36 km/hr. Hence,rate of stream=1/2(36-12)km/hr=12 km/hr. Answer is B. #### B QUESTION:In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there? options: A)1140 B)1160 C)1180 D)1200 E)1040 SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12. Number of sweets 80 children got = 70 * 12 = 840. Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20. Number of sweets 10 youngsters got = 10 * 20 = 200. Total number of sweets = 840 + 200 = 1040. E) #### E QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: options: A)1.8h B)3h C)4h D)5h E)None of these SOLUTION:Explanation: Upstream speed = B-S Downstream speed = B + s B - S = 15/5 = 3 km/h Again B = 4S Therefore B - S = 3 = 3S => S = 1 and B = 4 km/h Therefore B + S = 5km/h Therefore, Time during downstream = 15/5 = 3h Answer: B #### B QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195 = 495 m Required time = 495 * 2/55 = 18 sec Answer: B #### B QUESTION:One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall? options: A)5/7 B)1 C)10/7 D)12/7 E)24/7 SOLUTION:Solution:Let work done by man, women and girl per hour be m,w,g respectively. Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3). No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6. So, n = 1/(7/24) = 24/7 Option, E #### E QUESTION:If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.) options: A)6:22 B)6:24 C)6:27 D)6:36 E)6:32 SOLUTION:6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D. Answer: D. #### D QUESTION:A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident? options: A)35 B)30 C)25 D)20 E)None of these SOLUTION:Let the truth spoken by A and B be pl and p2 respectively, i.e., pl = 3⁄4 and p2 = 4⁄5 They will contradict each other only when one speaks truth and the other is lying. i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35% Answer A #### A QUESTION:Find the greatest number of five digits to which if 7143 is added, the final number becomes exactly divisible by 18, 24, 30, 32 and 36. options: A)22391 B)81111 C)27999 D)27711 E)99417 SOLUTION:LCM of 18, 24, 30, 32 and 36 is 1440. 99999 + 7143 = 107142. Dividing 107142 by 1440, the remainder is 582. ∴ Required number = 99999 – 582 = 99417 Alternate Method: Cross check with options. Answer:E #### E QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive? options: A)$444 B)$445 C)$446 D)$447 E)$448 SOLUTION:A+B+C = 1200 Given ratio 10:12:13 Let us say the shares of A,B,C deducting 10,20,15 be a,b,c a+b+c = 1200-45= 1155 = 35K c share = (1155X13)/35 = 429 C = chandran share = 429+15 = 444 Option A #### A QUESTION:A certain quantity of 45% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? options: A)1/4 B)1/3 C)1/2 D)2/3 E)3/4 SOLUTION:Let's say that the total original mixture A is 100 ml The original mixture A thus has 45 ml of alcohol out of 100 ml of solution You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 20%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 10%. Therefore, 10 out of 20 is 1/2 and C is the answer. #### C QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago? options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4 SOLUTION:3x-25/2x-25 = 4/3 Therefore x=-25 Age cannot be negative. Answer: D #### D QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3 SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4x. Point (r, r+1) lies on line n means that (r+1)=1/4r --> r=-4/3. Answer: A. #### A QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price 100/(100+profit) C.P. = 100100/130 = $77(approximately) Answer is D #### D QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4PIR^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)(9C2) =736= 252 Answer : B #### B QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in? options: A)6 B)12 C)28 D)42 E)21 SOLUTION:The part of the tank filled by three pipes in one hour = 1/14 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/14= 1/21. The tank can be filled in 21 hours. Answer:E #### E QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:Find the simple interest on Rs.620 for 10 months at 10 paisa per month? options: A)277 B)620 C)640 D)678 E)121 SOLUTION:I = (6201010)/100 = 620 Answer: B #### B QUESTION:A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:The ratio of number of boys and girls in a school is 3:5. If there are 320 students in the school, find the number of girls in the school? options: A)150 B)250 C)300 D)200 E)280 SOLUTION:Let the number of boys and girls be 3x and 5x Total students = 320 Number of girls in the school = 5320/8 = 200 Answer is D #### D QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M. options: A)2574 B)2500 C)1485 D)1574 E)None of these SOLUTION:Explanation: HCF LCM = 17820, because we know Product of two numbers = Product of HCF and LCM LCM = 17820/12 = 1485 Option C #### C QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T? options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1 SOLUTION:Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D. #### D QUESTION:Two trains are moving in opposite directions with speed of 210 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds options: A)56 B)48 C)47 D)26 E)24 SOLUTION:Explanation: Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds Answer: Option E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)46 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 9) years. (x+9+10)=2(x�10) hence x=39. Present age of B = 39 years Answer: Option C #### C QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:125 + 83d = 90(d+1). 7d = 35. d = 5. The answer is B. #### B QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 370 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? options: A)237 B)287 C)197 D)740 E)720 SOLUTION:Explanation: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x. 2x/(x - 370) = 2 + 2(extra) => 2x - 740 = x => x = 740. Answer: D #### D QUESTION:John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour? options: A)30 B)40 C)50 D)55 E)70 SOLUTION:HiBunuel THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55. The question is correct. Here's the explanation: Let distance be D. We can find the total timeequate it, which comes as: 0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D). #### D QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ? options: A)1/3 kmph B)2/3 kmph C)1/4 kmph D)1/2 kmph E)1/6 kmph SOLUTION:Explanation: Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr. Speed in downstream = 3 x 60/18 = 10 km/hr Rate of current = (10-9)/2 = 1/2 km/hr. ANSWER IS D #### D QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November? options: A)$466 B)$470 C)$472 D)$484 E)$491 SOLUTION:if its prevoius november (before discount) then price is $470. but if its November of next year then 16% discount on $470=470(1-16/100)=$394.8 again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466 Ans A #### A QUESTION:Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal? options: A)600 B)700 C)840 D)940 E)1440 SOLUTION:Let the capital of Pyarelal be x, then capital of Ashok=x/9 So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x Hence out of the total loss of 1600, loss of Pyarelal= 16009x/10x=1440 ANSWER:E #### E QUESTION:A man can row with a speed of 10 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is? options: A)10 kmph B)5 kmph C)40 kmph D)22 kmph E)25 kmph SOLUTION:M = 10 S = 30 DS = 10 + 30 = 40 ANSWER:C #### C QUESTION:Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are: options: A)7, 6 B)5, 1 C)6, 3 D)8, 7 E)None of these SOLUTION:Explanation : Let A and B be such sets, i.e., n (A) = m, n (B) = n So, n (P(A)) = 2m and n (P(B)) = 2n Thus n (P(A)) – n (P(B)) = 56, i.e. 2m – 2n = 56 ⇒ 2n (2m-n - 1) = 23 x 7 ⇒ n = 3 , 2m-n – 1 = 7 ⇒ m = 6 Answer : C #### C QUESTION:Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in six hours, what fraction of the room can Joseph paint in 20 minutes? options: A)1/6x B)x/(x-3) C)(x-6)/18x D)x/(x-6) E)(x-6)/x SOLUTION:Let J be Joseph's rate per hour. 1/x + J = 1/6 of a room per hour J = 1/6 - 1/x, of a room per hour In 20 minutes, Joseph can paint 1/3(1/6-1/x) = 1/18-1/3x = (x-6)/18x The answer is C. #### C QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ? options: A)4x + 6y B)x + y + 4 C)4x - 9y D)9x + 4y E)x + y - 4 SOLUTION:By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11; (x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11; (9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11; (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11. correct answer C #### C QUESTION:Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year? options: A)1:2:1 B)2:3:6 C)3:2:1 D)1:2:3 E)1:4:3 SOLUTION:Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively. 3b = 2b = c. a = c/3. b = c/2. Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments = 2:3:6. ANSWER:B #### B QUESTION:Mary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? options: A) 124% B) 102% C) 96% D) 80% E) 64% SOLUTION:Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 102 (70 percent more than Tim's income). Thus, Mary's income (102) is 102% of Juan's income (100). Answer: B. #### B QUESTION:A,B,C can complete a piece of work in 24,6 and 12 days respectively. Working together, they will complete the same work in how many days? options: A)13/8 B)26/11 C)24/7 D)12/13 E)1/2 SOLUTION:(A+B+C)'s 1day work = (1/24)+(1/6)+(1/12) = 7/24 A,B,C together will complete the work in 24/7 days Answer is C #### C QUESTION:Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year? options: A)$2000 B)$6000 C)$4000 D)$1333 E)$3000 SOLUTION:Explanatory Answer Let the profit made during the year be $3x Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 7 : 3. i.e., 70% of 2x would go to Mary and 30% of 2x would go to Mike. Hence, Mary would get (70 - 30)% of 2x more than Mike Or 40% of 2x = $800 i.e.,(40/100)2x = 800 or 2x = 2000. Hence, the profit made by the company during the year $3x = $3000. The correct choice is (E) #### E QUESTION:Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Old mix has 20% oil. You add 2 kgs of 100% oil. You get new mix with 30% oil (70% material B). w1/w2 = (100 - 30)/(30 - 20) = 70/10 = 7/1 For every 7 parts of mix A, you have added 1 part of oil. Since you have added 2 kgs oil, mix A must be 72 = 14 kgs. You already had 8 kgs of mix A, so extra mix A added must be 14 - 8 = 6 kgs. Answer (A) #### A QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil? options: A)9 B)5 C)7 D)8 E)4 SOLUTION:Let the total length be xm Then black part =x/8cm The remaining part=(x-x/8)cm=7x/8cm White part=(1/2 7x/8)=7x/16 cm Remaining part=(7x/8-7x/16)=7x/16cm 7x/16=7/2 x=8cm Answer is D. #### D QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm? options: A)45% B)48% C)50% D)58% E)65% SOLUTION:When the storm deposited 120 billion gallons, volume of water in the reservoir = 200 + 120 = 320 billion gallons If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 320/0.8 = 400 billion gallons Therefore percentage of reservoir that was full before the storm = (200/400)100 = 50% Option C #### C QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)376 C)1267 D)198 E)621 SOLUTION:624/6 = 104 kmph Answer: A #### A QUESTION:Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is: options: A)30% B)100/3% C)35% D)44% E)None of these SOLUTION:Explanation : C.P. of 6 articles = Rs. 5 => C.P. of 1 article = Rs. 5/6 S.P. of 5 articles = Rs. 6 => S.P. of 1 article = Rs. 6/5 Profit earned per article = 6/5 - 5/6 = 11/30 % Profit = 11/30∗6/5∗100% = 44% Answer : D #### D QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a? options: A)67 B)197 C)91 D)199 E)42 SOLUTION:1) A and B are positive INTEGERS 2) A/B = 3.98 A = 398 B = 100 398/100 = 3.98 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 199 B = 50 199/50 = 2.86 There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A.... Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices. Answer: D #### D QUESTION:R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet? options: A)2 : 30 PM B)11 : 30 AM C)1 : 30 PM D)12 : 30 PM E)None of these SOLUTION:Let after t hours they meet then, 3t + 4t = 17.5 ⇒ t = 25 ∴ Time = 10 am + 2.5 h = 12 : 30 am Answer D #### D QUESTION:Find the value of (85 + 32/113) × 113 options: A)9263 B)9244 C)9636 D)9623 E)9637 SOLUTION:=(85 + 32/113) × 113 =(9605 + 32)/113× 113 =9637/113× 113 =9637 Answer is E. #### E QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 2) = 30 years. (A+B), now = (30+52)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:If Raj shares all of his amount equally among his five friends then each of his friend's amount increased by $10 then Raj had how much? options: A)$10 B)$20 C)$30 D)$40 E)$50 SOLUTION:Five friends amount increased by $10 and Raj shared equally so amount = 5 10 = 50 Answer:E #### E QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible? options: A)48 B)66 C)72 D)78 E)90 SOLUTION:Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120 - 48 = 72 C #### C QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)675.5 B)635.5 C)635.28 D)635.98 E)635.03 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer:B #### B QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station? options: A)A)9KM B)B)6.66KM C)C)7.25KM D)D)12.40KM E)E)13KM SOLUTION:Since time differences given are in minutes so let's convert speed in Km per minute 8 kmph = 8/60 km per minute = (2/15) km per minute 10 kmph = 10/60 km per minute = (1/6) km per minute Let, Time of train to depart from station = t minutes Distance between Point E and Railway Station = SpeedTime = (2/15)(t+5) Distance between Point E and Railway Station = SpeedTime = (1/6)(t-5) i.e. (2/15)(t+5) = (1/6)(t-5) i.e. 12t+60 = 15t - 75 i.e. 3t = 135 i.e. t = 45 minutes i.e. Distance = (1/6)(t-5) = (1/6)(45-5) = 40/6 = 20/3 Km = 6.66 Km Answer: Option B #### B QUESTION:The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches? options: A)31 B)46 C)88 D)13 E)12 SOLUTION:Total score of the batsman in 20 matches = 800. Total score of the batsman in the next 10 matches = 130. Total score of the batsman in the 30 matches = 930. Average score of the batsman = 930/30 = 31. Answer:A #### A QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? options: A)22 B)28 C)25 D)82 E)34 SOLUTION:M = 20 S = 5 DS = 20 + 5 = 20.Answer:C #### C QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 1.16.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 253 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)23 D)33 E)22 SOLUTION:E 22rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 = 253 Thus our anniversary falls on the 22rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### E QUESTION:The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is? options: A)2379 B)2889 C)5625 D)9000 E)28311 SOLUTION:Let their prices be 3x, 5x and 7x. Then, 2x + 6x + 8x = (15000 * 3) or x = 2812.5. Cost of cheapest item = 2x = Rs. 5625. Answer: C #### C QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)30 B)50 C)70 D)80 E)90 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 120 / (120+x) = 4/5 x = 30 The answer is A. #### A QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:In each term of a sequence, 7 is added to get the next term. If the first term is 3, what is the thirty-seventh term? options: A) 222 B) 284 C) 252 D) 263 E) 255 SOLUTION:1rst term + 36 terms = 3 + 7+7+7+7+7+7+7+...+7 (36 times) 3 + (7 x 36) = 3 + 252 = 255 Answer E #### E QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides. options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16 SOLUTION:CM=3 AREA=PM*CM/2, thus PM=12 By Pythagorean Theorem, we can now find the value of PC. D is the correct option. #### D <<<Examples ends QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food. options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400 SOLUTION:Part of salary left =1-(2/5+3/10+1/8) =7/40 Let the monthly salary be $x Then (7/40) of x=1400 X=8000 Expenditure on food=$2400 Option D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If BAT = 58 HAT = 52 CAT = 57 then whats RAT = ? options: A)42 B)45 C)34 D)76 E)25 SOLUTION:A 42 #### A QUESTION:The average (arithmetic mean) of four numbers is 5x + 3. If one of the numbers is 2x, what is the average of the other three numbers? options: A)x + 1 B)3x + 3 C)4x + 1 D)5x + 3 E)6x + 4 SOLUTION:The sum of all four numbers is 4 * (5x + 3) = 20x + 12. If one of the numbers is 2x, the sum of the other 3 numbers is 18x+12. The average of the remaining three numbers is (18x+12)/3 = 6x+4. The answer is E. #### E QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years? options: A)3 : 2 B)1 : 3 C)2 : 3 D)1 : 5 E)2 : 1 SOLUTION:Explanation : Simple Interest = PRT/100 Here Principal(P) and Rate of Interest (R) are constants Hence, Simple Interest ∝ T Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years =T1/T2 =2/10 =1/5 =1:5 Answer : Option D #### D QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36, find P (E\|F) and P(F\|E) options: A)5 B)8 C)2 D)6 E)12 SOLUTION:Here, E and F are events P(E\|F) = P(EnF)/P(F) = 36/36 = 1 P(F\|E) = P(EnF)/P(E) = 36/24 = 2. C) #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:A man starts walking at 3 pm . he walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way? options: A)12 B)66 C)77 D)88 E)91 SOLUTION:lets us consider t1 = time taken on level road. t2 = uphill. t3 = down hill; the distance traveled uphill and down hill same so t23 = 6t3; => t2 = 2t3;---> (1) total time = 2t1 + t2 + t3 = 6 hours ---> (2) 2t1+3t3 = 6 -->(3) total distance = 2(4t1) + 3t2+ 6t3 ---> (4) substitute (1) in (4) 8t1 + 12t3 => 4(2t1+3t3) then from (3) the total distance will become 46= 24 => one way distance = 12km Answer: A #### A QUESTION:A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? options: A)41.1 sec B)64.8 sec C)31.8 sec D)50.4 sec E)none of the above SOLUTION:Speed = 55 Km/hr (to convert km/hr in to M/s) = 55 x 5/18 M/s Distance = 470 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, ) = 990 m Time = Distance / Speed = 990 x 18 / (5 x 55) = 64.8 sec Ans is :B #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:What proximate value should come in place of the question mark (?) in the following question? 6.795 Ã— 1084 + 2568.34 â€“ 1708.34 = ? options: A)6,000 B)12,000 C)10,340 D)8,204 E)9,000 SOLUTION:? â‰ˆ 6.8 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7344 + 860 â‰ˆ 8204 Answer D #### D QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13 SOLUTION:The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C #### C QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 520 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(104)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? options: A)287 B)27 C)28 D)25 E)28 SOLUTION:[50/x + 50/(x/2)] – 100/x = 2 x = 25 Answer: D #### D QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:A car covers a distance of 624 km in 6 Â½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible? options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6 SOLUTION:So 4C3 for abcd - 4 choices 3 more for dd(b,c or a) 3 more for bb(a,c or d) 3 more for cc(a,b or d) total 4C3+9 Ans : B #### B QUESTION:How many quarters are equal to 4 dollars? options: A)16 B)8 C)12 D)9 E)7 SOLUTION:44 = 16 quarters Answer : A #### A QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Sol. By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6. Answer C #### C QUESTION:If 40% of a number is 16, then the number is options: A)number is 60 B)number is 70 C)number is 90 D)number is 40 E)None of these SOLUTION:Solution: Let "a" be the number we seek. We get 40% × a = 16 2 × 40% × a = 2 × 16 = 32 80% × a = 32 10% × a = 32 : 8 = 4 100% × a = 4 × 10 = 40 a = 40 Answer D #### D QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:An old priest fell on a bottom of the well of a church. The well is 16 inches deep. At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches. In how many days priest will come out of the well ? options: A)12-days B)14-days C)11-days D)19-days E)10-days SOLUTION:A 12-days In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern. From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)(rate) =23/8 = 3/4 th of the cistern . Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour. Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern. Answer: E. #### E QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996? options: A) $24 million B) $120 million C) $144 million D) $240 million E) $888 million SOLUTION:Convert units to millions as answer is in millions 1996 Imports = $1.44 bill = $1440 mill i.e. 1440/12 = $120 mill/month 1997 Imports = $388 mill/2 month i.e. $194 mill/month Difference/month = 194-120 = 74 Difference/year = $74 mill 12 = $988 mill ANSWER: E #### E QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n(n+1)/2 with n being 23, so equal to 23 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:You roll two six sided dices together. Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5? options: A)2/23 B)1/33 C)1/36 D)3/54 E)6/35 SOLUTION:C 1/36 The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36. Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5. Therefore, the probability will be 1 on 36 or 1/36. #### C QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10? options: A)2140 B)2520 C)2980 D)3260 E)3680 SOLUTION:The number needs to be divisible by 23, 7, 2^3, 3^2, and 25. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. #### B QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2007 B)2008 C)2002 D)2000 E)2001 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: D #### D QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest? options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33% SOLUTION:T = 30 years P= principle amount = x A = total amount = 2x SI = simple interest = A-P = 2x-x = x R = 100SI/PT = 100x/30x =3.33% Answer is B #### B QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year? options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7 SOLUTION:A : B (40004)+(10008) : (60008)+(30004) 24000 : 60000 2 : 5 Answer: A #### A QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : options: A)8 B)9 C)4 D)18 E)None SOLUTION:Ratio of rates of working of A and B = 2 : 1 So, ratio of times taken = 1 : 2 B's 1 day's work = 1/12 Therefore A's 1 day's work = 1/6 (A + B)'s 1 day's work = (1/6 + 1/12)= 1/4 So, A and B together can finish the work in 4 days. Answer: C #### C QUESTION:Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year? options: A)11% B)25% C)44% D)56% E)100% SOLUTION:Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year. Percentage Change = ( Change in value / Original value ) 100 Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100 Saving in 2nd year + Saving in 1st year = 540 Saving in 2nd year + 180 = 540 Saving in 2nd year = 540 - 180 = 360 Change in Value = 360 - 180 = 180 Original Value = 180 Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E...... #### E QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77 SOLUTION:Solution P( None is defective) = 18C2 / 22C2 = 51/77 P( at least one is defective) = (1- 51/77) = 26/77. Answer E #### E QUESTION:Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? options: A)1/8 B)1/4 C)2/4 D)1/4 E)3/4 SOLUTION:3/12 + x/13 = 1 x= 7 3/4 Answer: E #### E QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2 SOLUTION:(y^2 − xy)/x=y-x => y^2 − xy = xy -x^2 => x^2 - 2xy + y^2 = 0 => (x-y)^2 = 0 Answer E #### E QUESTION:A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has? options: A)102 B)60 C)75 D)90 E)95 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 544 16x = 544 x = 34. Hence, total number of notes = 3x = 102 Answer: Option A #### A QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all? options: A)10 B)19 C)04 D)12 E)07 SOLUTION:Add the numbers of watches. 2 + 1 + 1 =4. Answer is C. #### C QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? options: A)11 s B)10 s C)8 s D)12 s E)None of these SOLUTION:We know from the formula Time = Distance/ Speed Thus, Time = 120/ 54 x 5/18 or, Time = 8 sec. ANSWER:C #### C QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)2 D)3 E)4 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .250+.6x=.5(50+x) x=150 Answer E #### E QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true? I. x > y> z II. x = z III. x > y options: A)I and II B)I only C)II only D)III only E)None SOLUTION:3x-3y=-3z x-y=-z Since z<0; -z>0 x-y>0 x>y III correct. We can't say much about z though; x=-5; y=-100; z=-95 I and II incorrect. Ans:D #### D QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011 SOLUTION:Explanation: The value of the machine after two years = 0.8 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B #### B QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 C #### C QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(1518)/12 = 24 Answer:A #### A QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-902)/3=340 Answer : C #### C QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (527) - (425) = 135-100 = 35 Answer: Option A #### A QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 4040 = 1600 (here n=40) Answer : B #### B QUESTION:A row of ants comprised of 102 ants. A man walked upon it and all except 42 were crushed beneath his foot. How many ants are left alive? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:Solution: All except 42 were crushed means that all the ants except 42 were crushed beneath the man's foot. Hence, 42 ants are alive now Answer B #### B QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)615 m B)240 m C)168 m D)197 m E)691 m SOLUTION:Speed = 54 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m Answer: B #### B QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43 SOLUTION:P(1st ball is even) = 9/18 P(2nd ball is also even) = 8/17 P(both balls are even) = 9/18 * 8/17 = 4/17 The answer is B. #### B QUESTION:The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of present committee is; options: A)39 years B)38 years C)36 years D)35 years E)34 years SOLUTION:Exp. Total age of the committee = 408 = 320, Total age when a member is retired and a new one was joined = 320-55 +39, =304 Average age of present committee = 304/8 = 38. Answer: B #### B QUESTION:Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed. options: A)s. 5266 B)s. 5396 C)s. 5228 D)s. 5218 E)s. 52192 SOLUTION:Explanation: Let us assume Mr. Karan borrowed amount is Rs. A. (the principal) By formula of simple interest, S.I. = PRT / 100 Where P = The principal, R = Rate of interest as a %, T = Time in years S.I. = (P 6 * 9)/100 = 54 P/100 Amount = Principal + S.I. 8310 = P + (54P/100) 8310 = (100P + 54P)/100 8310 = 154P/100 P = (8310 * 100)/154 = Rs. 5396.104 ANSWER: B #### B QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)106 C)110 D)120 E)130 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Ans: 6 Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B #### B QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C 100 =50% Answer A #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) = options: A)S B)S+1 C)S/(S+1) D)(S+2)/(S+1) E)(2S+1)/(S+1) SOLUTION:x#y = x + x/y. If S>0, then 1#(1#S) = You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2 1#S= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3 So now you can check by filling in S, which is 2: A. S --> 2 B. S+1 --> 2+1=3 C. S/(S+1)-->2/(2+1)=2/3 D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3 E. (2S+1)/(S+1)-->(22+1)/(2+1)=5/3 So E is the answer. #### E QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds? options: A)5/6 B)4/5 C)3/4 D)2/3 E)1/2 SOLUTION:The searchlight completes one revolution every 15 seconds. The probability that the man's area will be lit up is 5/15=1/3. The probability that he will stay in the dark is 1-1/3=2/3 The answer is D. #### D QUESTION:Find 30 % of 240 options: A)72 B)94 C)86 D)74 E)110 SOLUTION:We know that R % of m is equal to R/100 × m. So, we have 30 % of 240 30/100 × 240 = 72 Answer:A #### A QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:If a positive odd integer N has p positive factors, how many positive factors will 3N have ? options: A)p B)2p C)P+1 D)2p+1 E)Cannot be determined SOLUTION:I have added some extra text to make this question more GMAT-like: Let's TEST some values of N Try N = 3 The factors of 3 are {1, 3}. Here, p =2 So, 2N = (2)(3) = 6 The factors of 6 are {1, 2, 3, 6}. So, we have a total of4 Now check the answer choices: A) p =2No good. We want an output of4. ELIMINATE B) 2p = (2)(2) = 4. PERFECT! KEEP B C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE E) Cannot be determined. POSSIBLE. KEEP E Let's TEST another value of N Try N = 7 The factors of 7 are {1, 7}. Here, p =2 So, 2N = (2)(7) = 14 The factors of 14 are {1, 2, 7, 14}. So, we have a total of4 Now check the REMAINING answer choices: B) 2p = (2)(2) =4. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E Let's TEST one more (non-prime) value of N Try N = 9 The factors of 9 are {1, 3, 9}. Here, p =3 So, 2N = (2)(9) = 18 The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6 Now check the REMAINING answer choices: B) 2p = (2)(3) =6. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E At this point, it SEEMS LIKELY that the correct answer is C #### C QUESTION:Convert the 9/36 m/s into kilometers per hour? options: A)0.9 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:9/36 m/s = 9/36 * 18/5 = 9/10 = 0.9 kmph. Answer: A #### A QUESTION:At a certain organisation, the number of male members went up by 15% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? options: A)1:2 B)1:3 C)2:3 D)3:2 E)2:1 SOLUTION:men increase by 15% ==> 1.15M = males in 2001 women decrease by 6% ==> 0.94F = women in 2001 total employees increase by 1.2% ==> 1.012(M + F) = total number of employees in 2001 Obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.15M + 0.94F = 1.012(M + F) 1.15M + 0.94F = 1.012M + 1.012F 1.15M - 1.012M = 1.012F - 0.94F 0.138M = 0.072F M/F = (0.072)/(0.138) = 72/138 = 1/2 Answer =(A) #### A QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:A fruit seller had some oranges. He sells 40% oranges and still has 300 oranges. How many oranges he had originally? options: A)420 B)700 C)220 D)500 E)None of these SOLUTION:Explanation : He sells 40% of oranges and still there are 300 oranges remaining => 60% of oranges = 300 ⇒ (60 × Total Oranges)/100 = 300 ⇒ Total Oranges/100 = 5 ⇒ Total Oranges = 5 × 100 = 500 Answer : Option D #### D QUESTION:A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? options: A)40 B)33 C)50 D)51 E)52 SOLUTION:Yes, ensure that you understand the relation thoroughly! Cost per liter = K * Fraction of Spirit 40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2. 20 = K * (1/2) K = 40 Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water) Cost for 3 liters = 40 * (1/3) * 3 = 40 cents A. 40 cents #### A QUESTION:A driver goes on a trip of 50 kilometers, the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? options: A)35 B)36 C)40 D)42 E)45 SOLUTION:The time for the first part of the trip was 25/60 = 5/12 hours. The time for the second part of the trip was 25/30 = 5/6 hours. The total time for the trip was 5/12 + 5/6 = 15/12 = 5/4 hours. The average speed for the trip was 50 / (5/4) = 40 kph The answer is C. #### C QUESTION:A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make? options: A)100% B)90% C)140% D)115% E)120% SOLUTION:The total CP = Rs. 18000 + Rs. 5000 = Rs. 2300 and SP = Rs. 46000 Profit(%) = (46000 - 23000)/23000 * 100 = 100% Answer:A #### A QUESTION:Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103? options: A)2500 m^2 B)2510 m^2 C)2520 m^2 D)2540 m^2 E)2590 m^2 SOLUTION:Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C #### C QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)11 B)25 C)77 D)99 E)21 SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25%.Answer:B #### B QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C? options: A)3377 B)2899 C)5000 D)2778 E)1991 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 400 C's capital = 300001/6 = 5000 Answer: C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way? options: A)3 B)5 C)9 D)4 E)7 SOLUTION:T = 40/36 18/5 = 4 sec Answer:D #### D QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score? options: A)662 B)672 C)654 D)642 E)721 SOLUTION:8 * 83 = 664 – 10 = 654 ANSWER:C #### C QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult? options: A)$111 B)$52.5 C)$210 D)$58.5 E)$6 SOLUTION:Explanatory Answer Step 1: Assign variables and frame equations Let the basic fare for the child be $X. Basic one-way air fare of a child costs half the regular fare for an adult Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Reservation charge is the same on the child's ticket as on the adult's ticket. Let the reservation charge per ticket be $Y Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1) And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2) Step 2: Solve the equations and determine basic fare for an adult Multiply equation (1) by 2: 4X + 2Y = 432 .... (3) Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327) ∴ X = $105. The basic fare of an adult ticket = 2X = 2105 = $210 Answer C #### C QUESTION:A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning? options: A)39 B)35 C)20 D)40.5 E)41.5 SOLUTION:let the average after 16th inning =x then total run after 16th inning=16x then total run after 17th inning=16x+100 then average run after 17th inning=(16x+100)/17 (16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15 x=15; average after 17th inning =15+5=20 ANSWER:C #### C QUESTION:A is a working partner and B is a sleeping partner in a business. A puts in 20,000 and B 90,000. A gets 20% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of B in profit of 11000. options: A)3500 B)7200 C)6800 D)4800 E)None of these SOLUTION:The amount A gets for managing = 20% of Rs. 11000 = 2200 Remaining profit = 11000 – 2200 = 8800 This is to be divided in the ratio 2 : 9. Share of B = 9/11 of 8800 = 7200 Answer B #### B QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint T, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change. 240−150=90 240−150=90 Then we find out how many percent this change corresponds to when compared to the original number of students a=r⋅b a=r⋅b 90=r⋅150 90=r⋅150 90150=r 90150=r 0.6=r=60% Option E is correct. #### E QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(46 + 86): (412) 72:48 => 3:2 Answer:C #### C QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 * 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)227 B)350 C)881 D)277 E)271 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =âˆšb : âˆša = âˆš400 : âˆš625 = 20 : 25 Answer D #### D QUESTION:Two Trains A and B start simultaneously from stations 500 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 50 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile? options: A) 112 B) 133 C) 150 D) 250 E) 288 SOLUTION:Since we know the distance (500) and the combined rate (100), we plug it into the formula: Distance = Rate * Time 500 = 100 * Time We can solve for the time they will meet cause we added the rate of Train A and Train B together. So the time will be 500/100 from dividing 100 on both sides to isolate Time in the equation above. Time will be 5 hours so now you can plug that in for Train A’s distance. Distance = Rate * Time Distance = 50 * 5 Distance = 250 according to answer choice D. #### D QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 34/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: options: A)2 B)4 C)7 D)12 E)15 SOLUTION:Sol. Speed in still water = 1/2 (9+5) kmph = 7 kmph. Answer C #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:John has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:Let there be a pennies , b nickels and c dimes so total amount can be 1+5b+10c cents to 4+5b+10c as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4) So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5. so answer is B #### B QUESTION:A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)42.3 B)560.45m C)79m D)26m E)111.12m SOLUTION:Explanation: A runs 1000 m while B runs 900 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. B can give C = 1000 - 888.88 = 111.12 m. ANSWER E #### E QUESTION:Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? options: A)4hrs B)6hrs C)8hrs D)10hrs E)16hrs SOLUTION:machine A will do 6/8 in 6 hrs, so A does 3/4 of the work .. Therefore, B will do the remaining 1/4 th work alone.. As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job... ans 8 C #### C QUESTION:A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code? options: A)05. B)06. C)03. D)04. E)02. SOLUTION:Given that 7 digit number is divisible by 5 we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5. Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A #### A QUESTION:In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn? options: A)2/3 B)1/3 C)1/4 D)1/6 E)2/5 SOLUTION:You can simply use sets concept in this question. The formula Total = n(A) + n(B) - n(A and B) is applicable here too. Set 1: Number 1 or larger Set 2: Number 15 or smaller 1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both) 2/3 + P(Set 2) - 1/3 = 1 P(Set 2) = 2/3 Answer A #### A QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers? options: A)121 B)133 C)145 D)150 E)165 SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by x + (x + 4) 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131 "The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131 Solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 As an exercise, check that the sum of the first and third is 131 less than three times B #### B QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:What sum of money put at C.I amounts in 2 years to Rs.7000 and in 3 years to Rs.9261? options: A)4000 B)8877 C)2877 D)2678 E)1011 SOLUTION:7000 ---- 2261 100 ---- ? => 32.3% x 1323/100 1323/100 = 7000 x1.75=7000 x=7000/1.75 => 3999.25 Answer: A #### A QUESTION:A square, with perimeter 40, is inscribed in a circle. What is the area of the circle? options: A)50π B)40π C)30π D)25π E)35π SOLUTION:Area of circuscribed circle = pi/2area of square Area of square = (40/4)^2 = 10^2= 100 Area of circle = pi/2100=50pi Answer : A #### A QUESTION:If Raj shares all of his amount equally among his five friends then each of his friend's amount increased by $10 then Raj had how much? options: A)$10 B)$20 C)$30 D)$40 E)$50 SOLUTION:Five friends amount increased by $10 and Raj shared equally so amount = 5 10 = 50 Answer:E #### E QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi12/4 =12- pi3 ANSWER:B #### B QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:If the price of a TV is first decreased by 20% and then increased by 45%, then the net change in the price will be : options: A)4% increase B)10% increase C)10% decrease D)16% increase E)None of these SOLUTION:Explanation : Solution: let the original price be Rs. 100. New final price = 145% of(80% of 100) =Rs. 145/100 * 80/100 * 100 = Rs. 116. .'. Increase = 16% Answer : D #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? options: A)39 B)88 C)3 D)7 E)62 SOLUTION:Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Answer:A #### A <<<Examples ends QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/11/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)2777 B)2999 C)2799 D)2781 E)10500 SOLUTION:Simran : Nanda = (50000 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $5760. What is the average monthly balance maintained by John in his account during the year? options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400 SOLUTION:bank balance is doubled with accumulation of interest tp 5760.. this means INTEREST is 5760/2=2880 for entire year.. although since interest is 10% of avg MONthly balance, it becomes 28800.. B #### B QUESTION:9log9(5) = ? options: A)1 B)2 C)3 D)5 E)8 SOLUTION:Exponential and log functions are inverse of each other. Hence aloga(x) = x , for all x real and positive. and therefore 9log9(5) = 5 correct answer D #### D QUESTION:A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1 options: A)After 3 months B)After 4 months C)After 6 months D)After 2 1⁄2 months E)None of these SOLUTION:Let B joined after x months. Then, 4500 × 12 : 3000 (12 – x) = 2 : 1 Ratio of their investments 4500×12/3000(12−x)=2/1 ⇒ x = 3 Answer A #### A QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:If 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 Then 9 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:C 3 As stated 3=9 => 9=3 Answer is C #### C QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,15 = 15/100 x= 8015/100 x= 12 12/10 = 1,2 = 120%, Answer C #### C QUESTION:A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram? options: A)769 1/7 grams B)769 3/13 grams C)769 8/3 grams D)769 1/3 grams E)769 1/13 grams SOLUTION:If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130. If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%. How many grams he has to give instead of one kilogram(1000 gm). 130 gm ------ 100 gm 1000 gm ------ ? (1000 100)/130 = 769 3/13 grams. Answer:B #### B QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number? options: A)20 B)22 C)27 D)28 E)30 SOLUTION:Given Ratio => 2:3 2x - 10 : 3x - 10 = 2 : 4 4[2x - 10] = 2[3x - 10] 8x - 40 = 6x - 20 8x - 6x = 40 - 20 x = 10 Then biggest number is = 3x 3x = 30 Ans = E #### E QUESTION:In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by options: A)64 B)8 C)4 D)64 E)1/64 SOLUTION:Say r=2 => V1 = 1/64 when r=1; V2 = 1/16 V2 = 4V1. Answer=C=4 #### C QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K? options: A)30 B)4 C)5 D)66 E)All of these SOLUTION:The first term divisible by 3, so any term could be the third term. Answer =(E) #### E QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used. The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost? options: A)981 B)1000 C)1011 D)1101 E)1110 SOLUTION:The number of codes possible if leading zero is allowed = 10101010=10^4 The number of codes possible if leading zero is NOT allowed = 9101010=910^3 The difference = 10^4 - 910^3 = 10^3(10-9) = 10^3.=1000 Answer: B. #### B QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k? options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0 SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A QUESTION:What is x if x + 3y = 33 and y = 10? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Substitute y by 10 in x + 3y = 33 x + 3(10) = 33 x + 30 = 33 If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence x = 3 correct answer C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:131,95,70,54, ? options: A)42 B)45 C)44 D)40 E)39 SOLUTION:131 - 95 = 36 = 6^2 95 - 70 = 25 = 5^2 70 - 54 = 16 = 4^2 so we can write 54 - x = 09 = 3^2 , where x is the next number x = 54 - 9 = 45 so the next number will be 45 ANSWER:B #### B QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? options: A)17603 B)17608 C)17628 D)17600 E)176023 SOLUTION:Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600 Answer: D #### D QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets? options: A)60 min B)50 min C)70 min D)65 min E)80 min SOLUTION:A 60 min Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. #### A QUESTION:Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We start by factoring 18. 18 = 29 = 63 = 233. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C. #### C QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ? options: A)240 B)140 C)230 D)130 E)105 SOLUTION:Let the number be x. Then, 4x/5 â€“(60% of x) = 21 4x/5 â€“ 60x/100 = 21 x = 105. Answer E. #### E QUESTION:A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit? options: A)Rs. 64 B)Rs. 69 C)Rs.72 D)Rs.75 E)Rs.90 SOLUTION:C.P. = Rs. (100/122.5)x392 = Rs. (1000/1225)x392 = Rs. 320 Profit = Rs. (392 - 320) = Rs. 72. Answer:C #### C QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)42.85 B)40 C)35 D)41 E)39 SOLUTION:step 1) took LCM of 40 and 50.. came as 200. step 2) 200 distance between B to C... do 200/50 hence 4 gallons used step 3) twice distance.. hence 2002= 400... do as above.. 400/40= 10 gallons used step 4) total gallons.. 4+10= 14 gallons step ) total miles= 200+400= 600 miles hence.. average of whole journey = 600/14 which comes to 42.85 Answer : A #### A QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 4518 -45x + 36x =3100 or 9x = -3100 +4518 x= 510/9 = 56.6% B #### B QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long? options: A)30 B)40 C)50 D)60 E)70 SOLUTION:Number of pieces = 42.5/0.85 = 42.50/0.85 = 4250/85 = 50. ANSWER:C #### C QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3Ã—7/36 = 7/12 Remaining work = 1 â€“ 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 C #### C QUESTION:How many even multiples of 55 are there between 549 and 1101? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:550 = 1055 1100 = 2055 The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature T in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median T will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:Which of the following is not divisible by 6? options: A)10032 B)21192 C)47816 D)91232 E)72031 SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3 Option A: 10032, Divisible by 2. Hence divisible by 6 Option B: 21192, Divisible by 2 & 3. Hence divisible by 6 Option C: 47816, Divisible by 2. Hence divisible by 6 Option D: 91232, Divisible by 2. Hence divisible by 6 Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E QUESTION:Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)70 m B)60 m C)80 m D)90 m E)100 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q? options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3 SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8 Answer:A #### A QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)64 B)72 C)80 D)90 E)99 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 11 and the total number of coins is 9k = 99. The answer is E. #### E QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively. options: A)200, 360,162 B)200, 460,160 C)200, 360,160 D)200, 360,138 E)200, 360,129 SOLUTION:Explanation: let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160 Answer: C) #### C QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3. In this case: the x-intercept is the value(s) of x for s = 0. 0 = x^2 - x^3; 0 = x^2(1 - x); x = 0 or x = 1. Answer: C. #### C QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.? options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None SOLUTION:Amount = [22000 * (1 + 12/100)3] = 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42 C.I. = (30908.42 - 22000) = Rs. 8908.42 ANSWER:A #### A QUESTION:45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/60045 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/80060 = 90 litres. Answer B #### B QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is? options: A)75 B)78 C)80 D)82 E)86 SOLUTION:Divisor = (6 * 3) + 2 = 20 5 * Quotient = 20 Quotient = 4. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 4) + 6 = 86 E) #### E QUESTION:In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers? options: A)25 B)26 C)27 D)28 E)29 SOLUTION:Sum of the 12 numbers=1+2+3+......+12=1213/2=78 So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be: 3+4+5+6+7=25 8+9+10=27 11+12+1+2=26 ANSWER:B #### B QUESTION:Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket? options: A)5min. 50sec. B)5min. 30 sec. C)6 min 36 sec. D)6mins. 32 sec. E)6 min. 15 sec. SOLUTION:Explanation: Part filled in 3 minutes = 3∗(1/12+1/15)=3∗9/60=9/20 Remaining part =1−9/20=11/20 =>1/12:11/20=1:X =>X=6.6 mins. =>X=6.6 mins. So it will take further 6 mins 36 seconds to fill the bucket. Option C #### C QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph SOLUTION:Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 C #### C QUESTION:If 144/0.144 = 14.4/x, then the value of x is: options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144 SOLUTION:=144/0.144 = 14.4/x =144 x 1000/144 =14.4/x =x = 14.4/1000 = 0.0144 Answer is C. #### C QUESTION:How many 4 letter words can we make from the letters in an alphabet? options: A)358800 B)358802 C)358801 D)358809 E)358810 SOLUTION:There are 26 letters in an alphabet to choose 4 from these 26 would mean 26P4 = 26!/(26-4)! We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words. Therefore the answer is 26!/ 22! = 26252423 = 358800 Answer:A #### A QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill? options: A)1/5 B)1/3 C)2/7 D)3/5 E)3/11 SOLUTION:1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 B #### B QUESTION:Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are: options: A)39,30 B)41,32 C)42,33 D)43,34 E)35,36 SOLUTION:Let their marks be (x + 9) and x. then x+9 = 56/100(x+9+x) 3x=99 x=33 their marks 42 and 33 ANSWER C #### C QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)81 km/hr B)88 km/hr C)62 km/hr D)46 km/hr E)56 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y - 4.5)(10/36) ---(1) x/8.5 = (y - 5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y - 4.5)/ (y - 5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4 0.1y = 8.5 × 5.4 - 8.4 × 4.5 => .1y = 45.9 - 37.8 = 8.1 => y = 81 km/hr ANSWER:A #### A QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)30000 B)20000 C)23000 D)21020 E)28211 SOLUTION:Explanation: Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer: B #### B QUESTION:A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? options: A)5% B)10% C)15% D)20% E)It can not be determined SOLUTION:Solution: let the total number of flags be 100(even number) let the total number of 'blue' flags alone be 'a' let the total number of 'red' flags alone be 'b' let the total number of 'both' flags be 'c' We have given, total number of blue flags = 60% = 60 = a+c total number of red flags=55%=55=b+c total number of flags = a+b+c=100 (since all the flags have been utilized) So, substituting for c in the third equation, we have, 60-c+c+60-c=100 c=20 Option D. #### D QUESTION:A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre options: A)s510 B)s780 C)s880 D)s480 E)s980 SOLUTION:area of the plot=110m65m=7150sq.m area of plot excluding gravel=105m60m=6300sq.m area of gravel =7150sq.m-6300sq.m =850sq.m cost of building it = 850sq.m60 = 51000p in Rs =51000/100=Rs510 ANSWER:A #### A QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:Ramu bought an old car for Rs. 43000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)22% E)of these SOLUTION:Total CP = Rs. 43000 + Rs. 13000 = Rs. 56000 and SP = Rs. 64900 Profit(%) = (64900 - 56000)/55000 100 = 16% ANSWER:B #### B QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is? options: A)54 B)77 C)36 D)88 E)21 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A #### A QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is options: A)u B)v C)w D)y E)z SOLUTION:a is one time, b,2 times so on... so 323=n(n+1)/2.. 0r n(n+1)= 646... now 2526=650...2425<646 so n= 25. and 25th alphabet is Y. ans D #### D QUESTION:HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10% options: A)36 B)40 C)32 D)42 E)45 SOLUTION:Let the weight of tea(25 per kg) to be used - X The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30) total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit) The equation follows like this 25X + 900 + (10 % of (25X + 900)) = 30( X + 30) 25X + 900 +2.5 X + 90 = 30 X + 900 27.5 X + 990 = 30 X + 900 2.5 X = 90 X= 90/2.5 = 36 ANSWER:A #### A QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 \Answer:C #### C QUESTION:If 0.5% of A =85 paise, then the value of A is ? options: A)Rs. 170 B)Rs. 17 C)Rs. 1.70 D)Rs. 4.25 E)None SOLUTION:Answer ∵ 0.5/100 of A = 85/100 ∴ A = Rs. (85 / 0.5) = Rs. 170 Correct Option: A #### A QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? options: A)3.625 B)3 C)4.5 D)4 E)3.5 SOLUTION:Set up two R x T =D cases. 1. 1/12 km/ min x T = 2.75 from which T= 33 mins. We know total journey time now is 51 +33 =84. The rate is the same ie 1/12km/min. set up second R x T =D case. 1/12 km/min x 84 = 7 km Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5 E. #### E QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? options: A)20 B)98 C)66 D)54 E)12 SOLUTION:Let C.P. of each article be Re. 1. Then, C.P. of 50 articles = Rs. 50; S.P. of 50 articles = Rs. 40. Loss % = 10/50 * 100 = 20% Answer: A #### A QUESTION:A reduction of 5% in the price of sugar enables a lady to obtain 5kgs more for Rs.500, find the original price per kg? options: A)5.26 B)5.0 C)5.52 D)6.2 E)5.8 SOLUTION:Answer: 500(5/100) = 25 --- 5 ? --- 1 => Rs.5 500 --- 475 ? --- 5 => Rs.5.26.Answer: A #### A QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant. options: A)250 m B)560 m C)100 m D)320 m E)240 m SOLUTION:Explanation : Abhishek's speed = 100/5=20 m/s. Time taken by Abhishek to cover 500 m =500/20=25 seconds. Dishu's speed = 500/20 or 25 m/s Prashant's speed = 15 m/s Time taken by Dishu to meet Prashant in 500m race in opposite direction: Distance covered by Abhishek: =>500/(15+25). =>12.5 sec. =>12.5(20)= 250 m. Answer : A #### A QUESTION:The average score of a cricketer for five matches is 45 runs. If the average for first three matches is 30, then average for last two matches is options: A)33.25 B)32.25 C)67.5 D)60.5 E)45.5 SOLUTION:Explanation: =(45×5)−(30×3)/2 =(225 −90)4=67.5 Answer: Option C #### C QUESTION:The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.? options: A)A)12PM B)B)4PM C)C)1PM D)D)3PM E)E)5PM SOLUTION:Let x hours be they will meet together distance covered by 1st person+distance covered by 2nd person = 450km 70x+80x = 450 x= 3 hr They will meet = 9AM +3hr = 12PM Answer is A #### A QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20 after 2nd year (now age become 21) 221+ 20=62 grades after 3rd year(now age becomes 22) 222+31=75 ANSWER:B #### B QUESTION:By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)20 kmph B)30 kmph C)87 kmph D)99 kmph E)77 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 40 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. Answer:A #### A QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days? options: A)4 B)4/5 C)7/9 D)10 E)24/7 SOLUTION:A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4 A,B,C together will complete the job in 4 days Answer is A #### A QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(66)/2 = 18 Answer:A #### A QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? options: A)4000 B)4500 C)5000 D)5500 E)6000 SOLUTION:35%-----------L 65%-----------W ------------------ 30% = 1350 10% = 450 100% of the votes = 4500 Answer: B #### B QUESTION:The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females? options: A)56% B)50% C)57% D)10% E)80% SOLUTION:Male = 45,000* 5/9 = 25,000 Female = 45,000* 4/9 = 20,000 Married Male = 25,000* 40/100 = 10,000 Married Female = 10,000 20,000 ------------ 10,000 100 ------------- ? => 50% Answer: B #### B QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:Two trains 200 m and 800 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? options: A)10.6 B)10.9 C)36 D)10.8 E)10.1 SOLUTION:Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 200 + 800 = 1000 m. Required time = 1000 * 9/250 = 36 sec. Answer: C #### C QUESTION:If x^2+(1/x^2)=7, x^4+(1/x^4)=? options: A)10 B)11 C)12 D)14 E)47 SOLUTION:-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47. Thus, the answer is E. #### E QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell? options: A)69 B)72 C)75 D)78 E)81 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.2x. Then she canned 1.40.2x=0.28x. The total amount of pears is x+0.2x+0.28x=1.48x The fraction of pears that she sold is 1/1.48=100/148=25/37. The number of pears she sold is (25/37)111=75. The answer is C. #### C QUESTION:Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 12 coconut doughnuts, and 10 jam-filled doughnuts. How many doughnuts did Anne buy in all? options: A)25 B)34 C)39 D)21 E)11 SOLUTION:Add the numbers of doughnuts. 12 + 12 + 10 =34. Answer is B. #### B QUESTION:In a simultaneous throw of pair of dice .find the probability of getting the total more than 7? options: A)12/5 B)5/12 C)6/4 D)2/3 E)4/7 SOLUTION:Here n(S)=(66)=36 let E=event of getting a total more than 7 ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)} P(E)=n(E)/n(S)=15/36=5/12 Option B #### B QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .250+.6x=.5(50+x) x=150 Answer E #### E QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A. options: A)240 B)388 C)288 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 * 756 = 288 Answer: C #### C QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 43!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C33!=60 total S=84 outcomes D #### D QUESTION:A retailer buys 100 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)175 C)212 D)218 E)220 SOLUTION:let the market price of each pen be $1 then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99 profit %=((63100)/36) %=175% Answer B #### B QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)2: 7 B)2: 0 C)2: 4 D)2: 3 E)2: 1 SOLUTION:80 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280.Answer:D #### D QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:Find the odd man out 2, 5, 14, 41, 122, 365, 1125 options: A)2 B)14 C)41 D)365 E)1125 SOLUTION:13-1 = 2 23-1 = 5 53-1 = 14 143-1 = 41 413-1 = 122 1223-1= 365 3653-1= 1094 ANSWER:E #### E QUESTION:If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used? options: A)180 grams B)220 grams C)250 grams D)350 grams E)1400 grams SOLUTION:I too think 1400 grams should be the answer. My reasoning is The h20 content in 700 gms of water is 1 h20 content in 24% solution is 0.76 Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84 Let amount of solution be X Then the equation can be set up 7001 + 0.76X = 0.84 (X+700) 0.08X = 112 8X = 11200 X = 1400 (ANS E) #### E QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years? options: A)60 percent decrease B)20 percent decrease C)20 percent increase D)60 percent increase E)140 percent increase SOLUTION:Let the value of the stock in 2000 be 100, then in 2001 its value would be 100(1-80/100)=1000.2=20 and in 2002 its value would be 20(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%. Answer: B. #### B QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1260, find the loss %? options: A)16% B)18% C)17% D)78% E)28% SOLUTION:1500 ---- 240 100 ---- ? => 16% Answer:A #### A QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:If $500 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years? options: A)500 (1.056)(3) B)500 (3+1.056) C)500 (1+3(0.056)) D)500 (1.056)^3 E)500 (1+(0.056)^3) SOLUTION:the formula is CI=P(1+r/100)^t in this case i think D is the ans #### D QUESTION:Machine A working alone can complete a job in 3 hours. Machine B working alone can do the same job in 4 hours. How long will it take both machines working together at their respective constant rates to complete the job? options: A)1.10 min B)1.714 hr C)4hr D)2hr E)1.714 hr SOLUTION:Machines ( A ) ( B ) (A+B) ---Time - 3 - ( 4 ) 1.714 ---Rate 4 --- 3 ---7 --Work 12 ---12 ---12 E #### E QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D <<<Examples ends QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122 SOLUTION:Explanation: Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 Answer: B #### B QUESTION:A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? options: A)18% B)20% C)17% D)18% E)None of these SOLUTION:Explanation: Let the CP of the article = Rs.100. Then labeled price = Rs.130. SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117. Gain = Rs.117 – Rs.100 = Rs.17 Therefore, gain/profit percent = 17%. Answer: Option C #### C QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? options: A)months B)months C)months D)months E)months SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 ANSWER:D #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 70 ⇒ 1.75x = 70 ⇒ x = 40 coins Answer C #### C QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009? options: A)80 B)126 C)95 D)100 E)108 SOLUTION:Assume a value at the beginning of 2007. As this is a % question, assume P=100. At the end of 2007 it becmae = 1.2100=120 At the end of 2008 it decreased by 25% = 120.75 = 90 At the end of 2009 it increased by 40% = 901.2 = 126 Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer. #### B QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100? options: A)1345 B)1576 C)2475 D)2578 E)1895 SOLUTION:numbers are 11,13,15-------,97,99 Average of the set: (largest+smallest)/2=(99+11)/2=55; # of terms: (largest-smallest)/2+1=(99-11)/2+1=45 The sum = 4555= 2475 Answer: C #### C QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ? options: A)64 B)1/8 C)1 D)4 E)1/64 SOLUTION:Say r=2 => V1 = 1/16 when r=1; V2 = 1/4 V2 = 4V1. Answer : D #### D QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 Ã· 16) Ã— 100 #### B QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? options: A)3. B)7. C)10. D)16. E)15. SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins Distance traveled by the bird traveling from West-Town = 4 4= 16 Answer: D #### D QUESTION:The area of playground is 6000 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter. options: A)a) $144 B)b) $150.50 C)c) $168 D)d) $158.60 E)e) $160.70 SOLUTION:total volume * unit cost = total cost or, 6000 * 0.01 * 2.8 = total cost = 168=C #### C QUESTION:There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? . options: A)75 Kg B)80 Kg C)85 Kg. D)90 Kg E)92 Kg SOLUTION:New average weight= 110+60/2= 85 kgs Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85 C is the answer #### C QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:14x + 75 = 15(x + 3) x = 30 + 3 = 33 Answer:C #### C QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)sec B)sec C)sec D)sec E)sec SOLUTION:The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. Answer: A #### A QUESTION:When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor? options: A)11 B)17 C)13 D)23 E)37 SOLUTION:let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27. now 242-15=227 =kx (k is an integer and 234 is divisble by x) similarly 698-27=671 = lx (l is an integer and 689 is divisible by x) adding both 698 and 242 = (227+671)+15+27 =x(k+l) + 42 when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37 hence E #### E QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(5251)/(21)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(2625)/(21)=325, N(B)=4C2=(43)/(21)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:During the months May through October, Teddy the bear triples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976? options: A)9m−1300 B)9m−300 C)4m−1200 D)3m−300 E)m−1300 SOLUTION:Nov ' 73 = m April ' 74 = m - 100 Oct ' 74 = 3m - 300 April' 75 = 3m - 400 Oct' 75 = 9m - 1200 April'76 = 9m - 1300 Hence answer will be (A) 9m - 1300 #### A QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K? options: A)30 B)4 C)5 D)66 E)All of these SOLUTION:The first term divisible by 3, so any term could be the third term. Answer =(E) #### E QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.915 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.920 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5100 = 107% of 7.5. Answer: B. #### B QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision? options: A)2003 B)2009 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009. Answer: B. #### B QUESTION:The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ? options: A)43 yrs. B)44 yrs. C)45 yrs. D)47 yrs. E)46 yrs. SOLUTION:Explanation: Total age of players in team = 35 x 11 = 385 When coach is included, total members = 12, Avg age increases by one becomes 23 Total age when coach is included = 36x12 = 432 Age of coach = 432-385 = 47 yrs. Answer:D #### D QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was: options: A)2500 B)2520 C)3000 D)3100 E)None of these SOLUTION:Explanation : Number of valid votes = 70% of 9000 = 6300. Valid votes polled by other candidates = 40% of 6300 (40/1006300) = 2520. Harsh Mishra a year ago 0 upvotes Answer : B #### B QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted? options: A)72% B)47% C)42% D)34% E)28% SOLUTION:Town A is 40%, therefore town B must be 60% Town A registered voters:0.70∗0.40=0.28 Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent ANSWER:B #### B QUESTION:If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units? options: A)50 hours B)40 hours C)25 hours D)12 hours E)8 hours SOLUTION:Here, we're told that 5 machines can produce 20 units in 10 hours.... That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units. 20 units/5 machines = 4 units are made by each machine every 10 hours Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to... 10 hours/4 units = 2.5 hours per unit when 1 machine is working. The prompt asks us how long would it take 20 machines to produce 200 units. If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME. (2.5 hours)(10 times) = 25 hours Final Answer: [Reveal]Spoiler: C #### C QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is options: A)862 B)864 C)866 D)868 E)None of these SOLUTION:Solution P.W = Rs.(4320 - 720) = Rs. 3600 S.I on Rs. 4320 =Rs.(720/3600 x 4320) = Rs. 864. Answer B #### B QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. options: A)I only B)II only C)I and II only D)II and III only E)None of the above SOLUTION:Let the 3 numbers be x, y and z. Question: Which of the following is equivalent to (x + y + z)/3 I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141 II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent Answer: C #### C QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is options: A)not an even B)an even C)a perfect square D)an odd E)a prime SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1 y = x^2 - x - 2 y = (x-2)(x+1) (Note that one factor is even and one factor is odd.) Then y must be even. The answer is B. #### B QUESTION:If a:b = 3:1, then find (a - 3b)/(2a - b)? options: A)0 B)1 C)2 D)1/7 E)2/7 SOLUTION:a/b = 3/1 => a = 3b (a - 3b)/(2a - b) = (3b - 3b)/(6b - b) = 0/7b => 0 ANSWER:A #### A QUESTION:Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)3.5 hours D)2.3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/4 Part filled by B in 1 hour = 1/8 Part filled by C in 1 hour = 1/16 Part filled by (A+B+C) in 1 hour = 1/4+1/8+1/16=7/16 So all pipes will fill the tank in 2.3 hours. Option D #### D QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form. options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11 SOLUTION:Solution We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions 3 2/3 = 33 / 3 + 2 / 3 = 11 / 3 7 1/3 = 73 / 3 + 1 / 3 = 22 / 3 The ratio 3 2/3 : 7 1/3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 Simplify = 11 / 22 = 1 / 2 The ratio is 1 / 2 or 1:2 ANSWER IS D #### D QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4PIR^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)70% C)100% D)180% E)200% SOLUTION:Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]). [(1.7 - 1)/1] * 100% = 70% ANSWER:B #### B QUESTION:If 2x = 3y = 20, then 12xy = ? options: A) 1,200 B) 800 C) 120 D) 40 E) 20 SOLUTION:2x = 20;x=10 3y = 20;y=20/3 Multiply: 12xy=121020/3=800. Answer: B. #### B QUESTION:A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes The answer is D. #### D QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/896=36 people in the room under the age of 21. Answer: B. #### B QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is options: A)1/2 B)1 C)2 D)4 E)8 SOLUTION:Given: 5/w + 5/x = 5/ywx=y Find: (w+x)/2 = ? 5(1/w + 1/x) = 5(1/y) - divide both sides by 5 (1/w + 1/x) = 1/y (x+w)/wx = 1/wx - sub'd in y=wx x+w - 1 = 0 x+w = 1 Therefore (w+x)/2 = 1/2 Ans: A #### A QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Find the fourth proportional to 2.8 , 3.4 and 5.2? options: A)5.98 B)6.14 C)6.29 D)6.31 E)5.64 SOLUTION:Formula = fourth proportion =(b x c)/a a=2.8 , b=3.4 and c=5.2 (3.4 x 5.2)/2.8=6.31 D #### D QUESTION:Tim and Élan are 120 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan? options: A)30 miles. B)35 miles. C)45 miles. D)60 miles. E)80 miles. SOLUTION:Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same. Plugging in the answer choice Only Answer Choice E meet the 2:1(Tim:Elan=80:40) ratio of maintaining total distance traveled 120 miles So Correct answer E #### E QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7? options: A)180 B)140 C)210 D)270 E)300 SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 140 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat B #### B QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7100/83.3 =20% ANSWER:C #### C QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01$330=$333.30. The answer is D. #### D QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate. options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10 SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity. Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job. Answers E, A and C are illogical, since the individual times must both be greater than 10 days. so we can TEST the values for Answers B and D. Using the values for Answers C and D... Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match Final Answer: C #### C QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Option A #### A QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? options: A)E982 B)27 C)12 D)14.6 E)28 SOLUTION:Explanation: T = 11/45 * 60 = 14.6 Answer: Option D #### D QUESTION:The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? options: A)40 B)41 C)46 D)42 E)49 SOLUTION:Total age of all students =23Ã—22 Total age of all students + Age of the teacher =24Ã—23 Age of the teacher =24Ã—23âˆ’23Ã—22=23(24âˆ’22)=23Ã—2=46 Answer is C. #### C QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)6 Answer: B #### B QUESTION:What will be in unit's place digit of 3 to the power 34. options: A)1 B)6 C)3 D)0 E)9 SOLUTION:as the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9.. ANSWER:E #### E QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:A baker sold twice as much bread in the afternoon than in the morning. If he sold 360 kilograms of bread that day, how many kilograms did he sell in the morning and how many in the afternoon? options: A)180kg B)240kg C)470kg D)641kg E)559kg SOLUTION:Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x.This must be equal to 360. 3x=360 x=3603 x=120 Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon. correct answer is B)240kg #### B QUESTION:Steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey? options: A)60 mph B)68 mph C)53.33 mph D)64 mph E)66.67 mph SOLUTION:Answer Average speed of travel = Total distance travelled/Total time taken Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours. Distance covered in the first 2 hours = speed time = 50 * 2 = 100 miles. Distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles. Therefore, total distance covered = 100 + 240 = 340 miles. Total time taken = 2 + 3 = 5 hours. Hence, average speed = Total distance travelled/Total time taken=340/5 = 68 miles per hour. Choice B #### B QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities options: A)100 km B)120 km C)150 km D)180 km E)None of these SOLUTION:Explanation : Let the distance between two cities = D, D = xt (x = usual speed and t is the actual time) D = (X + 20)(T -2) and D = (X +30)(T – 2.5) Solve the above equation, u will get T = 5 and X = 30, so distance = 305 = 150 km Answer – C #### C QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together? options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21) SOLUTION:A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 1/2 days. The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days. Answer:D #### D QUESTION:Operation#is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Any multiple of 10 is even. Any two-digit prime number is odd. (even+odd)/2 is not an integer. Thus # does not yield an integer at all. Therefore P=0. Answer: A. #### A QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 20505=10250 10250-10000=250 Answer E #### E QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 1410 = 140 sq cmV Answer: A #### A QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? options: A)12 days B)18 days C)15 days D)21 days E)22 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/10 work in 1 day B alone can do (1/6 -1/10) =1/15 work in 1 day => complete work can be done in 15 days by B Answer: Option C #### C QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2007 B)2008 C)2002 D)2000 E)2001 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: D #### D QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 Ã— 15 = 180 m. Then, speed of train = 180â„18 = 10 m/s Now, length of train = 9 Ã— 15 = 135m âˆ´ Required time = 135â„10 = 13.5 sec. Answer E #### E QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter? options: A)15 B)25 C)30 D)45 E)60 SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach... We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats. Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as... 15X/7X When we add the 16 cats and factor in the 'ending ratio', we have an equation.... 15X/(7X+16) = 15/11 Here we have 1 variable and 1 equation, so we can solve for X.... (15X)(11) = (7X+16)(15) (X)(11) = (7X+16)(1) 11X = 7X + 16 4X = 16 X = 4 With this X, we can figure out the initial number of dogs and cats... Initial dogs = 15X = 15(4) = 60 Final Answer: D #### D QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? options: A)76 sec B)89 sec C)87 sec D)15 sec E)16 sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 650)/10 = 89 sec. Answer:B #### B QUESTION:If you add all the numbers on your mobile phone , what is the answer? options: A)45 B)50 C)55 D)100 E)60 SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone. Therefore 0+1+2+3+4+5+6+7+8+9=45 Answer is A #### A QUESTION:The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ? options: A)440 B)512 C)550 D)620 E)750 SOLUTION:Large numbers are made in two ways: Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place. 312 = 62 (large prime number) 2^6 = 64 (many small prime numbers) To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 22), 2, 5 - relatively small prime numbers. You are left with 620 which is 31225 (sum greater than 32) Answer D #### D QUESTION:A ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)28.97 B)28.0 C)28.47 D)27.47 E)29.47 SOLUTION:Explanation : After 10 days : 200 women had food for 25 days. Suppose 175 women had food for x days. Now, Less women, More days (Indirect Proportion) 175 : 200 :: 25 : x => 175 x x = 200 x 25 => x = 200 x 25 / 175 => x =28.47 Answer : C #### C QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25 SOLUTION:Explanation : Face value of each share = Rs.20 Dividend per share = 9% of 20 = 9×20/100=9/5 He needs to have an interest of 12% on his money ie, Money Paid for a share 9×12/100=9/5 Money Paid for a share=9/5×100/12=15 ie, Market Value of the share = Rs.15 Answer : Option C #### C QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:The surface of a cube is 24sq cm. Find its volume? options: A)8 B)6 C)4 D)3 E)1 SOLUTION:6a2 = 24 a = 2 => a3 = 8cc Answer: A #### A QUESTION:If m^2-8m+1=0,then m^3+m^(-3)= ? options: A)487 B)488 C)489 D)457 E)495 SOLUTION:here from equation 1 we will get m^2-8m+1=0 m^2=8m-1 m=(8m-1)/m.........(1) m=8-1/m so m+1/m=8 now in equation 2 m^3+1/m^3 (m+1/m)(m^2 - m1/m + 1/m^2) (m+1/m)(m^2 - 1 + 1/m^2) (m+1/m)(m^2 + 1/m^2 - 1) (m+1/m){(m+1/m)^2 - 2m1/m - 1} {since a^2+b^2=(a+b)^2-2ab} (m+1/m){(m+1/m)^2 - 2-1} now putting the value of m from equation 1 8(8^2-2-1) 8(64-3) =488 ANSWER:B #### B QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2) options: A)1296 B)4 C)8 D)16 E)32 SOLUTION:(x+y)^2 - (x-y)^2 (x+y+x-y)(x+y-x+y) (2x)(2y) 4xy 4 6^4 = 1296 Answer A #### A QUESTION:The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries? options: A)3 : 3 : 10 B)10 : 11 : 20 C)23 : 33 : 60 D)Cannot be determined E)None of these SOLUTION:Explanation: Let A = 2k, B = 3k and C = 5k. A's new salary = 115/100 of 2k=23k/10 B's new salary =110/100 of 3k =33k/10 C's new salary = 120/100 of 5k =6k =23:33:60 Answer is C #### C QUESTION:The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)5000 B)4860 C)5400 D)4800 E)5120 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 6000 Ã— 90/100 Ã— 90/100 = 4860 B #### B QUESTION:The average height of 35 boys in a class was calculated as 185cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)178.27 cm B)183.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 185 cm. Wrong total height of 35 boys = 185 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 185 cm - (166 cm - 106 cm)/35 =185 cm - 60 /35 cm = 185 cm - 1.71 cm = 183.29 cm. Answer: B #### B QUESTION:If 9^y = 3^16, what is y? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:9^y = 3^2y = 3^16 2y=16 y = 8 The answer is E. #### E QUESTION:What is the remainder when 4^381 is divided by 5 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?E #### E QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 * 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:A company pays 20.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares? options: A)25 B)66 C)18 D)19 E)41 SOLUTION:Explanation: Dividend on 1 share = (20.5 * 50)/100 = Rs.10.25 Rs.25 is income on an investment of Rs.100 Rs.10.25 is income on an investment of Rs. (10.25 * 100)/25 = Rs.41 ANSWER: E #### E QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example options: A)100 B)610 C)729 D)900 E)1000 SOLUTION:The hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus, 9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D QUESTION:Amal borrowed a sum of money with simple interest as per the following rate structure: (a) 6 p.c. p.a. for the first three years (b) 8 p.c. p.a. for the next five years (c) 12 p.c. p.a. for the next eight years If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow? options: A)8,000 B)10,000 C)12,000 D)6,000 E)None of these SOLUTION:Let x be the amount Amal borrowed. ∴ 18% of x + 40% of x + 48% of x = 5040 or, 106% of x = 5040 ∴ x = 5040⁄106 × 100 = 4754.71 Answer E #### E QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)2.54% B)4.56% C)6.125% D)7.134% E)8.341% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved? options: A)2/4 B)3/4 C)4/5 D)5/6 E)6/7 SOLUTION:consider A,B,C events and AA,BB,CC not solving the problems now P(1)=1/2, P(B)=2/3 and P(C)=1/4 Not solving events =1/22/33/4 ==>1-1/4= 3/4 ANSWER B #### B QUESTION:Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? options: A)3/5 B)2/5 C)1/2 D)4/5 E)19/25 SOLUTION:There can be an odd product only if both integers are odd. P(odd product) = 1/22/5 = 1/5 P(even product) = 1 - 1/5 = 4/5 The answer is D. #### D QUESTION:How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest? options: A)8 years B)20 years C)72 years D)56 years E)None SOLUTION:In this case, Rs. 1000 has become Rs.5000. Therefore, the interest earned = 5000 – 1000 =4000 Interest for Rs 1000 @ 20% for 1 year = 200 200 - 1 4000 - ? => 20 years Answer : B #### B QUESTION:Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank? options: A)10 min. 20 sec. B)11 min. 45 sec. C)12 min. 30 sec. D)14 min. 40 sec. E)15 min. 40 sec. SOLUTION:Take LCM of 15 and 20 and get the total capacity of tank as 60 . Then A will fill 4li in 1 min and B will fill 3 li in 1 min so total will be 7 . A left after 4 min so they worked together for 4 min so 74= 28 . now subtract it from 60.(60-38=32). This will be filled by b so time taken would be..10 min 20 sec. ANSWER:A #### A QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:If abc ≠2 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a = options: A)(1 + bc)/(b + c) B)(1 – bc)/(b + c) C)(1 + b + c)/(bc) D)(1 – b – c)/(bc) E)(1 – b – c)/(b + c) SOLUTION:Answer is A though it took me around 4 minutes to get that. #### A QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)22200 B)21897 C)28799 D)30000 E)32782 SOLUTION:P(11/10)^4 - P(6/5)^2 = 723 P = 30000 Answer: D #### D QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Solution: 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. Answer C #### C QUESTION:Albert invested amount of 20000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit options: A)Rs. 8510 B)Rs. 22050 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(20000×(1+5/100)2) =>20000×21/20×21/20 =>22050 Option B #### B QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 = options: A)0 B)1 C)35 D)120 E)245 SOLUTION:8+2+3+4+3+5 = 25, so this number is not divisible by 3 and thus not divisible by 15. Therefore, k=0 5^k - k^5 =1-0=1 The answer is B. #### B QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter? options: A)3x B)4x C)9x D)12x E)27x SOLUTION:Original perimeter = x Hence original side = x/4 New side = 4x/4 New perimeter = 44x/4 = 4x Correct Option: B #### B QUESTION:A policeman spotted a criminal from a distance of 200 metres. When the policeman starts the chase, the criminal also starts running. If the criminal was running at 10 km/hr and the policeman was chasing at the speed of 12 km/hr, find the distance the criminal will run before he is catched by the policeman ? options: A)1.5 km B)700 m C)900 m D)1 km E)None of these SOLUTION:Explanation : Solution: Relative speed = (12 - 10) = 2 km/hr. Time taken by policeman to cover 200 m = (200/1000 1/2) hr = 1/10 hr. In 1/10 hrs, the criminal covers a distance of (101/10) km = 1 km. Answer : D #### D QUESTION:5216 × 51 = ? options: A)266015 B)266014 C)266016 D)266116 E)266226 SOLUTION:Normal way of multiplication may take time. Here is one alternative. 5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016 Answer is C. #### C QUESTION:What is the lowest possible common multiple M of 2 distinct integers, each greater than 329? options: A)330·331 B)330^2 C)33·331 D)660 E)330 SOLUTION:Lowest possible common multiple M of 2 distinct integers will have to be multiple of the number greater than 329...which 330.. so one number will be 330...another one will be 660.. Ans is D. #### D QUESTION:For all positive integers n and m, the function A(n) equals the following product: (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8 SOLUTION:For all positive integers n and m, A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2) B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive. A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...} A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2) The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ... missing numbers are 1/8, 1/13, 1/16, .... B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25) here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values The largest reciprocal that present in B(25) but not in A(5) is 1/3 Answer A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:The ratio of spinsters to cats is 2 to 9. If there are 63 more cats than spinsters, how many spinsters are there? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:Let 2x be the number of spinsters. Then 9x is the number of cats. 9x-2x=63 x=9 and the number of spinsters is 2(9)=18. The answer is E. #### E <<<Examples ends QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 60 + 27.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)(1/5) So it takes 25 men to complete this job = 25 (1/25) = 1 Answer: C #### C QUESTION:A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: options: A)49 B)4 C)12 D)9 E)27 SOLUTION:Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 14 : 6 :: 21 : x 14 * x = 6 x 21 x = (6 x 21)/14 x = 9. Answer is D. #### D QUESTION:The remainder obtained when a prime number greater than 4 is divided by 4 is options: A)a) 1 or 3 B)b) 1 or 5 C)c) 3 or 5 D)d) 4 or 5 E)e) 5 SOLUTION:The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5: 7/4 = 1 + remainder of 3 5 / 4 = 1 + remainder of 1 This is already sufficient to see that answer choice a) is correct. A #### A QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B QUESTION:Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m. options: A)25.8 B)26.8 C)27.8 D)20.5 E)21.8 SOLUTION:avg speed=2xy/(x+y) =21824/(18+24)=20.5 ANSWER:D #### D QUESTION:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours? options: A) $180,000 B) $185,000 C) $180,000 D) $200,000 E) $192,500 SOLUTION:30% of 1000 = 300 worked for 20 hours Payment @ 5/hr Total Payment = 300255 = 37500 50 % of 1000 = 500 worked for 40 hours Payment @ 5/hr Total payment = 500405 = 100000 Remaining 200 worked for 50 Hours Payment for first 40 Hours @ 5 /hr Payment = 200405 = 40000 Payment for next 10 hr @ 7.5/hr Payment = 200 * 10 * 7.5 = 15000 Total Payment = 37500+100000 + 40000 +15000 = 192500 Hence , answer is E #### E QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point? options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec SOLUTION:Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) } = LCM (90, 60) =180 sec. Answer:D #### D QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)y(y+3) B)y^2(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)y(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:100 identical coins each with probability 'pp' showing up heads & tossed. options: A)13/101 B)11/101 C)51/101 D)53/102 E)54/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 5/18 = 40 m/sec Time taken = 150/40 = 3.75 sec. ANSWER:C #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000? options: A)8275 B)1879 C)2779 D)2672 E)2782 SOLUTION:A = 25000(11/10)^3 = 33275 = 25000 ---------- 8275 Answer: A #### A QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 5002/25 =40sec ANSWER:A #### A QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)Rs.64.18 B)Rs.64.67 C)Rs.64.08 D)Rs.64.10 E)Rs.64.22 SOLUTION:S.I. = (1000 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 122222 = 32 ANSWER:B #### B QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x 5) = (0.75 9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 1000.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = t 5a2 + 7b2 = t 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)18.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 36 Paise is given as tax => Total tax incurred = 36 Paise = Rs.36/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−36/100−x)6/100 = 36/100 ⇒ 6(25 −0.36 −x) = 36 ⇒ (25 − 0.36 − x) = 6 ⇒ x = 25 − 0.36 − 6 = 18.7 B) #### B QUESTION:39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)9 B)12 C)10 D)13 E)15 SOLUTION:Explanation: Let the required number of days be x More persons, less days (indirect proportion) More hours, less days (indirect proportion) Hence we can write as (persons)39:30 (hours) 5:6}:: x:12 ⇒39×5×12=30 × 6 × x ⇒39×5×2=30 × x ⇒39=3×x ⇒x=13 Answer: Option D #### D QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:222 + 4 = 12 333 +4 = 31 444 + 4 = 68 555 + 4 = 129 666 + 4 = 220 7 7 7 + 4 = 347 ANSWER : D #### D QUESTION:If a and b are positive integers and a/b=0 then which of the following give positive Numbers and CANNOT be zero? options: A)ab/ba B)a/b-b/a C)b/a-a/b D)(a^2 -b^2)/ab E)a/b SOLUTION:(D) (a^2 -b^2)/ab = a/b-b/a gives negative value. The option C is Answer. (C)a/b-b/a If a/b=0, b/a gives positive numbers.(a and b are positive integers) #### C QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? options: A)12 B)9 C)3 D)7.5 E)2.5 SOLUTION:we have 2 equations 1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B #### B QUESTION:A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 * 5/18 = 20 = 400 â€“ 250 = 150m ANSWER:A #### A QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches? options: A)25 B)23 C)22 D)15 E)18 SOLUTION:Area of Carol's rectangle = 245 = 120 Let width of Jordan's rectangle= w Since , the areas are equal 8w = 120 =>w = 15 Answer D #### D QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? options: A)229 B)108 C)278 D)72 E)112 SOLUTION:S = 120/6 18/5 = 72 kmph Answer: D #### D QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. options: A)237 B)126 C)971 D)611 E)150 SOLUTION:Explanation: ANSWER: E #### E QUESTION:If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number. options: A)5 : 3 B)2 : 5 C)4 : 7 D)5 : 2 E)None of these SOLUTION:Explanation: Let the first number is A and second number is B. As per question (40/100)A = (2/3)B A/B = 2/3 x 100/40 A/B = 5/3 =>A:B = 5:3 Answer: Option A #### A QUESTION:A rectangular field is 20 yards long and 18 yards wide. A fence is needed for the perimeter of the field. Fencing is also needed to divide the field into three square sections. How many feet of fencing are needed? (It is a good idea to make a drawing for this one.) options: A)330 ft B)336 ft C)430 ft D)330 ft E)230 ft SOLUTION:20 + 18 + 20 + 18 = 76 yds. for outside of field. 18 + 18 = 36 yds. for dividing sections 76 + 36 = 112 yds. of fencing 112 x 3 = 336 ft. of fencing correct answer B #### B QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)(White / Total Coins) = (Blue / Total Coins) í.ẹ. RedWhite = BlueTotal Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a 3b = 3c3(a+b+c) í.ẹ. ab = c(a+b+c) For smallest values of a, b and c 23 = 1(1+2+3) í.ẹ. Minimum Total Coins = 3(1+2+3) = 15 Answer: Option C #### C QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)285 m B)240 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x = 285 m. Answer: A #### A QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ? options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4 SOLUTION:Say a = 2. Then: a/b = 1/3 --> b = 6; b/c = 2 --> c = 3; c/d = 1/2 --> d = 6; d/e = 3 --> e = 2; e/f = 1 --> f = 2. abc/def = (263)/(622) = 3/2. Answer: D. #### D QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ? options: A)6000 B)5400 C)6200 D)7200 E)8200 SOLUTION:Investment Ratio = Profit Sharing Ratio. Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6. Giri share = 13200 × 6 / 11 = Rs.7200 Hari share = 13200 × 5 / 11 = Rs.6000 Option A #### A QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(22003))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ? options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Expanding we have 6x^2 - 3x + 4x -2 6x^2 + x - 2 Taking coefficients, a = 6, k= 1, n = -2 Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9 The answer is C. #### C QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)170 C)175 D)195 E)180 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. 160 x 2.40 + x x 3.20 = 432 3.20x = 432 - 384 = 48 x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER :C #### C QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered: 2 skeins at $2.50 per skein (not discountable) 8 skeins at $8.40 per skein (discountable) 7 skeins at $5.99 per skein (discountable) Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn? options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64 SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.) 7 x $5.99 = $41.93 $67.20 + $41.93 = $109.13 discountable $109.13 x .10 = $10.91 (rounded) $109.13 - $10.91 = $98.22 for discounted yarn 2 x $2.50 = $5.00 for un-discounted $98.22 + $5.00 = $103.22 cost of yarn $103.22 x 1.13 = $116.64 with tax and shipping (5% + 8% = 13%) correct answer A #### A QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:The rate of the pump + leak = 5/14 1/2 - leak's rate = 5/14 leak's rate = 1/2 - 5/14 = 1/7 The leak will empty the tank in 7 hours. The answer is D. #### D QUESTION:The wages earned by Robin is 50% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)18.75% B)23% C)30% D)50% E)7% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.510 = 15 Wage of Charles = 1.6 10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-15)/15 100% = 1/15 * 100% =7% Answer E #### E QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)64% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5(4/5) of the original price, which nets to 0.64 of the original price, or 64%. E #### E QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B QUESTION:A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea. Time taken to finish the job = XY / (X + Y) = 10 x 15 / (10 + 15) = 150 / 25 = 6 days Answer: B #### B QUESTION:Average between two sets of numbers is closer to the set withmore numbers? options: A)70 B)80 C)90 D)95 E)98 SOLUTION:If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86. Here, 90 has a weight of 3 => it occurs 3 times. Whereas 80 has a weight of 2 => it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated. B #### B QUESTION:The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is options: A)17.2 km B)7.2 km C)7.6 km D)17.6 km E)27.2 km SOLUTION:speed of a boat in still water = 15 km/hr Speed of the current = 3 km/hr Speed downstream = (15+3) = 18 km/hr Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km Answer is B #### B QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)50.5 E)67.5 SOLUTION:Total price of six cans = 637.5 = 225 Total price of 4 cans = 431 = 124 Total rice of two cans = 225 - 124 = 101 Average price of two cans = 101/2 = 50.5 c Another way to do it is this: Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 237.5 + 46.5 = 101 Avg cost of the two cans = 101/2 = 50.5c Answer (D) #### D QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 21=2. Answer: C. #### C QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 505/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 50018/250 = 36sec Answer is C #### C QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 150001/6 = 2500.Answer: C #### C QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages? options: A)25 years B)28 years C)32 years D)26 years E)28 years SOLUTION:let rhea age be x rick age be y given x-8=1/2(y-8)......a also given x/y=(3/4) =>x=3/4(y).......b by solving a and b we get y=16 x=12 then x+y=12+16=28 ANSWER:B #### B QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 40 pints of Perfect Pink paint? options: A)9 B)16 C)21 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 12/17=9/17.. 40 pints will require 9/17 * 40= 21 pints.. C #### C QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/84=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m. Answer: B. #### B QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:If P * Q implies (P2 + Q2), 8 * (3 * 2) = ? options: A)239 B)278 C)233 D)2697 E)771 SOLUTION:Explanation: We have, P * Q = (P2 + Q2) ......... Given 8 * (3 * 2) = ? 8 * 13 = (64 +169) = 233 ANSWER: C #### C QUESTION:Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made? options: A)500 B)1000 C)1500 D)2000 E)None of these SOLUTION:C.P. for one coconut = 150⁄100 = 3⁄2 S.P. for one coconut = 2 Profit on one coconut = 2 - 3⁄2 = 1⁄2 ∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000 Answer B #### B QUESTION:Find value of x from given equation 2x + 1 = -17 options: A)-8 B)-9 C)-7 D)7 E)6 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)85 B)91 C)97 D)103 E)110 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 7C4 = 35 The number of combinations with at least one paperback is 126-35 = 91 The answer is B. #### B QUESTION:If x and y are non-zero integers, and 36x^4 – 4y^4 = 6x^2 + 2y^2, which of the following could be the value of x2 in terms of y? options: A)2y^2+1/6 B)2y^2+1/8 C)2y^2+1 D)2y^2 E)2y SOLUTION:36x^4 – 4y^4 = 6x^2 + 2y^2 (6x^2 + 2y^2) (6x^2 - 2y^2) = 6x^2 + 2y^2 6x^2 - 2y^2 = 1 6x^2 = 2y^2+1 x^2 = 2y^2+1/6 Answer : A #### A QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)a^2 = (3/2)a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to bsqrt2 so, b sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)a^2 so, a^2 = (2/3)b^2 = (2/3)18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold? options: A)24 B)12 C)20 D)4 E)2 SOLUTION:The wording of the question is slightly misleading. When a question asks what is thefewestthatcouldhave been sold, it is suggesting that there could be many different quantities sold. In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold. To solve, we have 2 equations and 2 unknowns Let x = number of $3 Frisbees sold Let y = number of $4 Frisbees sold x + y = 60 3x + 4y = 200 x = 60 - y 3(60-y) + 4y = 200 180 - 3y + 4y = 200 y = 20 Answer: C #### C QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin? options: A)23% B)18.75% C)30% D)30.55% E)100% SOLUTION:Explanatory Answer Let the wages earned by Erica be $100 Then, wages earned by Robin and Charles will be $144 and $160 respectively. Charles earns $44 more than Robin who earns $144. Therefore, Charles' wage is 44/144100 = 30.55%. The correct choice is (D) #### D QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(5251)/(21)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(2625)/(21)=325, N(B)=4C2=(43)/(21)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely. options: A)15 sec B)11.6 sec C)31.6 sec D)12.6 sec E)23 sec SOLUTION:Explanation: D = 170 m + 170 m = 340 m RS = 55 + 50 = 105 * 5/18 = 146/5 T = 340 * 5/146 = 11.6 sec Answer: Option B #### B QUESTION:In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school? options: A)5:2 B)2:3 C)10:3 D)3:7 E)2:5 SOLUTION:10% of B = 1/3 G 10B/100 = G/3 B = 10G/3 B/G = 10/3 B:G = 10:3 Answer is C #### C QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed? options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr SOLUTION:Average speed = (24555)/(45+55) = 49.5km/hr Answer is B #### B QUESTION:What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad? options: A)814 B)266 C)287 D)999 E)661 SOLUTION:Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = Required number of tiles = = 814 Answer: A) 814 #### A QUESTION:If x and y are even integers, which of the following is an odd integer? options: A)x+y B)xy C)xy+2 D)x^2+y^2 E)None of these SOLUTION:even+even = even even * even = even even+even =even Answer : E #### E QUESTION:Rs.8000 become Rs.11256 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)6 YEARS B)7 C)5 D)3 E)4 SOLUTION:Explanation: 11256 = 8000(21/20)N (21/20)7 = (21/20)N => N = 7 Answer: Option B #### B QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:In a bag, there are 4 white, 1 brown and 5 red pens. One pen is picked up randomly. What is the probability that it is neither white nor red? options: A)1/5 B)1/10 C)1/2 D)1/3 E)1/4 SOLUTION:Explanation : Neither white nor red means the pen drawn is brown. Total number of outcomes = (4+1+5) = 10. Number of Favourable outcomes = 1 = Number of brown pens. Hence, Probability of the event = 1/10. Answer : B #### B QUESTION:Virat buys an old car for Rs. 40000 and spends Rs. 4000 on its repairs. If he sells the car for Rs. 60000, his gain percent is: options: A)3 (4/7) % B)11 (1/9) % C)12 (2/3) % D)12% E)36.36% SOLUTION:Explanation: C.P. = Rs. (40000 + 4000) = Rs. 44000 S.P. = Rs. 60000. Gain% = ( (16000 / 44000) * 100 ) % = 36.36% ANSWER E #### E QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: options: A)30 B)28 C)24 D)20 E)35 SOLUTION:Product of two nos = product of HCF and LCM Let one number = x => 25 * x = 5 * 150 x=5150/25=30 ANSWER A #### A QUESTION:In how many years will a sum of money doubles itself at 30% per annum on simple interest? options: A)7% B)3% C)5% D)8% E)2% SOLUTION:P = (P30R)/100 R = 3% Answer:B #### B QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:A shopkeeper cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 20% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)32% C)23.365% D)22.109% E)2% SOLUTION:Anyways, one can infer that he 'steals' 20% from suppliers and then charges 10% extra to customers So basically 1.2 * 1.1 = 1.32 Given that 1 is start point, we get 32% more Hence answer is B #### B QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:If k^3 is divisible by 120, what is the least possible value of integer k? options: A)15 B)30 C)60 D)90 E)120 SOLUTION:k^3 = 120x = 2^335x The factors of k must at minimum include 235 = 30. The answer is B. #### B QUESTION:117 x 217 + 83 x 83=? options: A)79698 B)20578 C)80698 D)81268 E)None of them SOLUTION:=(117)^2 + (83)^2 =(100+17)^2 + (100-17)^2 =2[(100)^2+(17)^2] =2[10000+289] =2 x 10289 = 20578 Answer is B #### B QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 828 / (28-20) = 28 Answer is B #### B QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings? options: A)Rs.3600 B)Rs.3629 C)Rs.3279 D)Rs.3629 E)Rs.3283 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 18000 => x = 3600 Savings = Income - expenditure = 5x - 4x = x So, savings =Rs.3600. Answer: A #### A QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 25 = 10. So, we need 10 to be in x! at least in power of 3. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:If A lends Rs.1200 to B at 10% per annum and B lends the same sum to C at 18% per annum then the gain of B in a period of 2 years is? options: A)190 B)188 C)192 D)145 E)188 SOLUTION:(120082)/100 => 192 Answer: C #### C QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)12 greater B)12 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/6 * 480 =80 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 80-68 =12>>> therfore answer is 28 fewer B #### B QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had: options: A)a profit of $5 B)a profit of $3 C)a loss of $3 D)a loss of $5 E)neither a profit nor a loss SOLUTION:The cost of the first stock was 36/1.2=30, so the profit from it is 6. The cost of the second stock was 36/0.8=45, so loss from it is 9. Overall the loss is $3. The answer is C. #### C QUESTION:Square A has an area of 121 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/25 B)1/5 C)16/121 D)105/121 E)6/25 SOLUTION:I guess it's mean that square B is placed within square Aentirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 121-16=105 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=105/121. Answer: D. #### D QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these SOLUTION:Explanation: Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 34 => 300+L = 15×34 = 510 => L = 510-300 = 210 meter Answer: Option C #### C QUESTION:A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done? options: A)572 B)672 C)472 D)372 E)None SOLUTION:Solution: 10C5: when both are not included. 10C4: when one of them is included. Number of ways = 10C5 +10C4+ 10C4 = 672 Answer: Option B #### B QUESTION:Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 15% and its breadth is decreased by 10%? options: A)3.5 percent increase B)9.5 percent increase C)1.5 percent increase D)3.9 percent increase E)3.5 percent increase SOLUTION:let L and B be 100 each 100 * 100 = 10000 L increase by 15% = 115 B decrease by 10% = 90 115 * 90 = 10350 3.5 percent increase ANSWER:E #### E QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 109876 # of 4 letter code words: nPr = 10! / (10 – 4)! = 10987 # of 5 words / # of 4 words = (109876)/(10987) = 6 = 6/1 Answer is E. #### E QUESTION:How many possible integer values are there for x if \|4x - 3\| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: \|4x-3\| < 6 let 4x=a therefore we have \|a-3\| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)21 B)24 C)88 D)99 E)26 SOLUTION:(1618)/12 = 24 Answer: B #### B QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:Rosy is 2 years elder than Mary. After 6 years the total of their ages will be 7 times of their current age. Then age of Rosy is : options: A)10 Years B)16 Years C)17 Years D)20 Years E)Data inadequate SOLUTION:E Given data are inadequate. #### E QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years? options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150 SOLUTION:P= $2000 R = 20% T = 2 years Machine value before 2 years = P/[(1-R/100)^T] =20005/4 * 5/4 =$3125 Answer is A #### A QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? options: A)3 B)4 C)2 D)9 E)12 SOLUTION:Rate of machine R =1/8 Rate of machine S =1/4 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/8 +x/4 =1/2 3x/8=1/2 x=8/6=1.3=2 So no of machine R is 2 Answer C #### C QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 8015010 cu.ft ,100% full = 60100101 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80150101/ 60 min= 2000 min E #### E QUESTION:we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight options: A)19 B)18 C)24 D)21 E)32 SOLUTION:select 5 weight out of 7, 7C5=21 ANSWER:D #### D QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (44)+(11)=17 MASS = 13+1+19+19=52 i.e (55)+(22)=29 DON = 4+14+15=33 i.e(33)+(33)=18 Hence (C) is correct Answer : C #### C QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice. options: A)25 B)34 C)50 D)67 E)100 SOLUTION:A =25 1 oz concentrate + 3 oz ofwater = 4 oz jucie 300 oz concentrate +900 oz of waer = 1200 oz juice no of cans==300/12=25 Ratio of juice to water ===> 1:3 total 2006 ounces 12 ounce juice cans ==> 1200/12 == 1001/4 (ratio of jiuce to total) == 25 #### A QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D <<<Examples ends QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper? options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075 SOLUTION:Cost of 8 kg apples= 70 × 8 = 560. Cost of 9 kg of mangoes = 70 × 9 = 630. Total cost he has to pay = 560 + 630 = 1190. D) #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value J? options: A)2r B)2s C)r +s D)2r-s E)2s-r SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES. We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value. IF.... R = 8 S = 2 Answer A: 2R = 2(8) = 16 Answer B: 2S = 2(2) = 4 Answer C: R+S = 8+2 = 10 Answer D: 2R-S = 2(8) - 2 = 14 Answer E: 2S-R = 2(2) - 8 = -4 Final Answer: A #### A QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product? options: A)12.5% B)13% C)13.15% D)14% E)15% SOLUTION:Quantity X Rate = Price 1 x 1 = 1 0.7 x 1.25 = 0.875 Decrease in price = (0.125/1) × 100 = 12.5% A) #### A QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %? options: A)30% B)40% C)50% D)56% E)78% SOLUTION:Gain=16 apples Total 56 apples CP 56-16=40 (16/40)100 =40% Ans B #### B QUESTION:A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement? options: A)150 B)450 C)400 D)600 E)300 SOLUTION:150 ---- 31 150 ---- 15 x -----5 x5 = 15015 x = 450 150 ------- 300 Answer: E #### E QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank? options: A)12 hrs B)14 hrs C)16 hrs D)18 hrs E)20 hrs SOLUTION:1/20 + 1/30 = 1/12 1 + 1/3 = 4/3 1 --- 12 4/3 --- ? 4/3 * 12 = 16 hrs C #### C QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A QUESTION:By selling 99 pens, a trader gains the cost of 11 pens. Find his gain percentage? options: A)11 1/3% B)11 7/3% C)11 1/8% D)11 1/3% E)11 1/9% SOLUTION:Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 11 pens = Rs. 11 Profit% = 11/99 * 100 = 11 1/9% Answer: E #### E QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 663373, so we need one 7 and one 3 to make it a square of a number. so 73= 21 Ans: B #### B QUESTION:A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished. options: A)10 days B)12 days C)14 days D)5 days E)6 days SOLUTION:Explanation: A & B completes the work in 1224/12+24 = 1224/36 = 8 days 2 days work = 2+1/8 = ¼ work Remaining work = 1-1/4 = ¾ A completes ¾ work in ¾16 = 12 days Answer: Option B #### B QUESTION:which of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d? options: A)0<d<1 B)0<d<5 C)0<d<7 D)1<d<5 E)1<d<7 SOLUTION:This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c . Thus, \|a-b\| < c < a+b \|b-c\| < a < b+c \|c-a\| < b < a+c Thus, if the sides of the triangle are 3,4 and d, 4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer. #### E QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? options: A)1:3 B)9:13 C)5:11 D)11:3 E)15:4 SOLUTION:The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7) = 11/7 : 3/7 = 11:3 Answer is D #### D QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days G will the work get over? options: A)60 B)70 C)G=75 D)G=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 10010=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:machine E finish the job in 212 shifts = 24 shifts machine B finish the job in 215 shifts = 30 shifts Lets assume total work require 120 shifts Therefore, rate of E = 5 shifts/day rate of B = 4 shifts/day rate of (E+B) = 9 shifts/day According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D #### D QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8 SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected) = = 2/5 B #### B QUESTION:When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x? options: A)-4 B)-2 C)5 D)13 E)22 SOLUTION:The equation that can be formed is: 3x-4=16-x or, 4x=20 or, x=5. Answer : C #### C QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 2) = 30 years. (A+B), now = (30+52)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8. Answer C #### C QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed against the current will be options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these SOLUTION:Explanation: Speed with current is 20, speed of the man + It is speed of the current Speed in sƟll water = 20 - 5 = 15 Now speed against the current will be speed of the man - speed of the current = 15 - 5 = 10 kmph Answer: B #### B QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? options: A)14 B)12 C)10 D)16 E)18 SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000, and it is given that length means no of factors. for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal. hence, lets start with smallest no 2. 2^1 =2 2^2 =4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512 2^10 =1024 (it exceeds 920, so, x can't be 2^10) so, max value that X can take is 2^9 , for which has length of integer is 9. now, since x =512 ,x+3y<920 so, 3y<408 ==> y<136 so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7 for 2^7 has length of integer is 7. SO, combined together : 9+7 = 16. D #### D QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 3001 = revenue (eq -1) if he reduced his price by 20% then , 240(customer) = 125/100revenue customer = 1.25300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? options: A)70 B)52 C)62 D)59 E)50 SOLUTION:total number of players= 16+12+18+13= 59 Answer is D #### D QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z? I. 9 II. 10 III. 11 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:Average gives us an idea that 3 nos. are close to 10. so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations. Let us see options. If 9 has to be median W. 1st term has to less than 9 or equal to 9. (also maintain z-x = 3) 9 9 12 --> satisfies all conditions so 9 can be a median value. If 11 has to be a median 3rd term has to be 11 or more than 11. (also maintain z-x = 3) 8 11 11 -->satisfies all conditions so 9 can be a median value. Now for 10 to be median. z+ x = 20 and z-x = 3, we wont have integer values of z. 10 cannot be a median E is the answer. #### E QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? options: A)4328 B)5382 C)6174 D)7690 E)8436 SOLUTION:The number of ways for the ships to go to the ports is 3! = 6. At Port A, the number of ways to choose two winners is 7C2 = 21. At Port B, the number of ways to choose one winner is 7. At Port C, the number of ways to choose one winner is 7. The total number of ways to give out gift certificates is 62177 = 6174 The answer is C. #### C QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days SOLUTION:A 6.4 days 1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300 So, all three together will complete the work in 300/47 = 6.4 days.- #### A QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is: options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these SOLUTION:Explanation: Let the thickness of the bottom be x cm. Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000 => 320 × 250 × (160 - x) = 8000 × 1000 => (160 - x) = 8000×1000/320= 100 => x = 60 cm = 6 dm. Answer: B #### B QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:If n ≠ 0, which of the following must be greater than n? I. 2n II. 2 - n III. n^2 options: A)I only B)II only C)I and II only D)II and III only E)None SOLUTION:n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only III =>answer is E #### E QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year? options: A)200 B)600 C)900 D)1600 E)2000 SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x. Let y be the number of female students this year. x/400 = 2(2x/y) y = 1600 The answer is D. #### D QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)45% C)32% D)40% E)28% SOLUTION:answer b male-employed - 64% female-employed-19% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 19/64 =28 E #### E QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)425 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence 3x + 5x = 680 Solve for x 8x = 680 x = 85 Number of boys 3x = 3 × 85 = 255 Number of girls 5x = 5 × 85 = 425 A #### A QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? options: A)299m B)287m C)279m D)100m E)277m SOLUTION:A can give B (5 min - 4 1/2 min) = 30 sec start. The distance covered by B in 5 min = 1000 m. Distance covered in 30 sec = (1000 30)/300 = 100 m. A can give B 100m start. Answer:D #### D QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate? options: A)12 Â½ years B)62 Â½ years C)18 Â½ years D)72 Â½ years E)12 Â½ years SOLUTION:100 ---- 200 ---- 5 200 ---- 5 100 ---- 2 1/2 ------------------ 900 ---- 18 Â½ years Answer:C #### C QUESTION:The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Let 2x be the number of spinsters. Then 7x is the number of cats. 7x-2x=40 x=8 and the number of spinsters is 2(8)=16. The answer is B. #### B QUESTION:The cost of raw material of a product increases by 30, the manufacturing cost increases by 20 and the selling price of the product increases by 60. The raw material and the manufacturing cost, originally, formed 40 and 60 of the total cost respectively. If the original profit was one-fourth the original manufacturing cost, find the approximation new profit percentage. options: A)48.38% B)54.68% C)62.48% D)42.36% E)None of these SOLUTION:Explanation : Let, the total initial cost of the product be Rs 100. Manufacturing cost = Rs 60 Raw materials cost = Rs 40 Also, original selling price => Rs100+(60/4)= Rs 115. New raw material cost =>Rs 40+30% of 40= Rs 52. New manufacturing cost =>Rs 60+20% of 60= Rs 72 New cost of the product = Rs124 New selling price =>115+60% of 115=Rs 184 New profit percentage =>60/124×100 =>48.38%. Answer : A #### A QUESTION:How many digits are in (8×10^10)(10×10^5)? options: A)17 B)25 C)26 D)27 E)28 SOLUTION:The question simplfies to (8×10^10)(10^6) => 810^16 => Will contain 16 zeros +1 digit 8 =>17 Ans A #### A QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)205 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 8 * 4) = 160. Therefore, 160 * 2.40 + x * 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER:B #### B QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 66 books, thus 76-68=7 books are NOT returned. {loaned out}0.30=7 --> {loaned out}=30. Answer: B. #### B QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = xx is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w? options: A)40 B)44 C)45 D)46 E)50 SOLUTION:Answer E = 50 We have (10^w)-74, where the sum of the digits is 440. 100-74 = 26, so we already have 2+6 = 8 from the 440. Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926. So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction. So we have 48 + 2 as an w = 50 #### E QUESTION:Tough and Tricky questions: Coordinate Geometry. Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L? options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices (A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need (B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong (C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong (D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong (E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong A #### A QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)y(y+3) B)y^2(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)y(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in six hours, what fraction of the room can Joseph paint in 20 minutes? options: A)1/6x B)x/(x-3) C)(x-6)/18x D)x/(x-6) E)(x-6)/x SOLUTION:Let J be Joseph's rate per hour. 1/x + J = 1/6 of a room per hour J = 1/6 - 1/x, of a room per hour In 20 minutes, Joseph can paint 1/3(1/6-1/x) = 1/18-1/3x = (x-6)/18x The answer is C. #### C QUESTION:A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)2/5 B)2/7 C)2/9 D)2/11 E)2/13 SOLUTION:Total number of ways to select 2 members = 10C2 = 45 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/45 = 2/9 The answer is C. #### C QUESTION:If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)? options: A)9. B)12. C)15. D)16 E)18. SOLUTION:Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW = 4 XZ + YW + 2XW + 2YZ [I rearranged the terms] = 3 + 2XW + 2YZ [replaced 4XZ + YW with 3] = 3 + 2(XW + YZ) factored out a 2 = 3 + 2(6) = 3 + 12 = 15 ANSWER:C #### C QUESTION:there is four light.all light glow in blue,white,yellow and red. all glow together and take different color.every time each light change its color in given four of the color.but at same time no two light have same color then tell how many design will form? options: A)20 B)24 C)18 D)16 E)22 SOLUTION:it is so simple,it is just permutation of 4 item. 4P4=4!=24 answer B #### B QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7. options: A)18 B)20 C)17.5 D)30 E)32 SOLUTION:Solution Average = (7+14+21+28)/4) = 70 / 4 = 17.5. Answer C #### C QUESTION:What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm? options: A)176 B)187 C)540 D)748 E)6 SOLUTION:The marbles used to tile the floor are square marbles. Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble. As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26. 3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm. The HCF of 339 and 226 = 113. Hence, the side of the square is 113. The number of such square marbles required, =339×226/113×113 =6 marbles Option(E) #### E QUESTION:If four coins are tossed, the probability of getting two heads and two tails is ? options: A)3/8 B)3/6 C)3/1 D)3/2 E)3/4 SOLUTION:Since four coins are tossed, sample space = 24 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = 6/24 = 3/8 Answer: A #### A QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ? options: A)10 hr B)50 C)20 D)250 E)260 SOLUTION:Explanation: 6C4 * 7C3 = 50 B #### B QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.61.2^3 = 1.0368 The answer is E. #### E QUESTION:Which of the following is NOT a prime number? options: A)21 B)31 C)41 D)11 E)51 SOLUTION:Ans is A A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number #### A QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? options: A)900 B)1000 C)1254 D)1795 E)1400 SOLUTION:Amount received by sanjay. 4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount So, the Amount received by sanjay is 1400. E #### E QUESTION:The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 75 terms of set X? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:754 + 7440 + 73400 = 300 + 2960 + 29200 = 32460 The hundreds digit is 4. The answer is C. #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (512/5)/100] P= 1500.Answer:A #### A QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers : options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer: B #### B QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 231 is 6. The answer is C. #### C QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)100 = (0.9)100 = 90%. A #### A QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 100 = 700 #### C QUESTION:From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 27 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning options: A)20 B)10 C)30 D)50 E)40 SOLUTION:Assume the number of boys at present = x Then, the number of girls at present = 5x Before the boys left, the number of boys were (x+27) and number of girls were 5x Hence, 2(5x) = x + 27 => 10x = x + 27 => x = 3 Number of girls in the beginning = (5x + 15) = (5×3 + 15) = 30 Answer is C. #### C QUESTION:A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? options: A)5,040 B)18,720 C)26,208 D)37,440 E)52,000 SOLUTION:4 character password: DLDD First digit can be chosen in 9 ways. The letter can be chosen in 26 ways. Next digit can be chosen in 8 ways. Next digit can be chosen in 7 ways. This gives us 92687ways Now, the letter can also be DDLD so there will be another 92687 ways Total = 926872 = 26,208 ways C #### C QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:How many pairs (w, w+1) have one or more prime factors common, where w is an integer and 2 ≤ w ≤9 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:w and w+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. Answer: A. #### A QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.9281.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:Worker A takes 12 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days SOLUTION:A's one hour work = 1/12. B's one hour work = 1/15. (A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20. Both A & B can finish the work in 20/3 days E #### E QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:The cost of 5kg of rice is equal to 17 kg of potatoes. Cost of 7 kg of rice is Rs.476. What will be the cost of 3 kg of rice and 5 kg of potatoes together? options: A)Rs.302 B)Rs.312 C)Rs.328 D)Rs.304 E)Rs.308 SOLUTION:Explanation: Price of 1 kg of rice = 476/7 = Rs.68. Price of 5 kg of rice = Rs.68 x 5 = Rs.340. Cost of 17 kg potatoes = Rs.340. :. Cost of 1 kg potato = Rs.340/17 = Rs.20. :. Cost of 3 kg rice + 5 kg potato = 3 x 68 + 5 x 20 = Rs.304. Answer: Option D #### D QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.24, find the sum of money? options: A)288 B)262 C)72 D)123 E)267 SOLUTION:A:B:C = 100:65:40 = 20:13:8 8 ---- 24 41 ---- ? => Rs.123 Answer: D #### D QUESTION:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)? options: A)72 B)180 C)70 D)90 E)140 SOLUTION:Length of side 1= 9+1=10 Length of side 2= 8+1= 9 Area of rectangle= 109= 90 D is the answer #### D QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)12 B)15 C)16 D)18 E)19 SOLUTION:one day work done by A=1/20 work done by A in 2 days=1/10 work done by A,B,C on 3rd day=1/10+1/10=1/5 1/5th of the work will be completed at the end of 3 days the remaining work =1-1/5=4/5 1/5 of work is completed in 3 days total work wiil be done in 35=15 days ANSWER:B #### B QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now? options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Q = P+10 Q-20 = 2(P-20) P-10 = 2P-40 P = 30 The answer is A. #### A QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10 SOLUTION:The total possible choices are 12C3 = 220 The ways to choose 3 apples: 6C3 = 20 The ways to choose 2 apples: 6C2 * 6C1 = 90 P(at least 2 apples) = 110/220 = 1/2 The answer is A. #### A QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:28=16.Answer is A. #### A QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 960/45 = 94/3 = 12 New time in minutes to cross 9 miles stretch = 960/35 = 912/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher? options: A)30 Years B)49 Years C)51 Years D)55 Years E)57 Years SOLUTION:Total age of students is 32X16 = 512 Years Total age inclusive of teacher = 33X (16+1) = 561 So, Teacher's age is 561-512 = 49 Yrs There is a shortcut for these type of problems Teacher's age is 16+(33X1) = 49 Years B) #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is options: A)276 B)299 C)312 D)322 E)None SOLUTION:Solution Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. Answer D #### D QUESTION:REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $15per set. They can sell the sets $40. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit? options: A)$2100 B)$2000 C)$2050 D)$2070 E)$2500 SOLUTION:Total Manufacturing cost = 10500+50015 = 18000 Total Selling cost = 50040= 20000 Profit = 20000-18000 = 2000 Answer : B #### B QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440 SOLUTION:Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 2640 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 1440. E is my answer. #### E QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 25001.5/1.4= 2478 Answer:- D #### D QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers total time taken = time taken by 1 worker 3. Time taken by 1 worker = 168 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7 total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 49 grams of protein daily, how many grams of food X are in the mixture? options: A)160 B)180 C)200 D)220 E)240 SOLUTION:Let x be the number of grams of food X in the mixture. 0.1x + 0.15(400-x) = 49 0.05x = 11 x = 220 The answer is D. #### D QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? options: A)32 : 48 B)32 : 42 C)32 : 45 D)32 : 41 E)42 : 45 SOLUTION:Explanation: A : B (80004)+(40008) : (90006)+(60006) 64000 : 90000 32 : 45 Answer:C #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:3! = 6 M L S C M S L C L M S C L S M C S M L C S L M C She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B. #### B QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 6c+3. The minimum is 3 when c=0. The maximum is 45 when c=7. There are 8 such numbers. The answer is D. #### D QUESTION:The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? options: A)20 years B)21 years C)22 years D)23 years E)24 years SOLUTION:Explanation: Let the average age of the whole team by x years. 11x â€“ (24 + 27) = 9(x -1) 11x â€“ 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B #### B QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges? options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2 SOLUTION:The cost of one orange=5/12=0.416 The cost of ten oranges= 0.416x10= $ 4.16 Answer: B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)20 D)21.1 E)23 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28 SOLUTION:Here capital is not the same. Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =( 200006 + 150006) Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ration = (300004 : 500004) Suresh : Kiran = ( 200006 + 150006) : (300004 : 500004) = (206 + 156) : (304 + 504) = (203 + 153) : (302 : 502) = 105:160 = 21:32 Answer is C #### C QUESTION:I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. My friend lost Rs 4 more than me in the second race. Then what is the amount lost by my friend in the second race? options: A)Rs 41 B)Rs 40 C)Rs 31 D)Rs 51 E)Rs 81 SOLUTION:I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. so I lost Rs 31 in first race and Rs 37 in 2nd race. My friend lost Rs 4 more than me in the second race. My friend lost 37+4= Rs 41 in the second race. ANSWER:A #### A QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered: 2 skeins at $2.50 per skein (not discountable) 8 skeins at $8.40 per skein (discountable) 7 skeins at $5.99 per skein (discountable) Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn? options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64 SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.) 7 x $5.99 = $41.93 $67.20 + $41.93 = $109.13 discountable $109.13 x .10 = $10.91 (rounded) $109.13 - $10.91 = $98.22 for discounted yarn 2 x $2.50 = $5.00 for un-discounted $98.22 + $5.00 = $103.22 cost of yarn $103.22 x 1.13 = $116.64 with tax and shipping (5% + 8% = 13%) correct answer A #### A QUESTION:A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent? options: A)18 1/9 % B)18 9/3 % C)18 1/3 % D)14 2/7 % E)18 7/3 % SOLUTION:C.P. of 1 kg = 595/85 = Rs. 7 S.P. of 1 kg = Rs. 8 Gain % = 1/7 * 100 = 100/7 = 14 2/7 % Answer: D #### D QUESTION:A cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is? options: A)24 B)48 C)64 D)2744 E)100 SOLUTION:Volume = 343 = side^3 i.e. Side of Cube = 7 New Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube Volume = 141414 = 2744 square feet Answer: option D #### D QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)20 B)18 C)12 D)14 E)15 SOLUTION:A's 2 day's work = 1/20 x 2 = 1/10 (A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 1/10 Work done in 3 days = A's 2 day's work + (A + B + C)'s 1 day's work Work done in 3 days = 1/10 + 1/10 Now, work is done in 3 days = 2/10 = 1/5 So, 1/5 cork is done in 3 days. So, work will be done in (3 x 5) = 15 days. So, correct answer is E #### E QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5) Answer - C #### C QUESTION:1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now? options: A)76 days B)98 days C)32 days D)45 days E)24 days SOLUTION:1600 ---- 28 days 1600 ---- 24 1200 ---- ? 160024 = 1200x x = 32 days Answer: C #### C <<<Examples ends QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000 SOLUTION:3 children got = 315% = 45% wife got = 30% orphan house = 5% total = 45+30+5 = 80% remaining = 100-80 = 20% 20% = 40000 100% = 40000100/20 = $200000 Answer is B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses? options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4 SOLUTION:The ratio of beige:white:brown = 3:6:2 The answer is C. #### C QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)45 B)20 C)25 D)27 E)22 SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5 = 100/5 = 20. Answer:B #### B QUESTION:Sum of 53 odd numbers is? options: A)2709 B)2809 C)2909 D)3009 E)3109 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 53 odd numbers = 53^2 = 2809 ANSWER:B #### B QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:A certain ski shop sells pairs of gloves in 11 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color? options: A)1/144 B)1/143 C)1/21 D)1/23 E)1/12 SOLUTION:there are 11 different colours sothere are 11 pairs of gloves dropped.. first can be any of 22..so 22/22.. second has to be its pair, which will be just one out of remaining 21.. 1/21.. overall prob=22/221/21= 1/21.. C #### C QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)4 Km C)4 1/5 Km D)3 2/5 Km E)3 3/5 Km SOLUTION:Formula = S1S2/S2-S1 * T1+T2/60 = 46/2 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:In a coconut grove, (x + 3) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 3) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. options: A)3 B)4 C)5 D)6 E)None of the above SOLUTION:(x+3)×60+x×120+(x−3)×180/(x+3)+x+(x−3)=100 ⇒ 360x−360/3x = 100 ⇒ 60x = 360 ⇒ x = 6 Answer D #### D QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm? options: A)45% B)48% C)50% D)58% E)65% SOLUTION:When the storm deposited 120 billion gallons, volume of water in the reservoir = 200 + 120 = 320 billion gallons If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 320/0.8 = 400 billion gallons Therefore percentage of reservoir that was full before the storm = (200/400)100 = 50% Option C #### C QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm. options: A)227 B)299 C)300 D)161 E)212 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) (perpendicular distance between them) = 1/2 (22 + 18) * (15) = 300 cm2 Answer: C #### C QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. options: A)456 B)234 C)285 D)342 E)213 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: Option C #### C QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight? options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb SOLUTION:Sol. 66÷6 = 11. Answer : B #### B QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10? options: A)5 B)7 C)4 D)9 E)3 SOLUTION:30,40,50,60,70 total 5 Answer is A #### A QUESTION:Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. If he now has an equal amount of money in each pocket, then how much money did he originally have in his left pocket? options: A)$120 B)$130 C)$140 D)$150 E)$160 SOLUTION:Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120 in his left pocket (and $80 in his right pocket) before moving $20 from his left to his right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120). correct answer E #### E QUESTION:Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range? options: A)3 B)4 C)cannot be determined D)6 E)8 SOLUTION:Yes, the correct answer is C #### C QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide. Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E QUESTION:How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same? options: A)1236 B)504 C)4096 D)4608 E)6561 SOLUTION:First digit.. 9 posibilities Second digit, 8 possibilities third digit, 7 possibilities 987 = 504. B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)240 B)377 C)2908 D)287 E)201 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A #### A QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is options: A)60 B)75 C)90 D)105 E)120 SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 9 = 135 sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75 Answer: B #### B QUESTION:(1+0.0001)/(0.04+10000) The value of the expression above is closet to which of the following? options: A)0.0001 B)0.001 C)0.1 D)1 E)10 SOLUTION:Notice that we need approximate value of the fraction. Now, the nominator is very close to 1 and the denominator is very close to 10, hence the value of the fraction is very close to 1/10000=0.0001. Answer: A #### A QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 101215/20 = 2420x/32 X=4 Answer: Option A #### A QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr. SOLUTION:Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=24 or x=12. Rate upstream=12 km/hr,rate downstream=36 km/hr. Hence,rate of stream=1/2(36-12)km/hr=12 km/hr. Answer is B. #### B QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/63/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings? options: A)12 B)13 C)46 D)37 E)26 SOLUTION:16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D #### D QUESTION:Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price? options: A)(YP)/100X B)100X/(YP) C)(YP)+100X D)(YP)-100X E)(YP)100X SOLUTION:Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P 100 = 100X/(YP) Answer : B #### B QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:If n = 20! + 19, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:19 divides 20! so 19 also divides 20! + 19. 15 and 17 divide 20! so they do not divide 20! + 19. The answer is C. #### C QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9 SOLUTION:Original share of 1 person =1/6 New share of 1 person =1/5 Increase =1/5 - 1/6 =1/30 Required fraction = (1/30)/(1/6)=1/5 Answer is D. #### D QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:Reeya obtained 40, 60, 70, 80 and 80 out of 100 in different subjects, What will be the average options: A)66 B)75 C)80 D)85 E)90 SOLUTION:Explanation: (40+60+70+80+80 / 5)=66 Option A #### A QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area? options: A)26% B)21% C)15% D)18% E)12% SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification) New h = 220a / 100 = 22a / 10 New b =(110a x 100) ==11a/10 New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100) increased area== (121a²/100) - a² Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21% answer :B #### B QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: options: A)130 B)360 C)500 D)540 E)580 SOLUTION:L = 800 m S = 78kmph = 65/3 mps Time to pass tunnel = 1min = 60 sec t.f (800+X)/(60) = (65/3) =500 ANSWER:C #### C QUESTION:A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? options: A)2880. B)4860. C)5780 D)4320 E)6380. SOLUTION:Normal Day = 600 kw/h Stormy Day = 6001.2=720 kw/h 3 windmills for 2 hours on stormy day 72032=4320 Answer: D #### D QUESTION:A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days? options: A)7 B)6 C)5 D)8 E)9 SOLUTION:Let the total units of work be 48. Units of work completed by A and B in one day = 6. Units of work completed by B and C in one day = 4 Units of work completed by A, B, and C in one day = 8. From the above information we get the work completed by A and C in one day is 6 units. Therefore, the number of days taken by A and C to complete the whole work = 48/6 = 8 days. ANSWER:D #### D QUESTION:A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase? options: A)25% B)44% C)38% D)9% E)90% SOLUTION:Let the annual bonus be X. A corporation triples its annual bonus. So new bonus = 10X. Increase = 10X-X =9X The increase is what percent of the employees’ new bonus = (9X/10X)100 = 90% Hence E. #### E QUESTION:How many digits are required to number a book containing 260 pages? options: A)784 B)672 C)492 D)372 E)300 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 902=180 digits. 260-(90+9)=161 pages will require 1613=483 digits. The total number of digits is 9+180+483=672. The answer is B. #### B QUESTION:A man buys 1kg of sandalwood and 1kg of teakwood. He sells one for 10% profit and other for 10% loss. What is total profit/loss percentage? options: A)1% loss B)2% loss C)3% loss D)4% loss E)5% loss SOLUTION:if x is both the profit and loss % then it must be loss of x^2/100; so 1010/100=1; 1% loss ANSWER:A #### A QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have. p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24. Answer: D. #### D QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ? options: A)240 B)140 C)230 D)130 E)105 SOLUTION:Let the number be x. Then, 4x/5 â€“(60% of x) = 21 4x/5 â€“ 60x/100 = 21 x = 105. Answer E. #### E QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.42^10=0.41024=409.6 The answer is C. #### C QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Minimuum should be 1 Maximum should be 4: 1 out of a or b to make the multiplication negative 3 out of c, d, e or f to make the multiplication negative. Negative+Negative<0 Answer:C maximum will be 5.. you dont require both the multiplicatin to be negative for entire equation to be negative... any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers... actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation.. ans D #### D QUESTION:Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ? options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9 SOLUTION:Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)(4/5) = ? 47/75 or (D) #### D QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))? options: A)1 B)16 C)81 D)256 E)144 SOLUTION:f(x)=x^2 f(f(x)) = (x^2)^2 =x^4 A. 1 , x=1 B. 16 , x=2 C. 81 , x=3 E. 144 f(x)=12 Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) . D. 256 , x=4 Answer E #### E QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 25=55 35=57 GCF = 5 P.S you can make squares with side of 5 Answer : A #### A QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m? options: A)29798 B)27908 C)24000 D)25000 E)27991 SOLUTION:24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x 24 = 1/100 * x => x = 24000 Answer: C #### C QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)? options: A)50.5 B)88.5 C)37.5 D)55.5 E)23.5 SOLUTION:The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s In 27 seconds, the relative difference in distance traveled is 27 * 25/9 = 75 meters This distance is twice the length of each train. The length of each train is 75/2 = 37.5 meters The answer is C. #### C QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7? options: A)35 B)16 C)17 D)can’t be determined E)None of these SOLUTION:Answer C Solution In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is (770-210/35)+ 1 = 17 Hence option C #### C QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(248$ / 7children) = 35.42 Took the lowest number = 35 * 7 children = $245 $248 - $245 = staying $3 Correct option: C) 3$ #### C QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. âˆ´ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 70 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/8,100 C)7/48,000 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 70/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=70/8001/600=7/48,000. Answer: C. #### C QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 245= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 245 + 2y =124 then y=2 244 + 2y = 124 then y=14 243 +2y = 124 then y= 26 242 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)54 m B)64 m C)74 m D)84 m E)94 m SOLUTION:Let breadth = x metres. Then, length = (x + 28) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 28) + x] = 200 2x + 28 = 100 2x = 72 x = 36. Hence, length = x + 28 = 64 m B #### B QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 560/60 = 51/1 = 5 New time in minutes to cross 5 miles stretch = 560/40 = 53/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work? options: A)20days B)15days C)30days D)45days E)50days SOLUTION:10days work of A = 10/40 = 1/4 remaining work = 1-1/4 = 3/4 B can finish 3/4 work = 603/4 = 45days Answer is D #### D QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2(0.1)^3(0.9)^2 1 Tail and 4 Heads, Probability = 5C1(0.1)^4(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years? options: A)14000 B)14400 C)14500 D)15625 E)14700 SOLUTION:Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D #### D QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)58 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec ANSWER:A #### A QUESTION:The equation of line s is y = 4/3x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.510075=0.5125* x => x=60; SO answer is 60=C #### C QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)6 B)7 C)8 D)4 E)2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1 When B starts: No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1 Solving the above two equations for xy x = 1/8 y = 1/8 → Total work done by AB in a day = 1/8 + 1/8 = 1/4 → No. of days to complete the work when both work together = 4 Answer: D #### D QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 * 75 = 20.93 ANSWER:D #### D QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: options: A)12 B)24 C)34 D)48 E)54 SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.Answer: Option D #### D QUESTION:Two trains 200 m and 800 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? options: A)10.6 B)10.9 C)36 D)10.8 E)10.1 SOLUTION:Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 200 + 800 = 1000 m. Required time = 1000 * 9/250 = 36 sec. Answer: C #### C QUESTION:One-third of 600 is what percent of 120 ? options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6 SOLUTION:Answer Let one-third of 600 is N% of 120. ∵ 600/3 = (N x 120)/100 ∴ N = (200x 100) / 120 = 166.6 Correct Option: E #### E QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:A sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:w:x:y = 100:30:20 20:6:4 20 --- 10 30 --- ? => 15 Answer:D #### D QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(69006)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:The total number of books the students borrowed is 202=40. The students who borrowed zero, one, or two books borrowed 81+32=14 books. The 7 students who borrowed at least three books borrowed 40-14=26 books. If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books. The answer is A. #### A QUESTION:The number 0.8 is how much greater than 1/2 ? options: A)½ B)3/10 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .8-1/2=x 8/10-1/2=x x= 3/10 ans B #### B QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/21/5+x/21/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank? options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is options: A)Rs.1820 B)Rs.1040 C)Rs.1120 D)Rs.1680 E)None of these SOLUTION:Explanation: Let the sum of money be x then (x × 4 × 8)/100 = (560 × 12 × 8)/100 x × 4 × 8 = 560 × 12 × 8 x × 4 = 560 × 12x = 560 × 3 = 1680 Answer: Option D #### D QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24144)= 30. Answer is C. #### C QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet) options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy) SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 6. The price per square yard is 27 / (xy/6) = 162/(xy). The answer is E. #### E QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:How many 0's are there in the binary form of 61024 + 464 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:61024 + 464 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)7 C)9 D)11 E)15 SOLUTION:223 + 43 = 266/17 = 11 (Remainder) D #### D QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 10 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? options: A)$506.00 B)$726.24 C)$900.00 D)$920.24 E)$926.24 SOLUTION:If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away. Interest earned after the first time interval: $10,0002%=$200; Interest earned after the second time interval: ($10,000+$200)3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$726.24. Answer: B. #### B QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1400 B)1500 C)1600 D)1200 E)None of these SOLUTION:Explanation : Assume that the total profit is x. Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2 => A's profit = (95x/100) * (3/5) = 855 => 95x/100 = 8555/3 = 2855 = 1425 => x = 1425 * 100/95 = 285 * 100/19 = 1500 Hence the total profit = 1500. Answer : Option B #### B QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1x5)/100 + (1600-x)6/100 = 16005.67/100 Simplifying we get x= 528 B #### B QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:The area of a triangle is with base 4m and height 5m? options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2 SOLUTION:1/2 * 4 * 5 = 10 m2 Answer:B #### B QUESTION:If y = \|\|x – 3\| – 2\|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = \|\|x – 3\| – 2\| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:Two trains are moving in the same direction at 126 kmph and 54 kmph. The faster train crosses a man in the slower train in 14 seconds. Find the length of the faster train? options: A)280 B)290 C)300 D)310 E)320 SOLUTION:Relative speed = (126 - 54) * 5/18 = 4 * 5 = 20 mps. Distance covered in 27 sec = 14 * 20 = 280 m. The length of the faster train = 280 m. Answer:A #### A QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:Two trains 300 m and 450 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? options: A)10.6 B)27 C)10.4 D)10.8 E)10.1 SOLUTION:Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 300 + 450 = 750 m. Required time = 700 * 9/250 = 27 sec. Answer: B #### B QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D #### D QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:What is the area of a square field whose diagonal of length 12 m? options: A)288 B)72 C)200 D)112 E)178 SOLUTION:d2/2 = (12 * 12)/2 = 72 Answer: B #### B QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^ba^c=a^(b+c). Answer: C #### C QUESTION:A is the average (arithmetic mean) of the first 7 positive multiples of 4 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:If A^2 - B^2 = 0, then let's assume that A = B. A must equal the 4th positive multiple of 4, thus A = 16, which also equals B. B is the second positive multiple of n, thus n = 16/2 = 8. The answer is D. #### D QUESTION:The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? options: A)20 years B)21 years C)22 years D)23 years E)24 years SOLUTION:Explanation: Let the average age of the whole team by x years. 11x â€“ (24 + 27) = 9(x -1) 11x â€“ 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B #### B QUESTION:A boat crossed a lake from East to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:One way of solving this is: Speed of boat on still water (lake)=5kmph Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph =>Speed downstream = speed in still water + speed of river = 5+1 =6kmph Ans is C #### C QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 9 women? options: A)A)144 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C39C2 = 4*36 = 144 Answer is A #### A QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is: options: A)28 B)30 C)40 D)50 E)72 SOLUTION:Let the numbers be 1x and 2x. Then, their L.C.M = 2x. So, 2x = 48 or x = 24. The numbers are 24 and 48. Hence, required sum = (24 + 48) = 72. ANSWER:E #### E QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed Ã— time =9Ã—4=36 metre i.e., A beat B by 36 metre Answer is E #### E <<<Examples ends QUESTION:Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology? options: A)30 B)90 C)120 D)168 E)188 SOLUTION:I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168 Using your analysis: We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232 So, in the image we know that the number of students in the zone with the black boundary = 232 Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize) And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w Since the total number of students = 400, we can write: 232 +b+w= 400 Or,b+w= 400 - 232 = 168 That is,b= 168 -w So, the maximum value ofbwill happen forw= 0 This is how we get, the maximum value ofb= 168 D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be options: A)21 B)5193 C)77 D)9275 E)19 SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!. So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!. So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320) So remainder is 5193. Answer:B #### B QUESTION:A ball is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.480/- B)Rs.490/- C)Rs.500/- D)Rs.520/- E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? options: A)2200 B)2550 C)5050 D)6275 E)11325 SOLUTION:Set A contains 8, 10, 12... 50 Set B contains 108 , 110 , 112 ... 150 Number of terms in each set = 22 Difference between corresponding terms in set A and B = 100 Difference between Sum of set B and set A = 10022 = 2200 Answer A #### A QUESTION:A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? options: A)200 minutes B)240 minutes C)220 minutes D)210 minutes E)77 minutes SOLUTION:Time taken to reach = 6400/32= 200 minutes ANSWER:A #### A QUESTION:A company spends an average of $500 for its 20 employees's salaries and an average of $100 for its 5 drivers' salaries. What is the average expenditure of the company? options: A)$360 B)$290 C)$420 D)$600 E)$240 SOLUTION:Number of employees is 20 Their average salary is $500 Number of drivers is 5 Their average salary is $100 Total salary of the employees is 20500=$10,000 Total salary of the drivers is 5100=$500 Total expenditure for company is 10,000+500=$10,500 Average expenditure is 10,500/20+5=$420 Answer is C #### C QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:Find a sum for first 12 prime no's from number series? options: A)190 B)178 C)197 D)189 E)100 SOLUTION:Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197 Note: 1 is not a prime number Option C #### C QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct? options: A)A > 4. B)0 < A <4. C)-4 < A < 0. D)A < -4. E)A < -20. SOLUTION:B is +veC is -ve Eliminate AB For min. value max. numerator and minimize dinominator take B=4.1A=-0.9 A=4.1/-0.9 A<-4 Ans D #### D QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3. options: A)131 B)197 C)207 D)219 E)227 SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3. Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131. ANSWER:A #### A QUESTION:In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr? options: A)3.5 B)2.7 C)2.9 D)2.3 E)2.1 SOLUTION:Speed = 130 * 5/18 = 36 m/sec Time taken = 125/36 = 3.5 sec. Answer: A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? options: A)28% B)25% C)11.11% D)28% E)55% SOLUTION:900 --- 100 100 --- ? => 11.11% Answer: C #### C QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is options: A)862 B)864 C)866 D)868 E)None of these SOLUTION:Solution P.W = Rs.(4320 - 720) = Rs. 3600 S.I on Rs. 4320 =Rs.(720/3600 x 4320) = Rs. 864. Answer B #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)45 B)20 C)25 D)27 E)22 SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5 = 100/5 = 20. Answer:B #### B QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these SOLUTION:Explanation: Error = (25.5 - 25.461) = 0.039 Required percentage = 0.039/ 25.461Ã—100=0.153 Option B #### B QUESTION:The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. options: A)47.55 kg B)48 kg C)48.55 kg D)49.25 kg E)59.25 kg SOLUTION:1650.25+845.15/24=48.55 ANSWER:C #### C QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)(25/100)x = 18; => x=480; Ans is (C). #### C QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 1000(1 + 2/100)^4 = 1000 51/50 * 51/50 * 51/50 * 51/50 = $1082.43 C.I. = 1082.43-1000 = $82.43 Answer is B #### B QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 1334 = 156 Answer: E #### E QUESTION:Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? options: A)4hrs B)6hrs C)8hrs D)10hrs E)16hrs SOLUTION:machine A will do 6/8 in 6 hrs, so A does 3/4 of the work .. Therefore, B will do the remaining 1/4 th work alone.. As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job... ans 8 C #### C QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:Some of the 68% solution of acid was removed and this was replaced with an equal amount of 11% solution of acid. As a result, a 35% solution of acid was obtained. What fraction of the original solution was replaced? options: A)7/11 B)7/17 C)8/17 D)8/19 E)11/19 SOLUTION:Let x be the fraction of the original solution that was replaced. 0.68(1-x)+0.11(x)=0.35 0.57x=0.33 x=33/57=11/19 The answer is E. #### E QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item? options: A)17% B)21% C)24% D)29% E)42% SOLUTION:The price decreased by 23.99 - 16.99 = $7. $7 is a bit more than 29% of original price of $24. Answer: D. #### D QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)21:22 B)7:8 C)2:1 D)21:24 E)14:16 SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). = (120/100) 7x and (110/100) 8x = 42x/5 and 44x/5 Therefore, The required ratio = (42x/5):(44x/5) = 21 : 22. Answer is A. #### A QUESTION:If the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)7 E)18 SOLUTION:Let length of rectangle = L 5^2 = L4 => L = 25/4 = 7 Answer D #### D QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:Find the odd man out. 12, 24, 36, 48, 61, 72, 84 options: A)15 B)25 C)61 D)90 E)115 SOLUTION:Explanation : All except 61 are multiples of 7 Answer : Option C #### C QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest? options: A)The average (arithmetic mean) of set S B)The median of set S C)The mode of set S D)The range of set S E)The standard deviation of set S SOLUTION:A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107. B) The list is of 7 numbers and median is 105. C) Mode is number of repetition of a number in the list , here it is 100. D) Range = Max value - min value = 124 -99 = 25. E) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100 IMO option A is correct answer.. #### A QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.151.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar? options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9) SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg Actual price of sugar = 10100/((100-10 )4) = Rs. 2(7/9) B #### B QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream? options: A)5 kmph B)67 kmph C)22 kmph D)88 kmph E)12 kmph SOLUTION:Speed of the boat in still water = (60+70)/2 = 65 kmph. Speed of the stream = (70-60)/2 = 5 kmph. Answer:A #### A QUESTION:Which of the following describes all values of x for which 4–x^2 >= 0? options: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –2 <= x <= 2 SOLUTION:4 - x^2 >=0 means x^2 - 4 <=0 => (x-2)(x+2) <= 0 => -2 <= x <= 2 Answer - E #### E QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)1687 B)1478 C)1480 D)14000 E)1500 SOLUTION:2512: 3012: 358 15:18:14 14/47 47000 = 14000 Answer: D #### D QUESTION:If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be . options: A)90 seconds B)70 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 1 mint 1/3 filled in 1/2 mint thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec ANSWER:A #### A QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =2516=400 Answer: E #### E QUESTION:In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores B earned to the total amount store A earned? options: A)3:1 B)2:3. C)1:3. D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 40x X:4X Price : 4y:3y Total revenue 4xy : 12xy 3:1 Answer : A #### A QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed? options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph SOLUTION:424/(13/2) = 4242/13 =65.2 kmph ANSWER:C #### C QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)4:5 B)3:5 C)6:8 D)3:5 E)5:4 SOLUTION:third number be x. first no = 120% of x = 6x/5 second no = 150% of x = 3x/2 ratio in first two nos = (6x/5:3x/2)=> 4:5 ANSWER A #### A QUESTION:A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in? options: A)days B)days C)days D)1/2 days E)days SOLUTION:Explanation: 10/40 + 10/30 + 10/x = 1 x = 24 days Answer: A #### A QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? options: A)4 B)9 C)39 D)48 E)63 SOLUTION:Given: z=s^2+2s for 0≤s≤7 z(4) = 4^2 + 24 = 24 z(7) = 7^2 + 27 = 63 Therefore z(7) - z(3) = 63 - 24 = 39 km/hr Option C #### C QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7% SOLUTION:Explanation: SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively? options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18 SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10. Given (x + 4) + (x + 10) = 30 => 2x + 14 = 30 => x = 8 The third number = x + 4 = 8 + 4 = 12. The sixth number = x + 10 = 8 + 10 = 18. Answer: E #### E QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white? options: A)3/4 B)4/5 C)7/8 D)1 E)None of these SOLUTION:Explanation: Total cases = 6 + 24 = 30 Favourable cases = 24 So probability = 24/30 = 4/5 Answer: A #### A QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo? options: A)10 B)12 C)15 D)20 E)30 SOLUTION:Two students can be selected from 6 in 6C2 =15 ways. Therefore, the teacher goes to the zoo 15 times. Option C is answer #### C QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:26=12.Answer is B. #### B QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week? options: A)25% B)30% C)35% D)40% E)45% SOLUTION:E for me. Let managers comminsion rate be M. m5000+ 20.055000=2750 5000m=2250 m=45/100=45% #### E QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? options: A)7.16 B)7.59 C)7.12 D)7.15 E)7.11 SOLUTION:T = (141 + 165)/ (80 + 65) 18/5 T = 7.59 Answer: B #### B QUESTION:Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank? options: A)10 min. 20 sec. B)11 min. 45 sec. C)12 min. 30 sec. D)14 min. 40 sec. E)15 min. 40 sec. SOLUTION:Take LCM of 15 and 20 and get the total capacity of tank as 60 . Then A will fill 4li in 1 min and B will fill 3 li in 1 min so total will be 7 . A left after 4 min so they worked together for 4 min so 74= 28 . now subtract it from 60.(60-38=32). This will be filled by b so time taken would be..10 min 20 sec. ANSWER:A #### A QUESTION:Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? options: A)Rs.21.60 B)Rs.21.68 C)Rs.21.18 D)Rs.21.98 E)Rs.21.29 SOLUTION:Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000 He lend the same amount for C.I at 6% p.a. for two years. => Siddharth's income = C.I - S.I = p[1 + r/ 100]n - p - pnr/100 = p{ [1 + r/ 100]2 - 1 - nr/100 = 6,000{ [1 + 6/100]2 - 1 - 12/100} = 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12) = 6,000 (0.0036) = 6 3.6 = Rs.21.60 Answer: A #### A QUESTION:In a class of 50 students, 20 play SNOOKER, 15 play Cricket and 11 play Football. 7 play both SNOOKER and Cricket, 4 play Cricket and Football and 5 play SNOOKER and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? options: A)10 B)12 C)34 D)45 E)566 SOLUTION:Notice that7 play both SNOOKER and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and SNOOKER/Football. [color=#ffff00]{Total}={SNOOKER}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more check ADVANCED OVERLAPPING SETS PROBLEMS [/color] 50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2; Those who play ONLY SNOOKER and Cricket are 7-2=5; Those who play ONLY Cricket and Football are 4-2=2; Those who play ONLY SNOOKER and Football are 5-2=3; Hence, 5+2+3=10 students play exactly two of these sports. Answer: A. #### A QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 11 = (5,6)(6,5)= 2 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 11 in any attempt =2/36=1/18 Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18 Probability of losing game =(17/18)(17/18)(17/18)=139/165 I.e. Probability of wining game = 1-(139/165) =26/165 Answer : Option C #### C QUESTION:Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? options: A)7cdx/100 B)d + 7cx/100 C)7d + xc/100 D)7d + 7xc/100 E)7cdx SOLUTION:Answer is D. #### D QUESTION:A line has a slope of 3/4 and intersects the point (-12, -39). At which point E does this line intersect the x-axis? options: A)(40,0) B)(30,0) C)(0,40) D)(40,30) E)(0,30) SOLUTION:Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept. You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above. Thus you get -39=m(-12)+c , with m=3/4 as the slope is given to be 3/4. After substituting the above values, you get c = -30. Thus the equation of the line is y=0.75x-30 and the point where it will intersect the x-axis will be with y coordinate = 0. Put y=0 in the above equation of the line and you will get, x=40. Thus, the point E of intersection is (40,0). A is the correct answer. #### A QUESTION:A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work? options: A)12/15 B)37 1/2 C)3/7 D)4/9 E)5/2 SOLUTION:Explanation : Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 ½ days ANSWER:B #### B QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/85/74/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts. options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22 SOLUTION:Solution : Given SI1 = SI 2 P1 : P2 = 1/R1T1 : 1/R2T2 = 1/(105) : 1/(9:6) 27:25 B #### B QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 636.5 = 219 Total price of 4 cans = 430 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 236.5 + 46.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)100=10% Answer:A #### A QUESTION:What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ? options: A)4722 B)4725 C)4728 D)4731 E)4733 SOLUTION:Here smallest number means LCM Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7 = 4725 Therefore required number is 4725 - 3 =4722 Ans - A #### A QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:Which is the following is divisible by 11 options: A)A)4305 B)B)4825 C)C)1635 D)D)4805 E)E)4906 SOLUTION:Explanation: Sum of first 'n' natural numbers = n(n + 1)/2 Sum of first 9 natural numbers = 5(5 + 1)//2 = 5 x 3 = 15 Sum of first 99 natural numbers = 55(55 + 1)//2 = 55 x 30 = 1650 1650 - 15 = 1635 Answer: Option C #### C QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6 SOLUTION:Explanation: Milk = 3/5 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1. ANSWER IS A #### A QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is: options: A)28 B)30 C)40 D)50 E)72 SOLUTION:Let the numbers be 1x and 2x. Then, their L.C.M = 2x. So, 2x = 48 or x = 24. The numbers are 24 and 48. Hence, required sum = (24 + 48) = 72. ANSWER:E #### E QUESTION:Of the 800 employees of Company X, 90 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ? options: A)200 B)160 C)112 D)80 E)600 SOLUTION:The # oflong-termemployees is 90%800=720. After y of them retire new # oflong-termemployees would become 720-y. Total # of employees would become 800-y. We want 720-y to be 60% of 800-y --> 720-y=(800 -y)60% --> y = 600. Answer: E. #### E QUESTION:The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9/4∗π B)18−9/2∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =18- pi18/4 =18- pi9/2 ANSWER:B #### B QUESTION:Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration 10 + 7b =560 7b = 290 b= 41 The total number of iterations --> 41+1 = 42 and 43rd iteration will be completed at 304seconds which is above 5 minutes ANSWER: B #### B QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A? options: A)29491 B)28491 C)39491 D)49491 E)59491 SOLUTION:Compound ratio of A:B:C A:B = 3:4 B:C = 5:6 ---------- A:B:C = 15:20:24 We can divide Rs.116000 in this ratio. Share of A = 15/59 116000 = 29491 ANSWER:A #### A QUESTION:A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge? options: A)$40,000 B)$45,000 C)$50,000 D)$55,000 E)$60,000 SOLUTION:The customer receives $75 for the first $5000. The customer receives $125 for the next $5000. Let x be the total amount of the customer's annual charge. $200 + 0.03(x-10,000)=0.028x 0.002x=100 x=50,000 The answer is C. #### C QUESTION:Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? options: A)670 B)710 C)750 D)790 E)830 SOLUTION:total pay = 40$12.50 + $0.16x = 620 x = 120 / 0.16 = 750 The answer is C. #### C QUESTION:Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is? options: A)10 B)12 C)19 D)18 E)20 SOLUTION:SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19 C #### C QUESTION:An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 x = 9 6 * 1000 or x = 961000/ 410 = 1350 Answer : B #### B QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speedâˆ—Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed against the current will be options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these SOLUTION:Explanation: Speed with current is 20, speed of the man + It is speed of the current Speed in sƟll water = 20 - 5 = 15 Now speed against the current will be speed of the man - speed of the current = 15 - 5 = 10 kmph Answer: B #### B QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 5x Hence, a1+a2+..+a20+n = 25x So, the fraction asked = 5x/25x = 1/5 Answer C #### C QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 12 = 492 Answer: B #### B QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number? options: A)74 B)76 C)70 D)68 E)65 SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) Their sum = 8x - 4 = 292 => x = 37 Smallest number is: 2(x - 2) = 70. ANSWER:C #### C QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3\|X^3-3 options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1 SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t\|(t+3)^2-3, which is equivalent to the condition t\|3^3-3, or t\|24. Therefore, it is necessary and sufficient for t to be an integer divisor of 24, hence t must be equal to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7, 9, 11, 15, and 27. Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B QUESTION:What will be the product of (50-1)(50-2)(50-3)..............(50-79)(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost? options: A)32 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 80 : x 250 x = (100 * 80) x = (100 * 80) / 250 x = 32 ANSWER: A #### A QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 3 specific shirts with 2 specific pants? options: A)66 B)51 C)36 D)70 E)56 SOLUTION:Total no of combinations available is= 8 shirts X 9 pants = 72 Eliminate the 3shirts X 2 pants combo = 6 which gives.......>> 72-6=66 ANSWER: A #### A QUESTION:Which of the following equations represents a line that is perpendicular to y=1/2x+3? options: A)y−2x=8 B)2x+4y=10 C)3y+6x=12 D)4y−8x=16 E)5x−10y=20 SOLUTION:For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2 Answer: E #### E QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:If 2x = 3y = 10, then 9xy = ? options: A) 1,200 B) 200 C) 150 D) 40 E) 20 SOLUTION:2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9510/3=150 Answer: C. #### C QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 918 = 162. Answer: Option A #### A QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)364 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)2 B)7 C)C)120 D)D)144 E)E)720 SOLUTION:The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E #### C QUESTION:A train 120 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)16 kmph B)88 kmph C)54 kmph D)18 kmph E)27 kmph SOLUTION:S = 120/16 * 18/5 = 27 kmph Answer: E #### E QUESTION:The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is : options: A)20 B)30 C)40 D)None of these E)Cannot be determined SOLUTION:Solution Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131. (a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 . ⇒ (a + b + c) = 400/20= 20 Answer A #### A QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C55C3 = 42 5 = 210 ANS:C #### C QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be options: A)15% B)25% C)35% D)40% E)55% SOLUTION:Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)100 = 25% Total markup should be = 25 + 30 = 55% Answer E #### E QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 Ã— 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit options: A)Rs. 8510 B)Rs. 8620 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(8000×(1+5/100)2) =>8000×21/20×21/20 =>8820 Option D #### D QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? options: A)x B)(85/12)x C)(85/24)x D)(85/36)x E)(85/48)x SOLUTION:Let Q be the number of homework questions. Q = 4Q/5 + (5/17)(Q/5) + x Q = 68Q/85 + 5Q/85 + x 12Q/85 = x Q = (85/12)x The answer is B. #### B QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pir^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)2121/4 = 346.5 sq m answer :C #### C QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(32^25) B)y/(3^225) C)y/(325^2) D)y/(5^32^2) E)y/(532) SOLUTION:Solution: As y and n are both integers so y is of the form of 3522K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A <<<Examples ends QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? options: A)2 months B)6 months C)7 months D)8 months E)None of these SOLUTION:Explanation : Let B joins for x months. Then A:B = 900012 : x 18000 = 3 : 1 => 912 : 18x= 3 : 1 => 912/ 18x = 3/1 = 3 => 94 /18x = 1 => 2/x = 1 => x = 2. Answer : Option A #### A QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T? options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1 SOLUTION:Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D. #### D QUESTION:If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10? options: A)7 B)2 C)4 D)6 E)8 SOLUTION:This one took me bout 3 1/2 min. Just testin numbers and what not. First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p. 1-7 stands for ^1 thru 6 1: 71=7 2: 77=9 3: 79=3 4: 73=1 5: 71=7 6: 77=9 7: 79=3 Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems. so 7^4n+3 ---> if n=1 then its ((7^7)6))/10 which can say is going to be 38--> 18/10 --> R=8 Now from here if id double check just to make sure. 7^4(2)+36^2 ---> 7^1136 or we can just say again 7^116 (b/c we are only interested in the units digit). Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern) so again 36=18/10 ---> R =7. A or J in this problem. #### A QUESTION:A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone. options: A)6 Â½ days B)1 Â½ days C)8 Â½ days D)5 Â½ days E)2 Â½ days SOLUTION:Explanation: 3/20 * 2 + (2 + x)/5 = 1 x = 1 Â½ days Answer:B #### B QUESTION:How many quarters are equal to 7 dollars? options: A)1 B)28 C)12 D)9 E)7 SOLUTION:7 * 4 = 28 quarters Answer : B #### B QUESTION:400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination? options: A)50 B)100 C)120 D)140 E)180 SOLUTION:60%x+80%(400-x)=65%400 Ans=100 ANSWER:B #### B QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50 9/10 x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? options: A)1 B)2 C)3 D)5 E)4 SOLUTION:Assume initial amount is x Annual Interest is 34.1% so after 1 year the amount will become x (100+33.34)/100 => x4/3 now we need to find n for x (4/3)^n = 3x or in other words n = 4 E #### E QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12 SOLUTION:Let the two numbers be x and y. 60/100 * x + y = 5/4y => 3/5 x = 1/4 y => x/y = 5/12 E) #### E QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 => v2 = 20 => v1 = 5 => p1 = 20 Answer - D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers? I. LCM : 24; HCF : 6 II. LCM : 18; HCF : 8 III. LCM : 16; HCF : 9 options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III SOLUTION:We need to keep two things in mind here: 1. Product of two numbers = LCMHCF 2. LCM should be a multiple of HCF Only Statement I follows these two rules. Correct Option A #### A QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students? options: A)17 years B)16 years C)15 years D)14 years E)13 years SOLUTION:Sum of the ages of 14 students = (18 35) - (20 * 25) = 630 - 500 = 130 Required average = (130/10) = 13 years. Answer:E #### E QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)21 C)25 D)26 E)24 SOLUTION:Solution Given Data 3 positive integers Average of a, b, and c = 20. So, a+b+c3a+b+c3 = 20 or a + b + c = 60 a ≤ b ≤ c Median = (a + 11) Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c Therefore, b = a + 11 Objective To find the least value of 'c' Theoretically, the least value of c is when c = b. Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11) Or 3a = 38 or a = 12.66 So, b = c = 12.66 + 11 = 23.66 However, we know that these numbers are all integers. Therefore, a, b, and c cannot take these values. So, the least value for c with this constraint is NOT likely to be when c = b Let us increment c by 1. Let c = (b + 1) In this scenario, a + (a + 11) + (a + 12) = 60 Or 3a = 37. The value of the numbers is not an integer in this scenario as well. Let us increment c again by 1. i.e., c = b + 2 Now, a + (a + 11) + (a + 13) = 60 Or 3a = 36 or a = 12. If a = 12, b = 23 and c = 25. The least value for c that satisfies all these conditions is 25. Correct answer is choice C. #### C QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is : options: A)427 B)859 C)860 D)4320 E)None of these SOLUTION:Solution Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? options: A)2777 B)2888 C)8400 D)2882 E)2781 SOLUTION:Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 13800 * 14/23 = Rs. 8400. Answer: C #### C QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c âˆ’ a? options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=160 --2 subtracting 1 from 2 we have c-a=70; ANSWER:B #### B QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))? options: A)0 B)2 C)1 D)6 E)9 SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1. Thus, the answer is C. #### C QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is: options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222 SOLUTION:Explanation: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x \therefore Cultivated land of village = 384000x \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833 Answer: D #### D QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:Find out the next word in the series below... FAG, GAF, HAI, IAH, ...? options: A)GAK B)JAK C)HGF D)JAH E)KHG SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets ANSWER:B #### B QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true? options: A) x + y > 4 B) xy>1 C) x/y + y/x < 1 D) (x - y)^2 > 0 E) None of the above SOLUTION:Answer is B: 1/X + 1/Y < 2 The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y. So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time. Another way of putting it is: XY>1.B #### B QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:The greatest number of four digits which is divisible by 7, 10, 40 and 60 is: options: A)9200 B)9300 C)9400 D)8400 E)7400 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 7, 10, 40 and 60 is 4200. On dividing 9999 by 4200, the remainder is 1599. Required number (9999 - 1599) = 8400. ANSWER :D #### D QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650 SOLUTION:Explanation: P - 340 = (P48)/100 P = 500 ANSWER IS D #### D QUESTION:3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is: options: A)2/9 B)1/9 C)8/9 D)7/9 E)1/4 SOLUTION:let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house there will be 1 case when x,y,z will buy house a another when they buy house b and another when they buy house c so the prob that they buy same house is 31/27=1/9 ANSWER:B #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? options: A)662 B)678 C)652 D)642 E)721 SOLUTION:8 * 86 = 688 – 10 = 678 ANSWER:B #### B QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)8837 C)2377 D)3772 E)3881 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer: A #### A QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform? options: A)150 B)145 C)165 D)162 E)152 SOLUTION:D = 130 + x T = 20 S = 130+x/15 * 18/5 = 70 kmph. => (130+x) * 18 = 5250 => 130 + x = 292 => x= 162 m Answer: D #### D QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -2.5 Prob =1/12 Answer - A #### A QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? options: A)7 years B)9 years C)6 years D)4 years E)5 years SOLUTION:28 * 2 = 56 20 * 3 = 60 ----------- 4 years Answer: D #### D QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(46 + 86): (412) 72:48 => 3:2 Answer:C #### C QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed? options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days SOLUTION:Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work. => In one day A came complete 1/9th of the task(x/9) => In one day B can complete 1/12th of the job.(x/12) First day x/9th work will be done next day x/12th and so on: Together A and B can do x/9 + x/12 work. =>(x/9) + (x/12) = 7/36th work done In 10 days 35/36th of the work will be done. On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work. So, 1/36th work will be done in 1/4 days. =>10.25 days ANSWER: D #### D QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42? options: A)1/16 B)5/42 C)1/8 D)3/16 E)1/4 SOLUTION:210=2357, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below); 42=237, so out of 16 factors only two are multiples of 42: 42 and 210, itself; So, the probability is 2/16=3/16. Answer: D #### D QUESTION:The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is? options: A)187 B)120 C)108 D)178 E)175 SOLUTION:150(80/100)(90/100) = 108 Answer:C #### C QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500? options: A)5000 B)5500 C)4991 D)5600 E)5700 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991 C #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is options: A)9 years B)11 years C)17 years D)21 years E)25 years SOLUTION:Solution Age of the 15th student =[15x15-(14x8+16x6)] = (225 - 208) = 17 years. Answer C #### C QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 2years ago? options: A)152460 B)214560 C)160000 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^2 = 176400* 20/21 * 20/21 =160000 Answer is C #### C QUESTION:If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is? options: A)1/2 B)1 C)-1/2 D)-1 E)0 SOLUTION:When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero. Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p => x = (p + q - r + p - q + r + q + r - p) / (r + q + p) => x = (r + q + p) / (r + q + p) = 1 p + q + r is non-zero. ANSWER:B #### B QUESTION:A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? options: A)16 B)24 C)26 D)30 E)160 SOLUTION:One of the approaches: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20. But each of these 3 couples can send two persons (husband or wife): 222=2^3=8. Total # of ways: 6C32^3=160. Answer: E. #### E QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 10 in any attempt =3/36=1/12 Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12 Probability of losing game =(11/12)(11/12)(11/12)=637/827 I.e. Probability of wining game = 1-(637/827) = 190/827 Answer : Option C #### C QUESTION:\|16 - 5\| - \|5 - 12\| = ? options: A)3 B)2 C)1 D)0 E)4 SOLUTION:\|16 - 5\| - \|5 - 12\| = \| 11 \| - \| -7 \| =11 - 7 = 4 correct answer E #### E QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)326,040 D)12,870 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All four 2. One symmetry and other three non 3. Two symmetry and other two non 4. Three symmetry and one non 4. All the three letters can be arranged in 24 ways ( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 15c1 ) 6 (330 +5005 + 5775+2475 ) * 24 326,040 IMO option C is the correct answer.. OA please...will correct if I missed anything.. C #### C QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)32% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 38 are employed males,hence 26% are employed females. (employed females)/(total employed people)=26/64=40% Answer: D. #### D QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)288 B)266 C)120 D)287 E)212 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 3232 !=476 #### C QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)295 C)322 D)345 E)354 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 41(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage? options: A)50% B)100% C)45% D)55% E)65% SOLUTION:Let the C.P of each book be Re 1. Then, S.P of 5 books= C.P of 10 books= Rs. 10 Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10 Gain = Rs ( 10 -5 ) = Rs 5. Gain% = ( 5/5× 100 ) % = 100% Answer : B #### B QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. wb + b^2 II. (w+ b)^2 III. w + b options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK; II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK. Answer: B. #### B QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D #### D QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:Rahul went to a shop and bought things worth Rs. 45, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)A)19.7 B)B)19.9 C)C)20.9 D)D)21.9 E)E)39.7 SOLUTION:Total cost of the items he purchased = Rs.45 Given that out of this Rs.45, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (45−30/100−x)6/100 = 30/100 ⇒ 6(45 −0.3 −x) = 30 ⇒ (45 − 0.3 − x) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 E) #### E QUESTION:N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is options: A)(a) 61250 B)(b) 65525 C)(c) 42455 D)(d) 62525 E)(e) 55425 SOLUTION:The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question. To start, we're given information on the sub-sets of numbers: -The 1st set has 1 number -The 2nd set has 2 numbers -The 3rd set has 3 numbers Etc. So the 50th set will have 50 numbers in it. Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching... The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers Etc. This pattern will continue all the way down to... The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'... So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive... Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)... 25(1226+1275) = 25(2501) = 62525 D #### D QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:The cube root of what integer power of 2 is closest to 50? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc. Let, Cube root of x is closest to 50 i.e. x is closest to cube of 50 = 505050 = 125000 But x must be equivalent to an Integer power of 2 2^10 = 1024 2^7 = 128 i.e. 2^17 = 1281024 = 128000 (approx.) i.e. 2^18 = 2561024 = 256000 (approx.) i.e. 2^16 = 641024 = 64000 (approx.) i.e. 2^17 which is closest to 125000 i.e. Integer power of 2 must be 7 Answer: option B #### B QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.450 B)Rs.500 C)Rs.550 D)Rs.640 E)Rs.650 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:The tax on a commodity is diminished by 30% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? options: A)20% B)18% C)15% D)12% E)14% SOLUTION:100 100 = 10000 70 * 115 = 8050 10000------- 1950 100 ------- ? = 20% ANSWER:A #### A QUESTION:A mixture of 150 liters of wine and water contains 15% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)10 B)30 C)20 D)15 E)17 SOLUTION:Number of liters of water in150 liters of the mixture = 15% of 150 = 15/100 * 150 = 22.5 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (22.5 + P) and total volume of mixture is (150 + P). (22.5 + P) = 25/100 * (150 + P) 90+4P = 150+P P = 20 liters. Answer: C #### C QUESTION:Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? options: A)$506.00 B)$726.24 C)$900.00 D)$920.24 E)$926.24 SOLUTION:If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away. Interest earned after the first time interval: $10,0002%=$200; Interest earned after the second time interval: ($10,000+$200)3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$926. Answer: E. #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 38.7%. What would have been the percentage of profit earned if no discount had been offered? options: A)28.5 B)46 C)30 D)Data inadequate E)None of these SOLUTION:Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100. Then printed price = 100Ã—(100+38.7)/(100âˆ’5) =146 Hence, required % Profit = 146 â€“ 100 = 46% Answer B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)28% B)25% C)95% D)05% E)22% SOLUTION:800 --- 200 100 --- ? => 25% Answer:B #### B QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:In 100 litres mixture milk and water are in the ratio 3:2. After adding how many liters of water its ratio will become 3:4 options: A)48 B)50 C)62 D)78 E)100 SOLUTION:Milk quantity = 3/5 60 = 36 water quantity = 100-36 = 64 new ratio of M:W = 36:64+x = 3:4 192+3x = 144 x = 48 Answer is A #### A QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:If n = 9^11 – 9, what is the units digit of n? options: A)0 B)1 C)4 D)6 E)8 SOLUTION:Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 9^3 - 9. Now 9^3 has last digit 9. , we subtract 9 from 9 , thus 9 -9 = 0 is the answer. Option A #### A QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes? options: A)100000 B)85236 C)89562 D)90083 E)95842 SOLUTION:winners votes = 100-45 = 55% invalid votes = 83 polled votes = [(1009000)/(255-100)]+83 = 90083 Answer is D #### D QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)46 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 9) years. (x+9+10)=2(x�10) hence x=39. Present age of B = 39 years Answer: Option C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform? options: A)240 B)188 C)177 D)260 E)320 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Length of the train = 20 * 20 = 400 m. Let the length of the platform be x m . Then, (x + 400)/36 = 20 => x = 320. Answer: E #### E QUESTION:A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? options: A)5,040 B)18,720 C)26,208 D)37,440 E)52,000 SOLUTION:4 character password: DLDD First digit can be chosen in 9 ways. The letter can be chosen in 26 ways. Next digit can be chosen in 8 ways. Next digit can be chosen in 7 ways. This gives us 92687ways Now, the letter can also be DDLD so there will be another 92687 ways Total = 926872 = 26,208 ways C #### C QUESTION:What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm? options: A)176 B)187 C)540 D)748 E)6 SOLUTION:The marbles used to tile the floor are square marbles. Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble. As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26. 3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm. The HCF of 339 and 226 = 113. Hence, the side of the square is 113. The number of such square marbles required, =339×226/113×113 =6 marbles Option(E) #### E QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 999998 = 472392 Hence option (A). #### A QUESTION:By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.500 D)s.450 E)s.420 SOLUTION:SP = 700 Profit = 25% CP = (SP)[100/(100+P)] = 700 * [100/125] = 560 Loss = 25% = 25% of 560 = Rs.140 SP = CP - Loss = 560 - 140 = Rs.420 ANSWER:E #### E QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 84030/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. Aâ€™s 1 dayâ€™s work = (1/20) (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 800018 : (80004) + (400014) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =250=100m ANSWER:D #### D QUESTION:If an amount of Rs 41,800 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1900 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41800/22 = Rs 1900 Answer A #### A QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of? options: A)150 B)339 C)342 D)359 E)362 SOLUTION:Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer W= 19 + 290 + 351 = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol. What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol? options: A)32 B)21 C)27 D)None of these E)18 SOLUTION:Explanation: Let t be the time after Kajol starts, when she meets Ajay, then \inline t=\frac{300}{(x+y)} This should be less than 2.5 or (x+y)>120 Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72 This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol. Answer: D #### D QUESTION:Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 42 can be put in each wooden box in 3 boxes 342 can be accommodated = 24=A #### A QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:Sum of the local value and the face value of 4 in the numeral 153489216 is options: A)40004 B)4004 C)4000004 D)400004 E)44 SOLUTION:(Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 D #### D QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of options: A)20% B)19% C)18% D)11% E)10% SOLUTION:Say the original price of the TV was $p, then the final price would be (0.9p)∗0.9=0.81p. Therefore the original price was discounted by 19%. Answer: B. #### B QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is: options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in one years is: 5,870,000,000,000 = 587 * 10 ^10 The distance of the light travels in 1000 years is: = 587 * 10^10 x 10 ^3 = 587 x 10^13 miles Answer :A #### A QUESTION:A train 200 m long passed a pole in 20 sec. How long will it take to pass a platform 610 m long? options: A)46 B)54 C)92 D)76 E)81 SOLUTION:Speed = 200/20 = 10 m/sec. Required time = (200 + 610)/10 = 81 sec. Answer: E #### E QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:If (5^15)(9^8)=3(15^x), what is the value of x? options: A) 7 B) 9 C) 11 D) 13 E) 15 SOLUTION:(5^15)(9^8)=3(15^x) => 5^15 * 3^16 = 3 * 3^x * 5^x => 5^15 * 3^16 = 3^(x+1) * 5^x Value of x = 15 Answer E #### E QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2(44 + 124) = 2(16+48) = 128 Then, Finally Length (L) = 212 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2(22 + 242) = 2(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)100 /Initial Area i.e. % change in Area of four walls = (104-128)100 /128=- 18.75% (Decrease) Answer: Option D #### D QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B QUESTION:A goods train runs at the speed of 72 kmph and crosses a 250m long platform in 26seconds. what is the length of the goods train? options: A)230 m B)240 m C)260 m D)270 m E)250 m SOLUTION:Speed =(72 5/18)m/sec= 20 m/sec. then (x+250)/26=20 x+250 =520 x=520-250 then x=270 Answer: D #### D QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire? options: A)2 B)8 C)7 D)3 E)10 SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 72,000 m : C is the circumference C = 3 meters #### D QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 541=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D <<<Examples ends QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ? options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these SOLUTION:Explanation: Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24) =12:15:16=12:15:16. ANSWER IS D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Let number of pounds of 5$ candy to be used be w 6 = (158 + 5w)/(15 +w) =>90 + 6w = 120 + 5w => w = 30 Answer B #### B QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 311. All other products are too big. The answer is B. #### B QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 185x+152x=180 x=180/215 x=0.837209 time taken for type A problem=1520.837209=25.11628min ANSWER:B #### B QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (7505R)/100 R = 4% Answer :C #### C QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)? options: A)-f(x) B)f(x) C)2f(x) D)1/f(x) E)2/f(x) SOLUTION:If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) answer A #### A QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year? options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7 SOLUTION:A : B (40004)+(10008) : (60008)+(30004) 24000 : 60000 2 : 5 Answer: A #### A QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3 SOLUTION:total 9 from take one. 9c1=9 red 5 from one 5c1=5 5/9 ANSWER:C #### C QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? options: A)28 B)10 C)28 D)27 E)13 SOLUTION:4/12 + x/15 = 1 x = 10 Answer:B #### B QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 30 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)20 miles B)30 miles C)40 miles D)50 miles E)60 miles SOLUTION:Every hour, Nil gets ahead of Ethan 30 - 20 = 10 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 30 × 1 = 30 miles. correct answer B #### B QUESTION:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 3 can be used only once? options: A)20 B)150 C)225 D)250 E)316 SOLUTION:4 options for the first digit: 2, 4, 6, 8; 5 options for the second digit: 1, 3, 5, 7, 9; 4 options for the third digit: 2, 3, 5, 7; 4 options for the fourth digit: 0, 3, 6, 9. Four digit # possible without the restriction (about the digit 6): 4544=320 Numbers with three 3-s, 3X3X3 4111=4 Thus there are 320-4=316 such numbers. Answer: E. #### E QUESTION:A car covers a distance of 624 km in 6 Â½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 Ã— 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24144)= 30. Answer is C. #### C QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? options: A) 400 B) 625 C) 1,250 D) 2,500 E) 312 SOLUTION:total fish = x percentage of second catch = (8/50)100 = 16% so, x 16% = 50 x = 312 ans.E #### E QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)309 D)285 E)324 SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them. There are still 90 on physics and 110 on chemistry The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry. Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309 C #### C QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business? options: A)2:35:16 B)2:15:16 C)2:15:77 D)2:15:98 E)2:15:23 SOLUTION:Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24) = 12:15:16 Answer: B #### B QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? options: A)27 B)26 C)25 D)24 E)20 SOLUTION:Explanation: n(A)=(60/100âˆ—96)=288/5 n(B)=(30/100âˆ—96)=144/5 n(Aâˆ©B)=(15100âˆ—96)=72/5 People who have either or both lunch n(AâˆªB)=288/5+144/5âˆ’72/5 =360/5=72 So People who do no have either lunch were = 96 -72 = 24 ANSWER IS D #### D QUESTION:One-third of 600 is what percent of 120 ? options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6 SOLUTION:Answer Let one-third of 600 is N% of 120. ∵ 600/3 = (N x 120)/100 ∴ N = (200x 100) / 120 = 166.6 Correct Option: E #### E QUESTION:What proximate value should come in place of the question mark (?) in the following question? 6.795 Ã— 1084 + 2568.34 â€“ 1708.34 = ? options: A)6,000 B)12,000 C)10,340 D)8,204 E)9,000 SOLUTION:? â‰ˆ 6.8 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7344 + 860 â‰ˆ 8204 Answer D #### D QUESTION:The ratio, by volume, of bleach to detergent to water in a certain solution is 4 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain? options: A)80 B)70 C)60 D)40 E)50 SOLUTION:B:D:W = 4:40:100 Bnew / Dnew = (1/3)(4/40) = (1/30) Dnew / Wnew = (1/2)(40/100) = (1/5) Wnew = 300 Dnew = Wnew/5 = 300/5 = 60 So, answer will be C #### C QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=? options: A)2515 B)2525 C)2535 D)2545 E)2555 SOLUTION:given,(x+ 1/x) = 5 x^2 + 1/x^2 = (x+ 1/x)^2 - 2x1/x = 5^2 - 2 = 23 -------(1) x^3 + 1/x^3 = (x+ 1/x)^3 - 3x1/x(x+ 1/x) = 5^3 - 35 = 110 -------(2) multiplying (1)& (2), we get =>(x^2+ 1/x^2)(x^3+ 1/x^3) = 23110 => x^5 + 1/x + x + 1/x^5 = 2530 => x^5 + 1/x^5 + (x+ 1/x)= 2530 => x^5 + 1/x^5 + 5 = 2530 => (x^5+ 1/x^5)= 2525 ANSWER:B #### B QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 804 / 60 = 5 hours 33 mins Answer â€“ B #### B QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price? options: A)197 B)476 C)279 D)278 E)268 SOLUTION:CP1 = 100 SP1 = 105 CP2 = 95 SP2 = 95 (105/100) = 99.75 5.25 ----- 100 25 ----- ? => 476 Answer:B #### B QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.90.8x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:23,8,34,81,33,... options: A)24 B)25 C)26 D)27 E)28 SOLUTION:23 : 2^3=8 34 : 3^4=81 33 : 3^3=27 ANSWER:D #### D QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? options: A)3002 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 100/247 7410 = 3000 Answer: B #### B QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits? options: A)53978 B)53916 C)53961 D)56781 E)None of these SOLUTION:Explanation: The greatest 5 digit number that can be formed using the given digits = 74320 The smallest 5 digit number that can be formed using the given digits = 20342 .: The required difference = 74320 - 20342 = 53978 Answer: Option A #### A QUESTION:2 identical circles intersect so that their centre and point at which they intersect form a square of 1 cm.the area of portion that is common two circles is 4 options: A)π2-1 B)4 C)√2-1 D)√5 E)π/2-1 SOLUTION:the area of the sector is pir^290/360 (as it is a square, so the angle is 90) =pir^2/4 =pi/4 (as the area of the square is 1cm^2, so the sides are 1 cm each. the sides of the square are the radii of the circle) now, the area of the triangle formed by two radii and a line which joins the point of intersection of the two circles = 0.511=0.5 So, half of the portion of our desired area= (pi/4 - 0.5) therefore, the area of our desired portion is 2 (pi/4 - 0.5) = pi/2 - 1 ANSWER:E #### E QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides? options: A)3 B)6 C)5 D)9 E)1 SOLUTION:S = (1 + 2 + 7)/2 = 5 Answer:C #### C QUESTION:Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x? options: A)4 B)5 C)3 D)9 E)6 SOLUTION:9 x + x = 13 + 27 10 x = 40 => x = 4 Answer:A #### A QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k? options: A)y = -4x + 2m B)y = 1/4x - 8m C)y = 4x + 2m D)y = 1/4x + 2m E)y = -1/4x - 8m SOLUTION:The slope of the line is 2m/8m=1/4. The y-intercept is 2m. the equation of the line is: y = 1/4x +2m The answer is D. #### D QUESTION:12,?,68,129,220,347,516 options: A)129 B)220 C)347 D)31 E)520 SOLUTION:222 + 4 = 12 444 + 4 = 68 555 + 4 = 129 666 + 4 = 220 7 7 7 + 4 = 347 8 8 8 + 4 = 516. 333 +4 = 31 ANSWER : D #### D QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 10 in any attempt =3/36=1/12 Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12 Probability of losing game =(11/12)(11/12)(11/12)=637/827 I.e. Probability of wining game = 1-(637/827) = 190/827 Answer : Option C #### C QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400 SOLUTION:6600:4400:11000 3:2:5 3/10 11000 = Rs.3300 AnswerA #### A QUESTION:After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article? options: A)12000 B)15000 C)1200 D)1000 E)10000 SOLUTION:CP* (44/100) =4400 CP= 100 * 100 => CP = 10000 Answer:E #### E QUESTION:J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r? options: A)93.5 B)90 C)6.75 D)6.25 E)2 SOLUTION:Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables. Let, P = 400 then J = (75/100)400 = 300 also J = (80/100)T i.e. T = 300100/80 = 375 and T = [1-(r/100)]P i.e. 100-r = 100T/P = 100375/400 = 93.75 i.e. r = 6.25 Answer: Option D #### D QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:John bought 2 shares and sold them for $98 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-98 20-? $18 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-98 20-? $22 loss on the sale of 1 share. 18-22=Loss of $4 Answer: C #### C QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank? options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x) Solve the equation. 262.85(32)+3,104.35x = 1,399.45(32 + x) 8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x 8,411.2 + 1,704.9x = 44,782.4 1,704.9x = 36,371.2 x ≈ 21.3 Answer is B. #### B QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)10 D)8 E)9 SOLUTION:US = 15 DS = 35 M = (35 - 15)/2 = 10 Answer: C #### C QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)9.30 a.m B)10 a.m C)10.40 a.m D)11 a.m E)11.40 am SOLUTION:Suppose they meet x hours after 7 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 10 a.m. answer B #### B QUESTION:Rs.8000 become Rs.11256 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)6 YEARS B)7 C)5 D)3 E)4 SOLUTION:Explanation: 11256 = 8000(21/20)N (21/20)7 = (21/20)N => N = 7 Answer: Option B #### B QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232? options: A)1000 B)2217 C)1100 D)2777 E)2991 SOLUTION:1232 = P [1 + (512/5)/100] P= 1100 Answer: C #### C QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63 SOLUTION:Required probability = 1 - 1/126 = 125/126 ANSWER:C #### C QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)5 C)8 D)13 E)15 SOLUTION:Total # of students = 40 Avg # of books per student = 2 Total # of books = 402 = 80 # of student borrowed at least 3 books = 40-2-12-10 = 16 # of books borrowed by above 16 students = 80-(121)-(102) = 48 Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 153 = 45 So maximum # of books borrowed by any single student = 48-45 = 3 option A #### A QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1SD=13 and 2 SD below the mean ismean-2SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:The sum of two numbers is 45. Their difference is 5. The bigger number is options: A)20 B)25 C)30 D)35 E)45 SOLUTION:X + Y = 45 X - Y = 5 Adding 2X = 50 ==> X = 25 and Y = 45 - 25 = 20 Bigger number is X = 25 Answer B. #### B QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:The age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father's present age is : options: A)50 years B)46 years C)20 years D)45 years E)30 years SOLUTION:Let the sum of present ages of the two sons be x years. then father's present age =3x years. (3x+5)=2(x+10) 3x+5=2x+20 x=15. Hence, father's present age =45 years. Answer is D #### D QUESTION:When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time. options: A)2 PM B)9 PM C)4 PM D)8 PM E)6 PM SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=4/8x⇒x=20 Time is 4 PM Answer:C #### C QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? options: A)87 B)89 C)90 D)93 E)95 SOLUTION:Total score on 3 tests = 813 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 834 = 332 Score required on the fourth test = 332 - 243 = 89 Option B #### B QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ? options: A)7.76 kms B)8.76 kms C)5.76 kms D)3.76 kms E)4.76 kms SOLUTION:Explanation: Speed in still water = 6 kmph Stream speed = 1.2 kmph Down stream = 7.2 kmph Up Stream = 4.8 kmph x/7.2 + x/4.8 = 1 x = 2.88 Total Distance = 2.88 x 2 = 5.76 kms Answer: C #### C QUESTION:65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? options: A)64 B)128 C)151 D)216 E)256 SOLUTION:65 small cube will make a large cube with 4 cubes in each line i.e. Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line. Total number of small cubes in new cube = 6^3 = 216 Extra cube required = 216 - 65 = 151 Hence, C is the answer. #### C QUESTION:At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)2 B)7 C)C)120 D)D)144 E)E)720 SOLUTION:The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E #### C QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work? options: A)4 B)5 C)7 D)8 E)10 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (2 women + 10 children)'s 1 day work = (2/70 + 10/140) = 1/10 2 women and 10 children will complete the work in 10 days. E #### E QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7) options: A)80 m2 B)84 m2 C)88 m2 D)86 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 4 = 88 m2 Answer C #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed. options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above SOLUTION:My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 57 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 #### D QUESTION:What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? options: A)3: 5 B)3: 9 C)3: 4 D)3: 1 E)3: 2 SOLUTION:d = 3d d = d a√2 = 3d a√2 = d a = 3d/√2 a = d/√2 => 3: 1 Answer: D #### D QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours? options: A)360 B)480 C)720 D)960 E)1000 SOLUTION:D 15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour. 5 grams sugar cubes will take less time to move. Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour. More ants, more sugar cubes they can move. 20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams. #### D QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)100}=4% Answer is A. #### A QUESTION:On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts? options: A)3/4 B)5/8 C)7/8 D)11/16 E)15/16 SOLUTION:P(missing all 4)=(1/2)^4=1/16 P(success on at least one attempt)=1-1/16=15/16 The answer is E. #### E QUESTION:A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is options: A)31 years B)32 years C)33 years D)34 years E)35 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+40. => 2(x+6) = (x+40+6) => 2x+12 = x+46 => x = 34 years Answer: Option D #### D QUESTION:In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 32 more than twice the number of heads => 2(d + 2c) = 32 + 2(c + d) => d + 2c = 16 + c + d => 2c = 16 + c => c = 16 i.e., total number of cows = 16 Answer is C. #### C QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 94025/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/60045 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/80060 = 90 litres. Answer B #### B QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is? options: A)625 B)298 C)269 D)200 E)267 SOLUTION:Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A QUESTION:In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr? options: A)3.5 B)2.7 C)2.9 D)2.3 E)2.1 SOLUTION:Speed = 130 * 5/18 = 36 m/sec Time taken = 125/36 = 3.5 sec. Answer: A #### A QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 918 = 162. Answer: Option A #### A QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 340 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 413 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:If a sum of money doubles itself in 20 years at simple interest, the ratepercent per annum is options: A)12 B)12.5 C)13 D)5 E)14 SOLUTION:Explanation: Let sum = x then Simple Interest = x Rate = (100 x) / (x * 20) = 5 Option D #### D QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? options: A)125 B)772 C)821 D)912 E)121 SOLUTION:Sum of the 35 numbers = 35 * 25 = 875 If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5. Thus, the new average = 25 * 5 = 125. Answer:A #### A QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4 and 5). Make the 4 number as large as possible and make the 5 number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6 and 7). Make the 6 number as large as possible and make the 7 number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:If the cost price is 99% of selling price then what is the profit percentage. options: A)1 B)1.11 C)1.01 D)1.1 E)1.21 SOLUTION:selling price=Rs100 : then cost price=Rs 99:profit =Rs 1. Profit={(1/99)100}%=1.01% Answer is C. #### C QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 16/100 = 136 Answer:A #### A QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.8 sec C)8.5 sec D)2.2 sec E)4.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. Answer:A #### A QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 312=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:What is the 10th term in this sequence? 3,5,8,15,25,40,67,104,171 options: A)273 B)278 C)279 D)377 E)277 SOLUTION:3+5 =8 +0 =8 8+5 =13+2 =15 15+8 =23+2 =25 25+15=40+0 =40 40+25=65+2 =67 67+35=102+2 =104 104+67=171+0=171 171+104=275+2=277 so 9th term is 277 ANSWER:E #### E QUESTION:The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is: options: A)400 B)500 C)600 D)800 E)1000 SOLUTION:Let the sum be $. P. (P(1+10/100)^2-P)=525 P((11/10)^2-1)=2500 SUM = 2500 So SI = 500 ANSWER B #### B QUESTION:Ravi can do a piece of work in 15 days while Prakash can do it in 30 days. In how many days will they finish it together? options: A)11 days B)9 days C)8 days D)12 days E)10 days SOLUTION:1/15 + 1/30 = 3/30 10/1 = 10 days ANSWER:E #### E QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h The answer is D. #### D QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20100/1000 = 2.0% Answer is A #### A QUESTION:number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9 options: A)1290 B)1296 C)1380 D)1480 E)1580 SOLUTION:we have to make 4 digit number in which the format is d> c > b > a __ __ __ __ 1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4) 2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3) 3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2) 4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1) hence every place can be filled by 6 digits, 6 6* 6* 6 = 1296 ANSWER:B #### B QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (204) days let X = number of machines needed to complete the job in 10 days 1/(420) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/10022000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2550 Price in 99 = 22000 - 3550 Price in 00 = 22000 - 4550 Price in 01 = 22000 - 5550 Price in 02 = 22000 - 6550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 16000, then find the annual income of A? options: A)Rs. 537600 B)Rs. 180000 C)Rs. 201600 D)Rs. 504000 E)None of these SOLUTION:B's monthly income = 16000 * 112/100 = Rs. 17920 B's monthly income = 2 parts ----> Rs. 17920 A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800 A's annual income = Rs. 44800 * 12 = Rs. 537600 ANSWER:A #### A QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places. options: A)73.41 B)74.31 C)72.43 D)73.43 E)73.82 SOLUTION:Total marks = 35 x 72 =2520 Corrected total marks = 2520 - 35 + 99 =2584 Correct Average = 2584/35 = 73.82 Answer : E #### E QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:At Bala's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009? options: A)700 B)1000 C)1300 D)1600 E)2000 SOLUTION:At Bala's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year: R2008= R2007(1+x) R2009= R2007(1+x)^2=1.44R2007 (1+x)^2 = 1.44 1+x=1.2 x=0.2 aka revenue increases 20% each year and cost increases 10% annually Next solve for R2007and C2007: R2007= C2007- 1000 1.2R2007- 1.1C2007= 0 1.2[C2007- 1000] - 1.1C2007= 0 0.1C2007= 1,200 C2007= 12,000 R2007= 11,000 Finally find 2009 profits: Profit2009= 1.4411,000 - 1.2112,000 Profit2009= 15,840 - 14,520 Profit2009= 1320 Answer: C #### C QUESTION:A set consists of 12 numbers, all are even or multiple of 5. If 4 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 12 = 4 + 10 - {Both} + 0; {Both}=2(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: C. #### C QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? options: A)8 B)10 C)12 D)14 E)16 SOLUTION:Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump. Both pumps together can fill 1/6 of the pool each hour. 2.5x = 1/6 x = 1/15 1.5x = 1.5/15 = 1/10 The faster pump could fill the pool in 10 hours. The answer is B. #### B <<<Examples ends QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform? options: A)240 B)188 C)177 D)260 E)320 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Length of the train = 20 * 20 = 400 m. Let the length of the platform be x m . Then, (x + 400)/36 = 20 => x = 320. Answer: E #### E QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference W= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together? options: A)120 B)110 C)105 D)140 E)135 SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8C6 + (8C5 * 2C1) this is 28 + 112=140 Answer : D #### D QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:What is the HCF of 2/3, 4/15 and 6/5 options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15 Answer: Option E #### E QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? options: A)2267 B)287 C)268 D)228 E)225 SOLUTION:1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = 1/6 15 women's 1 day work = (1/6 - 10/100) = 1/15 1 woman's 1 day work = 1/225 1 woman alone can complete the work in 225 days. Answer: E #### E QUESTION:For which of the following values of n is (500+n)/n NOT an integer? options: A) 1 B) 2 C) 3 D) 4 E) 5 SOLUTION:Solution: This problem is easiest solved by plugging in each answer choice. A) (500 + 1)/1 = 501/1 = 501 Answer choice A yields an integer. B) (500 + 2)/2 = 502/2 = 251 Answer choice B yields an integer. C) (500 + 3)/3 = 503/3 = 167, remainder 2 Answer choice C DOES NOT yield an integer. Although we believe answer choice C is correct, we should still test the other answer choices. D) (500 + 4)/4 = 504/4 = 126 Answer choice D yields an integer. E) (500 + 5)/5 = 505/5 = 101 Answer choice E yields an integer. Thus, the correct answer is answer choice C. #### C QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? options: A)229 B)108 C)278 D)72 E)112 SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: D #### D QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60? options: A)200 B)220 C)240 D)322 E)342 SOLUTION:Required Number = (LCM of 15, 30, 45 and 60) + 20 = 180 + 20 = 200 Option A #### A QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger? options: A)6 m B)5 m C)4 m D)3 m E)None of the above SOLUTION:Sol. Let the length of the tiger be x metres and its speed be y m/sec. Then, x / y = 1 ⇒ y = x ∴ (x + 20) / 5 = x ⇔ x = 5 m. Answer B #### B QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (512/5)/100] P= 1500.Answer:A #### A QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have. p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24. Answer: D. #### D QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is? options: A)22 B)28 C)27 D)36 E)88 SOLUTION:(912)/3 = 36 Answer:D #### D QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+1664=0 (x-32)^2=0 x=32 A #### A QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2. options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1 SOLUTION:Explanation: No explanation is available for this question! ANSWER: A #### A QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3% SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% Answer: A #### A QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean? options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5 SOLUTION:The value which is exactly two SD below the mean is: mean-2SD=13.5-20.5=12.5. Answer: E. #### E QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? options: A)39 B)41 C)42 D)43 E)44 SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5) = 4 so for 6 children = 6 x 4 =24 so mother's age is 63 - 24 =39 Answer: Option A #### A QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 Ã— 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x? options: A)2/5 B)3/4 C)4/5 D)5/4 E)2/7 SOLUTION:a/b = 4/5 m/x = (2/5)5 / (7/4)4 = 2/7 The answer is E. #### E QUESTION:If n = 20! + 19, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:19 divides 20! so 19 also divides 20! + 19. 15 and 17 divide 20! so they do not divide 20! + 19. The answer is C. #### C QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ? options: A)12 B)16 C)18 D)9 E)12 SOLUTION:Explanation: Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 27 3x = 27 x = 9. Answer:D #### D QUESTION:What are the next two letters in the following series and why? W A T N T L I T F S _ _ Hint : Look into the title of the Riddle options: A)A and W B)A and E C)B and W D)A and C E)S and W SOLUTION:A A and W. The letters are the first letters of the words in the question. Thus, the next two letters are A and W. #### A QUESTION:Two whole numbers whose sum is 72 cannot be in the ratio options: A)3 : 4 B)3 : 5 C)4 : 5 D)5 : 7 E)None SOLUTION:Sol. The sum of the ratio terms must divide 72. So, the ratio cannot be 3 : 4. Answer A #### A QUESTION:Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? options: A)1/6 B)1/4 C)5/9 D)1/3 E)1/2 SOLUTION:Group 1: 2 Men and 1 Woman Group 2: 1 Men and 2 Woman Need: 2 Men and 2 women Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C22C2 = 1 ways Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2112 = 4 ways Total Favorable cases = 1+4 = 5 Total Possible ways of selecting students 2 from each group = 3C23C2 = 33 = 9 Probability = 5/9 Answer : Option C #### C QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/1233 = 33 cents. Answer: C. #### C QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in? options: A)3 days B)5 days C)7 days D)11 days E)12 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. A) #### A QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)4! B)8! C)9! D)10! E)12! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:125 + 83d = 90(d+1). 7d = 35. d = 5. The answer is B. #### B QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr. SOLUTION:Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=24 or x=12. Rate upstream=12 km/hr,rate downstream=36 km/hr. Hence,rate of stream=1/2(36-12)km/hr=12 km/hr. Answer is B. #### B QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77x=45 --> x=4577/87=677/17=~40. Answer: C. #### C QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24 SOLUTION:Explanation: 10 * 16 + 36 – 26=170 => 170/10 = 17 A) #### A QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 79 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match options: A)36 B)37 C)38 D)39 E)40 SOLUTION:Explanation: Let the average after 17th match is x then the average before 17th match is x-3 so 16(x-3) + 87 = 17x => x = 87 - 48 = 39 Answer: Option D #### D QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:If mn > 0, which of the following must be negative? options: A)mn B)mn^2 C)m/-n D)m/n E)m+n SOLUTION:Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive. Answer :C #### C QUESTION:If 2994 Ã· 14.5 = 179, then 29.94 Ã· 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ] = 179/10 = 17.9 Answer is E. #### E QUESTION:If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is options: A)1032 B)1030 C)1034 D)1035 E)1036 SOLUTION:2(13 + 23 + 33 + ---------- + 103) 2 × 516 = 1032 A #### A QUESTION:For what value of x, is \|x – 3\| + \|x + 1\| + \|x\| = 8? options: A) 0 B) 3 C) -3 D) 4 E) -2 SOLUTION:For what value of x, is \|x – 3\| + \|x + 1\| + \|x\| = 8? It's easiest just to plug in answer choices: (E): -2 \|x – 3\| + \|x + 1\| + \|x\| = 8? \|-2 - 3\| + \|-2 + 1\| + \|-2\| = 8? \|1\| + \|5\| + \|4\| = 8 (E) #### E QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)200 B)300 C)400 D)500 E)600 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 5C2) = 200 ANSWER A #### A QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder options: A)1235 B)1456 C)1567 D)1678 E)1631 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 35 5x = 1330 x = 266 Large number = 266+1365 = 1631 E #### E QUESTION:If a man walks at the rate of 4 kmph, he misses a train by only 6 min. However, if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is options: A)3 km B)4 km C)5 km D)6 km E)7 km SOLUTION:Let the distance covered be d and time taken to reach the station in time t d/4 = t+6/60---(1) d/5 = t-6/60---(2) (1)-(2) gives d/4 - d/5 = (6+6)/60 d/20 = 12/60 d = 1220/60 =4 km ANSWER:B #### B QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:168: x4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)1/2 D)5/6 E)2/3 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/41/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/42/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: E. #### E QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)3.5 hours D)2.3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/4 Part filled by B in 1 hour = 1/8 Part filled by C in 1 hour = 1/16 Part filled by (A+B+C) in 1 hour = 1/4+1/8+1/16=7/16 So all pipes will fill the tank in 2.3 hours. Option D #### D QUESTION:1/2+[(2/33/8)+4]-7/16= options: A)29/16 B)19/16 C)69/16 D)9/13 E)0 SOLUTION:1/2+[(2/33/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C #### C QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability G that the first ball picked up is odd numbered? options: A) 0 B) 1/3 C) 1/2 D) 2/3 E) 1 SOLUTION:Answer-D Selecting the balls either Even or Odd is having probability 50/100=1/2 We have already selected 3 balls with 2 odd numbers and 1 even number. So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability G is 2/3.D #### D QUESTION:The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range: options: A)30 < x < 36 B)30 < x < 37 C)31 < x < 37 D)31 < x < 38 E)32 < x < 38 SOLUTION:f(n) = number of perfect squares less than n 1,4,9,16,25,36 f(25) = 4 f(26)=f(27)=...=f(35)=f(36) = 5 f(37) = 6 g(n) = number of prime numbers less than n 2,3,5,7,11,13,17,19,23,29,31,37 g(31)=10 g(32)=g(33)=...=g(36)=g(37) = 11 g(38)=12 f(x)+g(x)=16 implies that f(x)=5 and g(x)=11. So, x = 32,33,34,35,or36. Answer C, 31 < x < 37. #### C QUESTION:If 40% of a number is 16, then the number is options: A)number is 60 B)number is 70 C)number is 90 D)number is 40 E)None of these SOLUTION:Solution: Let "a" be the number we seek. We get 40% × a = 16 2 × 40% × a = 2 × 16 = 32 80% × a = 32 10% × a = 32 : 8 = 4 100% × a = 4 × 10 = 40 a = 40 Answer D #### D QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.49 C)Rs.4082.48 D)Rs.4082.40 E)Rs.4082.13 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer: D #### D QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:If an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)7168 SOLUTION:0.72^10=0.71024=716.8 The answer is E. #### E QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science? options: A)52 B)65 C)115 D)158 E)168 SOLUTION:Given, boys and girls are in the ratio of 7 : 6, So, Number of boys = 7/13 x 390 = 210 Number of girls = 390 - 210 = 180 Students studying Arts and Science are in the ratio of 3 : 7, Number of students studying Arts = 3/10 x 390 = 117 Number of students studying Science = 390 - 117 = 273 Also boys and girls studying Arts are in the ratio of 4 : 5, Number of boys studying arts = 4/9 x 117 = 52 Number of boys studying science = 210 - 52 = 158 ANSWER:D #### D QUESTION:A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 15% less than B, and C costs 20% less than A,and D costs 25% less than C what percent of B's cost is D? options: A)40% B)38% C)44% D)46% E)51% SOLUTION:Soln:- B=100 A 15% less than B = 85 C 20% less than A = 68 D 25% less than C = 51 D is what percent of B = D/B * 100 = 51/100 * 100 = 51% ANSWER:E #### E QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)150 B)100 C)280 D)360 E)496 SOLUTION:Explanation: Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 +2/3 of 48 80/100x=80 x=100 Answer: B #### B QUESTION:19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each for the dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total money spent by them? options: A)Rs1628.40 B)Rs1536 C)Rs1492 D)Rs1498 E)none of these SOLUTION:(1379)+(6(x+4)) = 19x 1027 + 6x + 24 = 19x 1051 = 13x x = 1051/13 total money = 19x = 1536 ANSWER:B #### B QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B? options: A)96 B)75 C)48 D)25 E)12 SOLUTION:.24 of B = Remainder .24 of B = 18 B = (18100) / 24 = 75. B #### B QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers? options: A)121 B)133 C)145 D)150 E)165 SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by x + (x + 4) 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131 "The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131 Solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 As an exercise, check that the sum of the first and third is 131 less than three times B #### B QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:Which of the following is a prime number ? options: A)33 B)81 C)97 D)93 E)none SOLUTION:Clearly, 97 is a prime number #### C QUESTION:Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? options: A)Rs.21.60 B)Rs.21.68 C)Rs.21.18 D)Rs.21.98 E)Rs.21.29 SOLUTION:Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000 He lend the same amount for C.I at 6% p.a. for two years. => Siddharth's income = C.I - S.I = p[1 + r/ 100]n - p - pnr/100 = p{ [1 + r/ 100]2 - 1 - nr/100 = 6,000{ [1 + 6/100]2 - 1 - 12/100} = 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12) = 6,000 (0.0036) = 6 * 3.6 = Rs.21.60 Answer: A #### A QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? options: A)21.4 sec B)77 sec C)25 sec D)18 sec E)17 sec SOLUTION:D = 100 + 150 = 250 S = 42 * 5/18 = 11.7 mps T = 250/11.7 = 21.4 sec Answer:A #### A QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 * 6 = 6. Answer:C #### C QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D QUESTION:Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible? options: A)10 B)25 C)126 D)252 E)630 SOLUTION:With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward.... 10C5 = 10!/(5!5!) = 256 possible groups of 5 Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default. The 'twist' is that the two teams of 5 can "show up" in either order: For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J ABCDE vs. FGHIJ is the SAME match-up as.... FGHIJ vs. ABCDE So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2. Final Answer:C #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36. options: A)5 B)4 C)12 D)32 E)35 SOLUTION:First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7. Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc and n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above) Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form n = 5a + 1 and n = 7b + 3 Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10. Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4) Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36 A #### A QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pir^2h Volume of a sphere = 4piR^3 / 3 94piR^3 / 3 = pir^2h R^3 = r^2h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:Several people are sitting around a round table playing a card game with a deck of 67 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table? options: A)4 B)5 C)7 D)11 E)13 SOLUTION:Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 67/n has a remainder of 1 and so 67-1 = 66 is a multiple of n. The answer is D. #### D QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction? options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40 SOLUTION:x / (1/18) = (2/5) / (7/9) x = 291 / 1857 = 1/35 The answer is D. #### D QUESTION:The ages of two person differ by 12 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively options: A)30, 10 B)25, 5 C)29, 9 D)50, 30 E)20, 8 SOLUTION:Let their ages be x and (x + 12) years. Then, 5(x - 5) = (x + 12 - 5) => 4x = 32 =>x =8 Their present ages are 20 years and 8 year. ANSWER:E #### E QUESTION:A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap? options: A)7203 B)2403 C)3603 D)4803 E)5803 SOLUTION:LCM of 16, 20, 25, 45 = 3600 1 * 3600 + 3 = 3603 not divisible by 21 2 * 3600 + 3 = 7203 is divisible by 21 ANSWER:A #### A QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/3 B)2/11 C)4/13 D)5/13 E)5/14 SOLUTION:Here, n(S) = 52 There are 13 cards of diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:If xy not equal 0 and x^2y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)100]%=50% Answer A) 50. #### A QUESTION:Find the simple interest on Rs.300 for 9 months at 6 paisa per month? options: A)142 B)152 C)162 D)172 E)182 SOLUTION:I = (30096)/100 = 162 ANSWER:C #### C QUESTION:x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true? options: A) x + y > 4 B) xy>1 C) x/y + y/x < 1 D) (x - y)^2 > 0 E) None of the above SOLUTION:Answer is B: 1/X + 1/Y < 2 The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y. So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time. Another way of putting it is: XY>1.B #### B QUESTION:Find the smallest four-digit number which is a multiple of 112. options: A)896 B)1008 C)1120 D)1024 E)None of these SOLUTION:The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104. 112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112. ANSWER:B #### B QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)287 m B)704 m C)278 m D)298 m E)286 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 115=55 Answer : B #### B QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a quarter of its new value. What is the stock's value at the end of Monday? options: A)X. B)3X/8. C)2X/3. D)X/3. E)X/4. SOLUTION:Stock value= X AT sunday end= x+.5X= 1.5 X On monday the value drop to 1/4rd of its value on sunday 1.5x/4= 3X/8 B is the answer #### B QUESTION:Fourthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? options: A) 60 B) 70 C) 100 D) 120 E) 140 SOLUTION:40% of the members have passed the test, thus 60% have not passed the test. We also know that 30+12=42 members have not passed the test, thus 0.6Total=42 --> Total=70. Answer: B. #### B QUESTION:Which of the following is equal to 3.14 x 10^6) ? options: A)3.14 B)3140000 C)31400 D)314 E)314000 SOLUTION:= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is B. #### B QUESTION:Helen went to the stationers and bought things worth Euro 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Euro 15 B)Euro 15.7 C)Euro 19.7 D)Euro 20 E)None SOLUTION:Explanation: Let the amount taxable purchases be Euro x. Then, 6% of x = 30/100 x = (30/100 x 100/6) = 5. Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70 Answer: Option C #### C QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 409/40 = 9 seconds. Answer: C #### C QUESTION:Which of the following equations represents a line that is perpendicular to y=1/2x+3? options: A)y−2x=8 B)2x+4y=10 C)3y+6x=12 D)4y−8x=16 E)5x−10y=20 SOLUTION:For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2 Answer: E #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D <<<Examples ends QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 = options: A)7 B)11 C)14 D)17 E)20 SOLUTION:but you cannot take xy+ 3 to mean xy=-3.. only if xy+3=0, it will mean xy=-3.. rest your solution is perfect and you will get your correct answer as 13-2*3=7.. Answer A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur? options: A)17 B)21.25 C)12.25 D)14.05 E)18 SOLUTION:radius=7mm. So dia= 14mm. putting D=14 in equation we can easily calculate t=21.25 ANSWER:B #### B QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)(White / Total Coins) = (Blue / Total Coins) í.ẹ. RedWhite = BlueTotal Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a * 3b = 3c3(a+b+c) í.ẹ. ab = c(a+b+c) For smallest values of a, b and c 23 = 1(1+2+3) í.ẹ. Minimum Total Coins = 3(1+2+3) = 15 Answer: Option C #### C QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)100 / Initial Value % Reduction= (Reduction in Price)100 / Initial Value i.e. % Reduction= (350)100 / 500 = 70% Answer: Option A #### A QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is: options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these SOLUTION:Explanation: Let the thickness of the bottom be x cm. Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000 => 320 × 250 × (160 - x) = 8000 × 1000 => (160 - x) = 8000×1000/320= 100 => x = 60 cm = 6 dm. Answer: B #### B QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)7 D)82 E)43 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 = options: A)7 B)11 C)14 D)17 E)20 SOLUTION:but you cannot take xy+ 3 to mean xy=-3.. only if xy+3=0, it will mean xy=-3.. rest your solution is perfect and you will get your correct answer as 13-23=7.. Answer A #### A QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 4x+ 4y > 4z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 4x+ 4y > 4z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected? options: A)1/7 B)2/7 C)3/7 D)4/7 E)5/7 SOLUTION:P(A)=1/7 P(B)=1/5 P(A’)=6/7 P(B’)4/5 Required probability= P((A and B’) or ( B and A’)) =(1/7x4/5)+(1/5x6/7) =2/7 ANSWER B 2/7 #### B QUESTION:If both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n? options: A)15 B)45 C)75 D)125 E)150 SOLUTION:(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10). Thus n must include at least 3 * 5 = 15 The answer is A. #### A QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B? options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above SOLUTION:et ratio of A and B be 6x & 7x so net loss = 6x+7x= 7800 x=600 A=6x=6(600)=3600 B= 7x=7(600)=4200 so, B= 4200 ANSWER:A #### A QUESTION:When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 48) 4n = 4(6) =24, which leaves a remainder of 0 when divided by 8. Answer A #### A QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.) options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360 SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit. OR For every $1 loss in the benefit, the recipient earns $3 above $9360 If earning is; 9360+3x Benefit = 12000-x Or the vice versa If benefit is 12000-x, the earning becomes 9360+3x He lost 50% of the benefit; Benefit Received= 12000-0.5512000 = 12000-6600 x=5400 Earning becomes 9360+3x=9360+35400=25560 Ans:C #### C QUESTION:In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1200 employees, then the no. of female employees who are computer literate ? options: A)504 B)674 C)672 D)960 E)None SOLUTION:Solution: Total employees, = 1200 Female employees, 60% of 1200. = (60 1200) /100 = 720. Then male employees, = 480 50 % of male are computer literate, = 240 male computer literate. 62 % of total employees are computer literate, = (62 1200) /100 = 744 computer literate. Thus, Female computer literate = 744 - 240 = 504. Answer: Option A #### A QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ? options: A)30 points B)20 points C)10 points D)12 points E)None of these SOLUTION:Solution A : B = 60 : 45 and A : C = 60 : 40. ∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80 ∴ B can give C 10 points in a game of 90. Answer C #### C QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:If x is less than y by 25% then y exceed x by: options: A)33.33% B)25% C)75% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)100) where x is Percentage decrease (here it is 25%) => 25(100-25)100 =33.33% ANSWER:A #### A QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 250 + 120 = 370 m. Time taken = 370/10 =37 sec. Answer: A #### A QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)288 B)165 C)881 D)1277 E)121 SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 25 = 375 m. Let the length of the platform be x m . Then, (x + 375)/36 = 15 => x = 165 m. Answer: B #### B QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/21/5+x/21/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer: D #### D QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train? options: A)230 m B)250m C)643m D)832m E)270m SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then, x + 270/26 = 20 x + 270 = 520 x = 250. Answer:B #### B QUESTION:John bought 2 shares and sold them for $98 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-98 20-? $18 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-98 20-? $22 loss on the sale of 1 share. 18-22=Loss of $4 Answer: C #### C QUESTION:If 15% of a class averages 100% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 63% on the test, what is the overall class average? (Round final answer to the nearest percent). options: A)76% B)77% C)78% D)79% E)80% SOLUTION:This question is a Weighted Average question with a series of dependent variables. The remaining portion of the class represents 100% - 15% - 50% = 35% of the class Converting the portions of the class population to decimal weights, we find: Class Average = 0.15x100 + 0.50x78 + 0.35x63 = 76.05 The class average (rounded) is 76% Final Answer A) 76% #### A QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail? options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27 SOLUTION:Probability of getting least one tail at the coin tossed five times. = There is not even a single tail. = 1/32 ; P(T) = 1 - 1/32 = 31/32 ANSWER B #### B QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C QUESTION:There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen? options: A)2 B)3 C)14 D)16 E)20 SOLUTION:60% of 30 = 18. So, there are 18 red socks and there are 12 blue socks. Check out this possible cases once we have selected TWO socks: case a: 2 red socks, in which case we have a pair of matching socks. DONE! case b: 2 blue socks, in which case we have a pair of matching socks. DONE! case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet. Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock. If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock. In both cases, we are guaranteed to have a pair of matching socks. So, selecting 3 socks guarantees that we have a pair of matching socks. ANSWER:B #### B QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500(1+(4/100)2] = Rs (7500 (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:M and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is: options: A)35000 B)40000 C)50000 D)60000 E)None SOLUTION:Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000. Answer C #### C QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of canoes. Then 2x/3 is the number of kayaks. 12x+(2x/3)18=504 12x+12x=504 24x=504 x=21 (canoes) 2x/3=14 (kayaks) There were 21-14 = 7 more canoes rented out. The answer is C. #### C QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? options: A)13 B)7 C)25 D)20 E)10 SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y be the green marble,z be the blue marble... x+y=15 y+z=13 x+z=12 solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7 ANSWER:B #### B QUESTION:Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete? options: A)ab/(a+b) B)(a-b)/(a+b) C)b/(b+a) D)a/(a+b) E)b/(a-b) SOLUTION:Randy can do the job in a hrs, Alvin can do the job in b hrs. When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin. Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b) So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work. Answer (C). #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 18/5 = 60 km/hr. Answer:C #### C QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph Total distance to be covered = 333 miles. Time taken would be: 333 miles/111 mph = 3 hours C is the answer. #### C QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? options: A)11 s B)10 s C)8 s D)12 s E)None of these SOLUTION:We know from the formula Time = Distance/ Speed Thus, Time = 120/ 54 x 5/18 or, Time = 8 sec. ANSWER:C #### C QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 60, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement. options: A)K+35 B)2K+35 C)(60+K)/2 D)(70-K)/2 E)2(70-K) SOLUTION:Say Sue was hired when she was already 60 years old (k=60), then she could retire right away, at the age of 60. Now, plug k=60 in the answer choices and see which yields 60. Only C fits. Answer: C. #### C QUESTION:A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls? options: A)1/12 B)5/36 C)1/9 D)1/3 E)17/36 SOLUTION:no. of possible outcomes = 66 = 36 no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) ) So, the probability = 1/9 (Option C) #### C QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 812=96 five-minute intervals, thus total of 9630 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=9630 --> x=2430 and 3x=3(2430)=2490. Therefore, the total revenue from ticket sales that day was 24306+249010=$25,920. Answer: B. #### B QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd? options: A) 1/2 B) 2/3 C) 3/4 D) 4/7 E) 5/8 SOLUTION:All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even. There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd. Therefore the probability that A + K is odd is 4/7. Answer: D. #### D QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:Two numbers are less than third number by 35% and 37% respectively. How much percent is the second number less than by the first options: A)8% B)10% C)33% D)41% E)42% SOLUTION:Let the third number is x. then first number = (100-35)% of x = 65% of x =65x/100 Second number is (63x/100) Difference =65x/100 - 63x/100 = x/50 So required percentage is, difference is what percent of first number (x/50 100/65x * 100 )% = 33% ANSWER :C #### C QUESTION:In the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r = options: A)6 B)5 C)4 D)3 E)2 SOLUTION:An easy way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units (both points are on y=-1 line so the distance will simply be 1-(-2)=3) So the radius must be more than 3 units. The distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units (both points are on x=-2 line so the distance will simply be 4-(-1)=5) So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4. Answer: C. #### C QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION:Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed) options: A)60 B)75 C)65 D)55 E)45 SOLUTION:There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and 4 ways respectively. Required number of numbers =3x5x4=60. Ans: A #### A QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x â€“ 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? options: A)720 B)760 C)680 D)780 E)880 SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is 10 x 9 x 8 = 720 ANSWER:A #### A QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:If 3log(45^2) = x, find x options: A)5 B)6 C)7 D)8 E)9 SOLUTION:3(log2^25^2)=x 3log(52)^2=x 32log(52)=x 6log10=x log10 base 10=1 so 61=x x=6 ANSWER:B #### B QUESTION:What Is The Next Number 12 13 15 17 111 113 117 119 ? options: A)123 B)220 C)129 D)428 E)224 SOLUTION:123. These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1 Answer : A #### A QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:A car travels first 160 km at 75 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour? options: A)71.11 B)71.12 C)71.1 D)71.17 E)77.42 SOLUTION:Car travels first 160 km at 75 km/hr Time taken to travel first 160 km = distancespeed=160/75 Car travels next160 km at 80 km/hr Time taken to travel next 160 km = distancespeed=160/80 Total distance traveled = 160+160=2×160 Total time taken = 160/75+160/80 Average speed = Total distance traveled/Total time taken=320/(160/75+160/80)=77.42 km/hr Answer:E #### E QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)53 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:B #### B QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill? options: A)1/5 B)1/3 C)2/7 D)3/5 E)3/11 SOLUTION:1/10 + 1/15 = 1/6 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 B #### B QUESTION:A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6. Answer: B. #### B QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? options: A)5/6 B)5/9 C)5/3 D)5/0 E)5/1 SOLUTION:No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4 = 120 favourable cases. The total cases are 6 * 6 * 6 = 216. The probability = 120/216 = 5/9. Answer: B #### B QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)52% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16 so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52% ANSWER:D #### D QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE SOLUTION:Solution: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000. => 3x = 36000. => x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. So A's share = Rs. (35000 x 21/50) = Rs. 14,700. Answer: Option D #### D QUESTION:Find a sum for first 12 prime no's from number series? options: A)190 B)178 C)197 D)189 E)100 SOLUTION:Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197 Note: 1 is not a prime number Option C #### C QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:Nirmala gains 10% by selling her bicycle for a certain price. If she sells it at 2 times the price, the percentage of profit will be : options: A)130% B)140% C)160% D)120% E)None of these SOLUTION:Explanation : Solution: Let C.P =Rs. x. then, S.P. = Rs. (110% of x) = Rs. 11x/10. New S.P. = Rs. (211x/10) =Rs. 22x/10. profit = Rs. (22x/10 - x) = Rs. 6x/5. .'. Profit% = (6x/5 1/x 100) = 120%. Answer : D #### D QUESTION:In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) options: A)1:2 B)3:5 C)1:1 D)3:7 E)2:4 SOLUTION:C 1:1 This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up. Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method. Number of girls = 0(Probability of 0 girls) + 1(Probability of 1 girl) + 2(Probability of 2 girls) + … Number of girls = 0(C1/2) + 1(C1/21/2) + 2(C1/21/21/2) + … Number of girls = 0 + C/4 + 2C/8 + 3C/16 + … Number of girls = C (using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms) The proportion of boys to girls is 1 : 1. #### C QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)45% C)32% D)40% E)28% SOLUTION:answer b male-employed - 64% female-employed-19% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 19/64 =28 E #### E QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Monday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Tuesday, Monday C)Thursday, Monday D)Monday, Friday E)none SOLUTION:Rajat returned on Monday -i.e. 3 days earlier so actual day to return home is Thursday. Rohit returned after days so Monday ANSWER:C #### C QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43 SOLUTION:P(1st ball is even) = 9/18 P(2nd ball is also even) = 8/17 P(both balls are even) = 9/18 * 8/17 = 4/17 The answer is B. #### B QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:A regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ? options: A)48 degrees B)54 degrees C)67.5 degrees D)84 degrees E)108 degrees SOLUTION:its a regular pentagon so divide the globe by 8. = 360/8 = 45 45 would be the angle at O. Angles at A and B are equivalent, so 45 + 2x = 180 2x = 135 x = 67.5 Angles OAB and OBA will be 67.5 degrees each. C #### C QUESTION:A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? options: A)76 sec B)89 sec C)87 sec D)95 sec E)16 sec SOLUTION:Speed = 360/30 = 12 m/sec. Required time = (360 + 780)/12 = 95 sec. Answer:D #### D QUESTION:A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $18 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item? options: A)$25 B)$26 C)$27 D)$28 E)$29 SOLUTION:Let x be the price that buyers see online. The distributor wants to receive 1.2(original price) which should be 80% of x. 1.2(18) = 0.8x x = 1.2(18) / 0.8 = 1.5(18) = $27 The answer is C. #### C QUESTION:Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock? options: A)60 miles B)70 miles C)90 miles D)120 miles E)400 miles SOLUTION:Answer = B. 70 miles Relational speed = 130 - 100 = 30 miles per hour In 3 hours, difference = 30 * 3 = 90 miles Fast train trailing 20 miles, so effective difference = 90 - 20 = 70 miles #### B QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages. options: A)20,35,45 B)8,20,28 C)16,28,36 D)16,28,46 E)None of these SOLUTION:Let the present ages of three persons be 4K,7K and 9K respectively. (4K - 8) + (7K - 8) + (9K - 8) = 76 20K = 100 K = 5 Therefore, then present ages are 20,35,45. ANSWER:A #### A QUESTION:A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? options: A)676 B)833 C)1023 D)839 E)1035 SOLUTION:Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted. Hence, the required number of ways = 45 - 1. = 210 - 1 = 1024 - 1 = 1023 Answer:C #### C QUESTION:The sum of three consecutive numbers is 87. The greatest among these three numbers is : options: A)22 B)24 C)26 D)30 E)44 SOLUTION:Sol. Let the numbers be x, x + 1 and x + 2. Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28. Greatest number = (x + 2) = 30. Answer D #### D QUESTION:On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000? options: A)15 B)16 C)18 D)20 E)24 SOLUTION:5,000(1 + x)^10 = 20,000 (1+x)^10 = 4 = 2^2 (1+x)^10 = ((1+x)^5)^2 = 2^2 Therefore, (1+x)^5 = 2 5000(1 + x)^n = 40,000 (1+x)^n = 8 (1+x)^n = 2^3 (1+x)^n = ((1+x)^5)^3 = (1+x)^15 Therefore, n = 15. The answer is A. #### A QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)12 B)50 C)87 D)26 E)12 SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer: B #### B QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:0.[u]225[/u = 0.225225225..... Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5. Answer E #### E QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Let the number of hens be x and the number of cows be y. Then, x + y = 48 .... (i) and 2x + 4y = 140 x + 2y = 70 .... (ii) Solving (i) and (ii) we get: x = 26, y = 22. The required answer = 26. Option E #### E QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4% ANSWER:B #### B QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? options: A)229 B)108 C)278 D)72 E)112 SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: D #### D QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies. Answer: C. #### C QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63 SOLUTION:Required probability = 1 - 1/126 = 125/126 ANSWER:C #### C <<<Examples ends QUESTION:There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly then what is the probability that neither blue nor green? options: A)2/21 B)3/31 C)4/17 D)3/19 E)probability=8/21 SOLUTION:Total number of balls = (8 + 7 + 6) = 21 Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/21. #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers){(n-1)!(111...........n times)-(n-2)!(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!(11111)-(5-2)!1111} = 10{(4!11111)-(3!1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)123 B)143 C)166 D)190 E)210 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7 SOLUTION:Total number of balls = 8+3 = 11 number of white balls = 8 Probability = 8/11 = 8/11 Answer is C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)49 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 140 / 20 = 7 sandwiches in one part For bologna we have 7 parts so: 7 7 = 49 Answer is E #### E QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:A train 350 m long passed a pole in 35 sec. How long will it take to pass a platform 650 m long? options: A)100 sec B)89 sec C)85 sec D)16 sec E)15 sec SOLUTION:Speed = 350/35 = 10 m/sec. Required time = (350 + 650)/10 = 100 sec. Answer: A #### A QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:The price of a T.V. set worth Rs. 30000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)22678 B)26699 C)29000 D)19000 E)26711 SOLUTION:Money paid in cash = Rs. 1000 Balance payment = (30000 - 1000) = Rs. 29000 Answer: C #### C QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)5:4 B)4:5 C)2:5 D)5:2 E)None of them SOLUTION:Let the third number be x. Then, first number = 120% of x = 120x/100 = 6x/5 Second number = 150% of x = 150x/100 = 3x/2 Therefore, Ratio of first two numbers = (6x/5 : 3x/2) = 12x : 15x = 4 : 5. Answer is B. #### B QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n? options: A)37 B)123 C)41 D)52 E)87 SOLUTION:123 is 3 * 41, so n needs to be at least 41, so the answer is C. #### C QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 * 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station? options: A)A)9KM B)B)6.66KM C)C)7.25KM D)D)12.40KM E)E)13KM SOLUTION:Since time differences given are in minutes so let's convert speed in Km per minute 8 kmph = 8/60 km per minute = (2/15) km per minute 10 kmph = 10/60 km per minute = (1/6) km per minute Let, Time of train to depart from station = t minutes Distance between Point E and Railway Station = SpeedTime = (2/15)(t+5) Distance between Point E and Railway Station = SpeedTime = (1/6)(t-5) i.e. (2/15)(t+5) = (1/6)(t-5) i.e. 12t+60 = 15t - 75 i.e. 3t = 135 i.e. t = 45 minutes i.e. Distance = (1/6)(t-5) = (1/6)(45-5) = 40/6 = 20/3 Km = 6.66 Km Answer: Option B #### B QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)205 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 * 8 * 4) = 160. Therefore, 160 * 2.40 + x * 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER:B #### B QUESTION:A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers Q are possible? options: A)2 B)4 C)6 D)3 E)Not possible SOLUTION:Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a3^b5^c. Also, (a+1)(b+1)(c+1) = 32. We can break down 32 into 3 integers as : 228 or 442 Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of Q= 6 possibilities. C. #### C QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 5 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10 So, 10-5 = 5 Answer A #### A QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is: options: A)260 B)262 C)270 D)272 E)None of these SOLUTION:Explanation: Volume will be length * breadth * height, but in this case two heights are given so we will take average, Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3 Option C #### C QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:What is the smallest positive integer x, such that 6000x is a perfect cube? options: A)4 B)6 C)36 D)12 E)18 SOLUTION:Take out the factors of 6000 that will come 2310^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2 C is the answer. #### C QUESTION:A grocer buys apples for 63¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price? options: A)66¢ B)70¢ C)75¢ D)77¢ E)84¢ SOLUTION:for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total . 10% apples lost...means 9 pounds left. further he wants 20% profit on 630 ¢ means he wants to earn 756¢ sales price should be 756/9==¢ 84 ANSWER:E #### E QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pir^2h Volume of a sphere = 4piR^3 / 3 94piR^3 / 3 = pir^2h R^3 = r^2h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14 years B)18 years C)20 years D)22 years E)16 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 24) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :B #### B QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day? options: A)10 B)15 C)20 D)25 E)None of them SOLUTION:Let the required number of days be x. More men, Less days (indirect proportion) Less hours per day, More days (indirect proportion) Men 18 : 15 Hours per day 8: 9 } : :16 : x (18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15 Hence, required number of days = 15. Answer is B. #### B QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 205 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)7 D)12 E)32 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 36 + 40 + 10 - (12) - 2x x = 7 So, answer will be C #### C QUESTION:In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn? options: A)2/3 B)1/3 C)1/4 D)1/6 E)2/5 SOLUTION:You can simply use sets concept in this question. The formula Total = n(A) + n(B) - n(A and B) is applicable here too. Set 1: Number 1 or larger Set 2: Number 15 or smaller 1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both) 2/3 + P(Set 2) - 1/3 = 1 P(Set 2) = 2/3 Answer A #### A QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:The area of a triangle is with base 4m and height 5m? options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2 SOLUTION:1/2 4 * 5 = 10 m2 Answer:B #### B QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest? options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years SOLUTION:Explanation: Time = (100 x 60)/(400 x 12) years = 1.25 years. Answer: D #### D QUESTION:Find the odd man out 864, 420, 200, 93, 40, 16, 6 options: A)420 B)200 C)16 D)93 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. 93 ANSWER:D #### D QUESTION:What number has a 3:4 ratio to the number 400? options: A)130 B)100 C)200 D)300 E)120 SOLUTION:3:4 = x: 200 4x = 3400 x=300 ANSWER:D #### D QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P20R)/100 R = 5% ANSWER:E #### E QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:The ratio of two quantities is 2 to 3. If each of the quantities is increased by 4, what is the ratio of these two new quantities? options: A)5/5 B)It cannot be determined from the information given. C)11/5 D)12/5 E)13/5 SOLUTION:let the actual ratio be 2k/3k, increase numerator and denominator by 4=> 2k+4/3k+4 Until the value of k is unknown we can not determine the actual ratio. OR let the actual be 3/4. After increasing 4 => 7/8 let the actual be 6/8. After increasing 4 => 10/12 Therefore without actual quantities we cannot determine the actual ratio. Answer : B #### B QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 12 =420 Answer: D #### D QUESTION:If 18!/3^x is an integer, what is the greatest possible value of x? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:18 - 332 15 - 53 12 - 43 9 - 33 6 - 23 3 - 13 Hence max of 3^8 is allowed. IMO E. #### E QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:If p and q are two different prime numbers, which of the following cannot be true? options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer SOLUTION:A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q). Answer: E. All other options are possible: A. pq is odd --> p=3 and q=5; B. p + q is even --> p=3 and q=5; C. p + q is odd --> p=2 and q=3; D. pq is even --> p=2 and q=3; E #### E QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y? options: A)560 B)616 C)672 D)728 E)784 SOLUTION:ans B 616... remainders = .32=32/100=8/25=16/50 and so on.. so two digit remainders are 16+24+32+....+96.. W=8(2+3+4....+12)=616 #### B QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is? options: A)1/50 B)1/13 C)1/26 D)1/52 E)1/4 SOLUTION:Probability of a spade = 13/52 = 1/4 Probability of a jack = 4/52 = 1/13 Probability of both = P1P2 = 1/(413) = 1/52 Answer is D. #### D QUESTION:Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ? options: A)12 B)15 C)25 D)30 E)35 SOLUTION:Explanation : The clocks make sound at intervals of 8, 10 and 12 minutes respectively. The LCM of 8,10 and 12 is 120. So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours. In 2 days(48 hours), they will make the sound together (48/2) = 24 times. At the end of 2nd day, they will make one more beep together. Therefore, totally (24+1) 25 times beep sound is made together. Hence the answer is 25 times. Answer : C #### C QUESTION:$500 will become $1000 in 6 years find the rate of interest? options: A)A)16.67% B)B)20% C)C)25% D)D)30% E)E)50% SOLUTION:SI = simple interest = A-P = 1000-500 = $500 R = 100SI/PT = 100500/5006 =16.67% Answer is A #### A QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final100 =21/121100=8/33100=17% approxiamately. option A is correct. #### A QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:A- B = 120 Miles B - C = 60 Miles Avg Speed = 45 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 45 = 180/4t t = 60 B-C = 60 mph Answer E #### E QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:8^100 is divisible by 17. Find the remainder? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? options: A)2267 B)287 C)268 D)228 E)225 SOLUTION:1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = 1/6 15 women's 1 day work = (1/6 - 10/100) = 1/15 1 woman's 1 day work = 1/225 1 woman alone can complete the work in 225 days. Answer: E #### E QUESTION:The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again? options: A)16:00. B)18:00. C)20:00. D)22:00. E)24:00. SOLUTION:Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10 If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours Answer A #### A QUESTION:There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)s. 99.75 B)s. 89.75 C)s. 72.75 D)s. 58.75 E)s. 49.75 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1 or, 35x + 42 = 39x – 39 or, x = 20.25 Thus the original expenditure of the mess = 35 x 20.25=708.75 Therefore x-1 = 19.25 hence 42 x 19.25 = 808.50 808.50 - 708.75 = Rs. 99.75 A #### A QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 54321 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 321 = 6ways Now, arrange all with the boys together 1206 = 720ways ANSWER:D #### D QUESTION:A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment? options: A)$503 B)$504 C)$505 D)$506 E)$507 SOLUTION:Explanation: Cash price = $21 000 Deposit = 10% × $21 000 = $2100 Loan amount = $21000 − $2100 = $18900 I=prt/100 I=11340 Total amount = 18900 + 11340 = $30240 Regular payment = total amount /number of payments Answer: B #### B QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500? options: A)Rs. 5870 B)Rs. 5991 C)Rs. 8870 D)Rs. 6850 E)None of these SOLUTION:Explanation: Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130 Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870 ANSWER C #### C QUESTION:In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate? options: A)358000 B)368000 C)357000 D)358000 E)367000 SOLUTION:Total number of invalid votes = 15 % of 560000 = 15/100 × 560000 = 8400000/100 = 84000 Total number of valid votes 560000 – 84000 = 476000 Percentage of votes polled in favour of candidate A = 75 % Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000 = 75/100 × 476000 = 35700000/100 = 357000 Answer:C #### C QUESTION:A contest will contain n questions each of which is to be answered either true or false. Anyone who answers all n questions correctly will be a winner what is the least value of n for which the probability is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner? options: A)5 B)10 C)50 D)100 E)1000 SOLUTION:The probability that a person will randomly guess all nn questions correctly is 1/2n1, so we want the value of nmin for which 1/2n<1<11000 --> 2n>1000 as nn is an integer nmin==10 (2^10=1024>1000). Answer: B. #### B QUESTION:The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number? options: A)40 B)50 C)65 D)70 E)90 SOLUTION:Let the original # be x then 1.25x−0.7x=22 --> x=40 Answer: A. #### A QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(90033)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours. What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). options: A)1 hour B)2 hour C)3 hour D)4 hour E)5 hour SOLUTION:In one hour, Soln 1: the large inlet tube fills 1 / 3 of the tank; the small inlet tube fills 1 / 6 of the tank; the outlet tube empties 1 / 9 of the tank; and therefore all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. Soln 2: Let V be the total volume of the tank. From equation (1), Flow Rate (large inlet tube) = V / 3 Flow Rate (small inlet tube) = V / 6 Flow Rate (outlet tube) = V / 9. Substituting in equation (2), Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9). Using the above result in equation (1), Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ]. Note that V cancels out on simplifying the above expression. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. #### A QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10? options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18 SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once. There are 66=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12. D #### D QUESTION:We have 8 people and 5 chairs. In how many ways chairs can be occupy? options: A)1200 B)1450 C)1680 D)1912 E)900 SOLUTION:no. of ways they can be occupy = 8765 = 1680 Answer is C #### C QUESTION:How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest? options: A)2 years B)3 years C)1 year D)4 years E)5 years SOLUTION:Explanation: P = Rs.900 SI = Rs.81 T = ? R = 4.5% T= (100×SI)/PR = (100×81)/(900×4.5) = 2 years Answer: Option A #### A QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? options: A)4 months B)5 months C)6 months D)7 months E)8 months SOLUTION:Explanation: Assume that C was there in the business for x months A:B:C =40000×12:60000×10:120000 × x =40×12:60×10:120x =40:5×10:10 x =8:10:2x =4:5:x C's share =375000 x/ 9+x=375000 x/9+x ⇒375000 x/9+x=150000 ⇒375x9+x=150 ⇒15x=6(9+x) ⇒5x=18+2x ⇒3x=18 ⇒x=6 It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined. Answer: Option A #### A QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)6620 B)9278 C)2782 D)5772 E)5286 SOLUTION:A = 20000(11/10)3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:(7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ? options: A)1 B)1 / 5 C)15 / 11 D)3 / 11 E)None SOLUTION:Answer Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = (14 + 1) / (10 + 1) =15 / 11 Option: C #### C QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%? options: A)8 B)3 C)5 D)6 E)None SOLUTION:C.P. of 9 Headphones= Rs100 S.P. of 9 Headphones = 150% of Rs 100 = Rs150 For Rs.150 , Headphones sold = 9. For Rs. 100,Pens sold=(9/150)100=6 Answer: Option D #### D QUESTION:How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%? options: A)100 ml B)60 ml C)120 ml D)130 ml E)150 ml SOLUTION:we can also go by answer choices Tke 100 ml for eg 400 (old)+100 (new concentr)ml 50026/100 = 130 ml (30ml is de old concentration +100 ml (newly added) Answer D #### D QUESTION:What was the day of the week on, 18th July, 1776? options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days. 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days) Total number of odd days = (0 + 4) = 4. Required day was 'Thursday'. Answer:A #### A QUESTION:(17)3.75 x (17)? = 178 options: A)2.29 B)2.75 C)4.25 D)4.5 E)None of these SOLUTION:Solution let (17)3.75 * (17)x = 178. then, (17)3.5 + x = (17)8. ∴ 3.75 + x = 8 ⇔ x = (8 - 3.75) ⇔ x = 4.25 Answer C #### C QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 301.5 more revolutions is 601.5 = 90 seconds. The answer is C. #### C QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? options: A)2 B)5 C)15 D)20 E)25 SOLUTION:Audery and Ferris collective Work rate: 1/4 + 1/3 = 7/12 Collective work Time = 12/7 = 1.7 Hrs Job Was actually done in = 2 (Includes breaks) Breaks = Actual time taken - Collective work time = 2 - 1.7 = .3 Hrs = 1/2 so ferrais took 6 breaks =.3/6=.06 hrs = 5 m so Answer is B) 10 mins #### B QUESTION:Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? options: A)648 B)1800 C)2700 D)10800 E)948 SOLUTION:Let the required number of bottles be x. More machines, More bottles (Direct Proportion) More minutes, More bottles (Direct Proportion) Machines 6 : 10 :: 270 : x Time (in minutes) 1 : 4 Therefore, 6 x 1 x x = 10 x 4 x 270 => x =(10 x 4 x 270) / (6) => x = 1800. Correct answer is B. #### B QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2254/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change. 240−150=90 240−150=90 Then we find out how many percent this change corresponds to when compared to the original number of students a=r⋅b a=r⋅b 90=r⋅150 90=r⋅150 90150=r 90150=r 0.6=r=60% Option E is correct. #### E QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:A car covers a distance of 630 km in 6 hours. Find its speed? options: A)105 B)7778 C)266 D)288 E)121 SOLUTION:624/6 = 105 kmph Answer:A #### A QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If the altered coffee will contain 16 grams of mate, how many grams of water does it contain after alteration? options: A)12 B)15 C)30 D)60 E)100 SOLUTION:c:m:w = 6:2:15 new c:m = 1/2(6/2) = 3:2 new c:w = 2(6:15) = 12:15 = 4:5 so new m:c:w = 2:3 4:5 = 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios) m = 16 g Let T = total amount of c + m + w then 8 / (8+12+15)T = 16 x 35/8 = 70g then w = 15/35 x 70 = 30g Answer C #### C QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 812=96 five-minute intervals, thus total of 9630 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=9630 --> x=2430 and 3x=3(2430)=2490. Therefore, the total revenue from ticket sales that day was 24306+249010=$25,920. Answer: B. #### B QUESTION:14,24,54,34,44,56,53, ? options: A)44 B)55 C)66 D)77 E)88 SOLUTION:14-24...dif -10 54-34..dif -20 44-56..dif-12 53-77...dif-24 ANSWER:D #### D QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number? options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63 SOLUTION:Let the numbers be 5x, 6x, 8x. Largest number = 8x. Smallest number = 5x. Third number = 6x. 8x + 5x = 6x + 49 7x = 49 =>x=7 6x=42=> third number is 42. Answer:D #### D QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:If a car went the first third of the distance at 80 kmh, the second third at 30 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip? options: A)36 kmh B)40 kmh C)42 kmh D)45 kmh E)50 kmh SOLUTION:Assume D/3 = 240 (this number is convenient because it is divisible by 80, 30 and 48) So: 240 = 80T1 = 3 hrs 240 = 30T2 = 8 hrs 240 = 48T3 = 5 hrs T = T1 + T2 + T3 = 16 hrs D = RT (2403) = R16 R = 45 ANSWER: D #### D QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k? options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0 SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 120 12-ounce smoothies? options: A) 120 B) 150 C) 180 D) 240 E) 600 SOLUTION:This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base? D #### D QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (4x - 2y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)I only B)I,II,III NOT TRUE C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 2y) is odd 4x - is always negative and EVEN 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always EVEN I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is B #### B QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years? options: A)2:6 B)3:5 C)1:4 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5 Answer B #### B QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the cent tossed is also a head. options: A)4/5 B)3/5 C)2/5 D)3/4 E)1/2 SOLUTION:There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent) How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin) Therefore probability = 4/5 Option A #### A QUESTION:It is required to seat 7 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)86,288 B)86,214 C)86,400 D)86,328 E)86,368 SOLUTION:Total number of candidates = 6 + 5 = 11. In the row of 11 positions, the even places are 2nd, 4th, 6th,8th,10th. Now, number of even places = 5. Number of girls to occupy the even places = 5. Even places can be filled = P (5, 5) ways. Number of boys = 6. The remaining 6 places can be filled by 6 boys = P (6, 6) ways By the fundamental principle of counting: The required number of seating arrangements P(5, 5) x P(6, 6) = 5! x 6! = 120 x 720 = 86,400 ANSWER:C #### C QUESTION:Tough and Tricky questions: Coordinate Geometry. Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L? options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices (A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need (B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong (C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong (D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong (E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong A #### A QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:If x is less than y by 45% then y exceed x by: options: A)33.33% B)25% C)81.81% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)100) where x is Percentage decrease (here it is 25%) => 45/(100-45)100 =81.81% ANSWER:C #### C QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .250+.6x=.5(50+x) x=150 Answer E #### E QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts. options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22 SOLUTION:Solution : Given SI1 = SI 2 P1 : P2 = 1/R1T1 : 1/R2T2 = 1/(105) : 1/(9:6) 27:25 B #### B QUESTION:If \|x^2 − 12\| = x, which of the following could be the value of x? options: A)-4 B)-3 C)1 D)2 E)3 SOLUTION:\|x2−12\|=x\|x2−12\|=x \|x2−12\|\|x2−12\|cannot be negative; anything that comes out of mod is always positive so \|x2−12\|>0\|x2−12\|>0 Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice \|−32−12\|=3\|−32−12\|=3 \|9−12\|=3\|9−12\|=3 \|−3\|=3\|−3\|=3 3=33=3 ANSWER IS E #### E QUESTION:Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose? options: A)5 B)8 C)11 D)15 E)17 SOLUTION:Explanation : Let a, b, c be the Englishmen and d, e, f be the Frenchmen. Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls. Answer : B #### B QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)6 kmph B)7 kmph C)9 kmph D)4 kmph E)2 kmph SOLUTION:S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A #### A QUESTION:A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 12 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:In 5 minutes, the cyclist travels a distance of (5/60)12 = 1 km. The time it takes the hiker to complete this distance is 1/4 hours = 15 minutes The cyclist needs to wait 15 - 5 = 10 minutes The answer is A. #### A QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(5251)/(21)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(2625)/(21)=325, N(B)=4C2=(43)/(21)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be: options: A)20 cm B)25 cm C)35 cm D)50 cm E)None of these SOLUTION:Explanation: Total volume of water displaced =(4 x 50) m3 = 200 m3 Rise in water level = 200/40×20= 0.25m = 25cm Answer: B #### B QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A <<<Examples ends QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A? options: A)a) 50% B)b) 53% C)c) 54% D)d) 55% E)e) 57% SOLUTION:Let total voters = 100 so D= 60, vote for the mayor 6075%=45 (603/4) R= 40, vote for the mayor 4020%= (401/5) 45+8=53 53/100100=55% D #### D QUESTION:S1 = 5 S2 = 8 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50? options: A)15 B)14 C)13 D)12 E)16 SOLUTION:term 16 = 316+4 = 52 Answer : E #### E QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph1/4hr=6.25 km total westward distance= 40kmph1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice. options: A)25 B)34 C)50 D)67 E)100 SOLUTION:A =25 1 oz concentrate + 3 oz ofwater = 4 oz jucie 300 oz concentrate +900 oz of waer = 1200 oz juice no of cans==300/12=25 Ratio of juice to water ===> 1:3 total 2006 ounces 12 ounce juice cans ==> 1200/12 == 1001/4 (ratio of jiuce to total) == 25 #### A QUESTION:hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620 options: A)22 B)12 C)14 D)16 E)None of these SOLUTION:? = 2620−256 /197=12 Answer B #### B QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are: options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186 SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62. The numbers are 62, 124, 186. ANSWER:A #### A QUESTION:In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ? options: A)30 B)45 C)42 D)72 E)75 SOLUTION:Let the number of benches in the class be x. Then, 6(x + 1) = 7x - 5 x = 11. Hence, number of students in the class = 6 ( x + 1) = 6 x 12 = 72. ANSWER:D #### D QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)22 B)30 C)48 D)99 E)12 SOLUTION:Relative speed = 90 + 30 = 120 km/hr. 120 * 5/18 = 100/3 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 3/100 = 30 sec. Answer: B #### B QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(69006)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:Harish can paint a wall in just 3 hours. However it takes 6 hours for Ganpat to complete the same job of painting the wall. How long would it take for both of them to paint the wall , if both work together ? options: A)3 Hours B)1 Hours C)3.20 Hours D)2 Hours E)1.35 Hours SOLUTION:D Two hours. Harish who could paint the wall in 3 hours could paint 2/3 of the wall in just two hours. Ganpat who paint the wall in 6 hours could paint 1/3 of the wall in two hours. 2/3 + 1/3 = 1. #### D QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)10years B)12 years C)5 years D)3 years E)24 years SOLUTION:Explanation: 9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 years Answer:D #### D QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? options: A)2400 B)2880 C)2787 D)3087 E)0728 SOLUTION:1200 12: x * 9 = 2:3 x = 2400 Answer: A #### A QUESTION:How many four letter words are formed using the letters of the word POLICE? options: A)280 B)321 C)330 D)360 E)370 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 6P4 = 6 * 5 * 4 * 3 = 360. Answer: D #### D QUESTION:The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ? options: A)76 B)29 C)26 D)19 E)11 SOLUTION:Explanation: Average = total runs / no.of innings = 32 So, total = Average x no.of innings = 32 x 10 = 320. Now increase in avg = 4runs. So, new avg = 32+4 = 36runs Total runs = new avg x new no. of innings = 36 x 11 = 396 Runs made in the 11th inning = 396 - 320 = 76 Answer: A #### A QUESTION:In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there? options: A)42 B)66 C)98 D)112 E)154 SOLUTION:Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x Total dogs and bunnies = 16x. And we are given that 16x = 352. Hence x = 22. Dogs = 3x = 322 = 66 (Option B) #### B QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 18/5 = 79.2 km/hr Answer:C #### C QUESTION:Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)326 B)372 C)375 D)381 E)312 SOLUTION:A+B+C = 1500 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1500 => 375 Answer: C #### C QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 250 + 120 = 370 m. Time taken = 370/10 =37 sec. Answer: A #### A QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h? options: A)25% B)50% C)69% D)80% E)100% SOLUTION:Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder. This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5. Original cylinder 7/8 New cylinder 3/5 So 3/5/7/8 = 3/58/7 = 0.69 or 69%. Answer C #### C QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? options: A)6 B)9 C)12 D)15 E)18 SOLUTION:2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 3024 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 3024 / 80 oxen = 9 days The answer is B. #### B QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards 10 minutes/y hards = 10x/y #### B QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West options: A)I,II only B)II,III only C)II only D)I and III only E)III only SOLUTION:It's evident if we make a diagram for the Movement of N respect to M. From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range. Thus it can only move north or west or anything in that curve. Answer : D #### D QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x 104.76/100 104.76/100 = 8840 x1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)5/18 = 45 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:The area of the maximum size of the circle described from the 10 inch square? options: A)75.5 sq inch B)76.5 sq inch C)77.5 sq inch D)78.5 sq inch E)79.5 sq inch SOLUTION:10 inch square means sides of sq are 10inch then circle is within square so diameter would be 10 inch maximum and radius is 5inch so area of the circle is = pirr=3.1455=78.5 sq inch ANSWER:D #### D QUESTION:If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w? options: A)64 B)67 C)99 D)133 E)147 SOLUTION:We have to check options 1 by 1. 64 rounded to nearest hundred = 100 64 rounded to nearest ten = 60 now difference = 40 the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. therefore 40/60)100 = 66 2/3 ==>this is the answer. 99 rounded to nearest ten = 100 133 rounded to nearest ten = 130 133 rounded to nearest hundred w= 100=A #### A QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 11030=3,300 copies. Answer: C. #### C QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:A reduction of 15% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)s.24 B)s.46 C)s.40 D)s.41 E)s.34 SOLUTION:800(15/100) = 120 ---- 5 ? ---- 1 => Rs.24 Answer: A #### A QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 109876 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 109876 / 5! = 109876 5! / (5!5!) = 10! / (5!5!) Answer: Option B #### B QUESTION:How many possible integer values are there for x if \|4x - 3\| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: \|4x-3\| < 6 let 4x=a therefore we have \|a-3\| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)14% B)23% C)30% D)50% E)100% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.410 = 14 Wage of Charles = 1.6 10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 100% = 2/14 * 100% =14% Answer A #### A QUESTION:The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number? options: A)3 B)6 C)9 D)12 E)15 SOLUTION:Sol. Let the numbers be x, x + 2 and x + 4. Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7. ∴ Middle number = x + 2 = 9. Answer C #### C QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+ SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers: L = 200 M = 10 N =20. So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans.. looking the the opion C to E, one can make out that they are incorrect, A. Out of which, i choose A. #### A QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store? options: A)36 B)54 C)72 D)90 E)101 SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18: (A) 36 = 182 (B) 54 = 183 (C) 72 = 184 (D) 90 = 185 (E) 101 = not a multiple of 18 ans is E #### E QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit. options: A)487 B)15 C)76 D)29 E)12 SOLUTION:If x is speed limit, Speed of first person = x + 10 Speed of 2nd person = x + 20 But speed of 2nd person = 35 kmph x + 20 = 35 x = 15 kmph. so speed limit is 15 kmph option D Answer: B #### B QUESTION:What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? options: A)3: 5 B)3: 9 C)3: 4 D)3: 1 E)3: 2 SOLUTION:d = 3d d = d a√2 = 3d a√2 = d a = 3d/√2 a = d/√2 => 3: 1 Answer: D #### D QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 20505=10250 10250-10000=250 Answer E #### E QUESTION:If cost of sugar increases by 50%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)33% B)50% C)20% D)90% E)60% SOLUTION:100 150 ----- 150 ----- 50 100 ------ ? => 33% Answer: A #### A QUESTION:3 Years ago, the average age of a family of 5 members was 16 years. A baby having been born, the average age of the family is the same today. The present age of the baby is options: A)1 year. B)1.5 Years. C)2 Years. D)3 Years. E)4 Years. SOLUTION:We're told that 3 YEARS AGO, the average age of a family of 5 members was 16 years. This means that the SUM of their ages was (5)(16) = 80 years. A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME. This means that the sum of the ages is (6)(16) = 96 years. We're asked for the PRESENT age of the baby. Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is... 80 + (5)(3) = 95. A #### A QUESTION:In a 8 x 8 chess board what is the total number of squares. options: A)238 B)204 C)678 D)169 E)161 SOLUTION:Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares" i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6 So Substituting 8 in the above formula we get 204 Answer:B #### B QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2â„5 Ã— 300 - 3â„5 Ã— 125 = 120 - 75 = 45 Answer D #### D QUESTION:A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time. options: A)80 B)120 C)140 D)180 E)200 SOLUTION:Upward distance traveled per hour - 15 km, distance traveled after 6 hours = 90 km. He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km (Answer : D) #### D QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:6C15C2 = 610 = 60 The answer is C. #### C QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs SOLUTION:Part filled by A in 1 hour = 1/50 part filled by B in 1 hour = 1/75 Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30 Both the pipes will together will fill the tank in 30 hours. Answer is D #### D QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3Ã—7/36 = 7/12 Remaining work = 1 â€“ 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:E = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33 SOLUTION:The total number of pairs E,B possible is 45=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2. Answer: B. #### B QUESTION:A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? options: A)288 m B)256 m C)400 m D)278 m E)287 m SOLUTION:Speed = 78 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (900 + x)/60 = 65/3 x = 400 m. Answer:C #### C QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300? options: A) 100 B) 150 C) 140 D) 200 E) 250 SOLUTION:{100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200. Answer: D. #### D QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If q of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present? options: A) y/R B) y/(R-x) C) xy/(R-x) D) qy/(R(R-q)) E) y/(R(R-x)) SOLUTION:y/(R-q)- y/R if we simplify this we get choice D, which is the correct answer. #### D QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)(5 choose 2) = 410 = 40 Jaune X = (4 choose 2)(5 choose 1) + (4 choose 3) = 65 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost? options: A)3 2/3 B)5 2/3 C)6 2/3 D)4 2/3 E)7 2/3 SOLUTION:x/10 + 2/15 + 4/20 = 1 x = 40/6010 = 6 2/3 Answer: C #### C QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:20 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)200 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 19 people 2nd person will shake hand with 18 people 3rd person will shake hand with 17 people ...... total no. of handshakes = 19+18+17+...+3+2+1 = 19(19+1)/2 = 190 or, if there are n persons then no. of shakehands = nC2 = 20C2 = 190 ANSWER:A #### A QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 11 = (5,6)(6,5)= 2 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 11 in any attempt =2/36=1/18 Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18 Probability of losing game =(17/18)(17/18)(17/18)=139/165 I.e. Probability of wining game = 1-(139/165) =26/165 Answer : Option C #### C QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 100 = 33% Answer:C #### C QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))? options: A)0 B)2 C)1 D)6 E)9 SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1. Thus, the answer is C. #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)11 B)77 C)36 D)47 E)99 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:3,8,18,38,78,__ options: A)158 B)156 C)154 D)150 E)148 SOLUTION:8=32+2 18=82+2 38=182+2 78=382+2 158=782+2 ANSWER:A #### A QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? options: A)120 B)335 C)784 D)217 E)210 SOLUTION:Let x be the number he chose, then 2x138=102 2x=240 x=120 correct answer A #### A QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? options: A)2399 B)2889 C)2830 D)2878 E)3000 SOLUTION:Explanation: 605:366:753 100: 72: 75 100/247 7410 = 3000 Answer: E #### E QUESTION:A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)235 m B)245 m C)247 m D)249 m E)252 m SOLUTION:length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = (130+x)/30 m/s = 45 × (10/36) = (130+x)/30 = 45 × 10 × 30 /36 = 130+x = 45 × 10 × 10 / 12 = 130+x = 15 × 10 × 10 / 4 = 130+x = 15 × 25 = 130+x = 375 = x = 375-130 =245 #### B QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 3.5) kg = 35 kg. Weight of new person = (65 + 35) kg = 100 kg. Answer: A #### A QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500? options: A)5000 B)5500 C)4991 D)5600 E)5700 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991 C #### C QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)17.6% E)None of these SOLUTION:Explanation: cost price = (225 + 30) = 255 sell price = 300 gain = (45/255)100 = 17.6%. Answer: D #### D QUESTION:A student scored an average of 65 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? options: A)86 B)165 C)76 D)125 E)26 SOLUTION:Given M + P + C = 65 3 = 195 --- (1) M + P = 90 * 2 = 180 --- (2) P + C = 70 * 2 = 140 --- (3) Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry. P = (2) + (3) - (1) = 180 + 140 - 195 = 125 Answer:D #### D QUESTION:If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y? options: A)3 1/13% B)3% C)3 11/13% D)4% E)None of these SOLUTION:Explanation: X = 125% Y = 130% Z = 100% X-Y/Y * 100 = 5/130 * 100 = 500/130 % = 3 11/13% smaller than Y Answer: Option C #### C QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both? options: A)975 B)1150 C)1175 D)1243 E)1525 SOLUTION:Failed in 1st subject = 342500/100 = 850 Failed in 2nd subject = 422500/100 = 1050 Failed in both = 152500/100 = 375 Failed in 1st subject only = 850-375 = 475 Failed in 2nd subject only = 1050-375 = 675 Passed in either subject but not in both = 675+475 = 1150 Answer is B #### B QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)$310 B)$395 C)$484 D)$512 E)$542 SOLUTION:4/15 A = 2/5 B A = 2/5 * 15/4 B A = 3/2 B A/B = 3/2 A:B = 3:2 B's share = 12102/5 = $484 Answer is C #### C QUESTION:In how many no. between 10 and 50 exactly Two of the digits is 5? options: A)47 B)65 C)1 D)35 E)65 SOLUTION:It's simple can be solved by elimination of answer choices. Option B and D are too large, not possible. Even AE are large to have correct choice. Ans : C #### C QUESTION:The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is : options: A)1 : 3 : 4 B)1 : 3 : 6 C)1 : 2 : 6 D)1 : 3 : 5 E)1 : 4 : 6 SOLUTION:Ratio of time taken : 1/12 :1/4 : 1/2 = 1 : 3 : 6 ANSWER:B #### B QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 23 x = 6 Answer is E #### E QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 = options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 22^7 we would have: sum=9(22^7)=182^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C. Answer: C #### C QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/42/3 = 1/6 of the attendees. Females who did not arrive on time are 1/61/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ? options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr SOLUTION:given upstream(u) =29km/hr down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr Answer is (D) #### D QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 Â½ sec B)6 Â½ sec C)9 Â½ sec D)8 sec E)7 Â½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Sandy walks 12 km in the first two hours so there are 40 km remaining. When Ed starts walking, they complete a total of 10 km per hour. They will meet four hours after Ed starts walking. Since Sandy walks for 6 hours, she walks 36 km. The answer is D. #### D QUESTION:The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is: options: A)20 B)30 C)48 D)58 E)68 SOLUTION:Explanation: Let the three parts be A, B, C. Then, A : B = 2 : 3 and B : C = 5 : 8 =53/5 : 83/5 =3: 24/5 A : B : C = 2 : 3 : 24/5=10:15:24 B = 98* 15/49 =30. Answer IS B #### B QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:A set consists of 12 numbers, all are even or multiple of 5. If 4 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 12 = 4 + 10 - {Both} + 0; {Both}=2(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: C. #### C QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 4? options: A)a. 220 B)b. 249 C)c. 432 D)d. 216 E)e. 288 SOLUTION:Taking Question with it's same language as given To make number divisible by 5, the unit digit should be either 0 or 5 only Case 1: If unit digit is fixed as zero With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15 With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120 Total Such cases = 120+15 = 135 Case 2: If unit digit is fixed as Five With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065] With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12 With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40 With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60 Total Such cases = 2+12+40+60 = 114 Total numbers = 135+114 = 216 ANSWER OPTION D #### D QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(490+x)/5=92 x=(592)-(490) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr. What is the speed of the boat? options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph SOLUTION:speed upstream = 10/3 speed of boat down stream = 10/6 speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph ANSWER:A #### A QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was? options: A)320000 B)120029 C)187899 D)178968 E)789698 SOLUTION:X (105/100) * (105/100) * (105/100) = 370440 X = 370440/1.157625 X = 320000 Answer:A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is? options: A)178 m B)240 m C)120 m D)168 m E)178 m SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 12 = 240 m. Answer: B #### B QUESTION:A furniture dealer purchased a desk for $100 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)40% B)45% C)50% D)55% E)60% SOLUTION:Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $100 but instead, 40% of Selling price which is obtained by adding mark up to $100. So if selling price is S, 100 + 40% of S = S or 100 = 0.6S therefore S = 100/0.6 = S = Profit = 100/0.6- 100 which is calculated on cost price in % terms. So 40/100 * 100 = 40% is profit. A #### A QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 1+(5/100)2 = 8000 21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 14p have. p = 3 --> 14p = 42--> 42 has 4 even divisors: 2, 6, 14, 42 . Answer: C. #### C QUESTION:A contest will contain n questions each of which is to be answered either true or false. Anyone who answers all n questions correctly will be a winner what is the least value of n for which the probability is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner? options: A)5 B)10 C)50 D)100 E)1000 SOLUTION:The probability that a person will randomly guess all nn questions correctly is 1/2n1, so we want the value of nmin for which 1/2n<1<11000 --> 2n>1000 as nn is an integer nmin==10 (2^10=1024>1000). Answer: B. #### B QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500 SOLUTION:OFFICIAL SOLUTION: The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve: 550 + (0.08)(x – 4,000) = 0.10x Distribute the 0.08: 550 + 0.08x – 320 = 0.10x Combine terms and subtract 0.08x from both sides: 230 = 0.02x Divide both sides by 0.02: 11,500 = x Your answer is A. #### A QUESTION:A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? options: A)240 B)250 C)260 D)270 E)300 SOLUTION:Let total capacity be x we know 200 = 0.50x x = 200/0.50 = 400 Prior to storm, we had 160 bn gallons 400-160 = 240 Answer : A #### A QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-2575)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:In each term of a sequence, 7 is added to get the next term. If the first term is 3, what is the thirty-seventh term? options: A) 222 B) 284 C) 252 D) 263 E) 255 SOLUTION:1rst term + 36 terms = 3 + 7+7+7+7+7+7+7+...+7 (36 times) 3 + (7 x 36) = 3 + 252 = 255 Answer E #### E QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.66 feet C)3.3 feet D)3.4 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+10=40 44/12=3.66 feet ANSWER:B #### B QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 (2/25) = 44 seconds Answer: E #### E QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten? options: A)30 B)25 C)20 D)15 E)10 SOLUTION:There are two conditions: 1. Roslin got at least one score of each of 1, 2, 3, 4, and 5. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30. Answer: A. #### A QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)(100%-19%) = 1.07.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D <<<Examples ends QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km. Speed = Distance/Time Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours] Required speed = 3000 x 3/5 km/hr = 1800 km/hr. Answer: Option B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2007 B)2008 C)2002 D)2000 E)2001 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: D #### D QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B QUESTION:If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is options: A)Rs.1820 B)Rs.1040 C)Rs.1120 D)Rs.1680 E)None of these SOLUTION:Explanation: Let the sum of money be x then (x × 4 × 8)/100 = (560 × 12 × 8)/100 x × 4 × 8 = 560 × 12 × 8 x × 4 = 560 × 12x = 560 × 3 = 1680 Answer: Option D #### D QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6 SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject. B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject. C. Hold. D. since p is a perfect cube, -p will also be a perfect cube. reject. E. (p-q)^6, is a perfect cube, so reject. By elimination C is the answer. Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube. ANSWER:C #### C QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 172+37+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 12)/60 =12/47 Answer B #### B QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20 after 2nd year (now age become 21) 221+ 20=62 grades after 3rd year(now age becomes 22) 222+31=75 ANSWER:B #### B QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (310^-3)^5 = 24310^-15 = 0.24310^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ? options: A)d B)3d C)15d D)d + 5 E)d + 15 SOLUTION:If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change. If we increase or decrease each term in a set by the same percent (multiply by a constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5. Answer: D. #### D QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order? options: A)AOTDSP B)AOTPDS C)AOTDPS D)AOSTPD E)None of these SOLUTION:Explanation : In alphabetical order : A D O P S T A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A. A D _ _ _ _ : empty places can be filled in 4!=24 A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24 this total crosses 42. So We should not consider all the words starting with AO. A O D _ _ _ : 3!= 6 A O P _ _ _ : 3!=6 Till this 36 words are obtained, we need the 42nd word. AOS _ _ _ : 3!= 6 Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD. So given word is AOSTPD Answer : D #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock options: A)47 B)76 C)28 D)66 E)99 SOLUTION:Explanation: For ticking 6 times, there are 5 intervals. Each interval has time duration of 45/5 = 9 secs At 12 o'clock, there are 11 intervals, So total time for 11 intervals = 11 × 9 = 99 secs. Answer: E #### E QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 541=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? options: A)106.75 B)213.5 C)427 D)729 E)1,156 SOLUTION:Diagonal of a square =√2side of square => side =Diagonal/(√2) Area of square =ss =(diagonal^2)/2 Difference of both tv's =(34^2-27^2)/2 =427 ANSWER:C #### C QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B the present age of B is options: A)37 B)38 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2(b-10) => 2b-a = 30 ......(i) a = b+9 =>2b-b-9 = 30 b=39 so the present age of b is 39 years ANSWER:C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time? options: A)70 1/7 min B)94 1/7 min C)110 1/7 min D)112 1/7 min E)131 1/7 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) Now the 4 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 = 5/2 so they complete one robot in 2/5th of an hour - (3) Now the 5 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2+1/2 = 3 so they complete one robot in 1/3th of an hour - (4) Now the 6 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2 so they complete one robot in 2/5th of an hour - (5) And now we have 7 robots So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes Answer - E #### E QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get? options: A)57% B)57.3% C)65% D)90% E)80% SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates) percentage of the total votes recd by the winning candidate = 10011620/20280 = 57.3% ANSWER:B #### B QUESTION:If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? options: A)4:9 B)4:3 C)3:7 D)2:5 E)1:6 SOLUTION:The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9. The ratio of apples to bananas to cucumbers is 4 to 3 to 9. The answer is A. #### A QUESTION:Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color? options: A)2/5 B)1/15 C)1/9 D)1/10 E)1/25 SOLUTION:Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1 Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color). Thus the total probability = 11/15=1/15. B is the correct answer. #### B QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6666 = 2^43^4 Total factors = (4+1)(4+1) = 64 = 24 Answer C. #### C QUESTION:Which of the statements can be dispensed with while answering the above question? options: A)A only B)B only C)A or C only D)B or C only E)C or D only SOLUTION:Explanation: Justification: We can find the code for 'home' from the second and third statements. For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data. Clearly, statement A is not necessary. Answer: A #### A QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2) options: A)1296 B)4 C)8 D)16 E)32 SOLUTION:(x+y)^2 - (x-y)^2 (x+y+x-y)(x+y-x+y) (2x)(2y) 4xy 4 6^4 = 1296 Answer A #### A QUESTION:Louie takes out a three-month loan of $2000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month? options: A)A)333 B)B)383 C)C)402 D)D)433 E)E)804 SOLUTION:Here's the calculation for that case, assume monthly payment is X. After 1st month: (2000)(1.1)-X = 2200-X After 2nd month: (2200-X)(1.1)-X = 2420-2.21X After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X Now, the amount after the last payment in 3rd month must bring the total to 0. Hence: 2662-3.31X = 0 X = 2662/3.31 = 804 Answer E #### E QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water? options: A)6 B)24 C)8 D)12 E)44 SOLUTION:40 --- 8 DS = 5 ? ---- 1 56 ---- 8 US = 7 ? ---- 1 M = ? M = (5 + 7)/2 = 6 Answer: A #### A QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 66 = Rs. 16.50 Answer: Option D #### D QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 Â½ = 75 km RS = 75 â€“ 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits? options: A)53978 B)53916 C)53961 D)56781 E)None of these SOLUTION:Explanation: The greatest 5 digit number that can be formed using the given digits = 74320 The smallest 5 digit number that can be formed using the given digits = 20342 .: The required difference = 74320 - 20342 = 53978 Answer: Option A #### A QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? options: A)66 B)83.5 C)84 D)95 E)76 SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4 = 84 ANSWER:C #### C QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 6 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter? options: A)1/2 B)1/3 C)1/4 D)2/3 E)2/5 SOLUTION:Tom paints 1/6 of the room in the first hour. Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6. The three people then paint the remaining 2/6 in a time of (2/6) / (4/6) = 1/2 hours Peter worked for 3/2 hours so he painted 3/2 * 1/3 = 1/2 of the room. The answer is A. #### A QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 256/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:If f(x) = -2x2 + 8x - 4, which of the follwoing is true? options: A)The maximum value of f(x) is -4. B)The graph of f opens upward. C)The graph of f has no x-intercept D)f is not a one to one function. E)The maximum value of f(x) is 4. SOLUTION:f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D correct answer D #### D QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum E of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: E=2550+(10050)=7550.B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)8 B)6 C)4 D)5 E)9/2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1 When B starts: No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1 Solving the above two equations for xy x = 1/9 y = 1/9 → Total work done by AB in a day = 1/9 + 1/9 = 2/9 → No. of days to complete the work when both work together = 9/2; Answer: E #### E QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 5/7 . 2/5 P (A n B) = 2/7. D #### D QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in. options: A)40 min B)25 min C)54 min D)65 min E)58 min SOLUTION:Distance = Speed * time 320/3= 20km New Speed = 18 kmph Therefore time = 20/18 = 10/9= 54min Answer : C. #### C QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)270 m B)245 m C)235 m D)220 m E)240 m SOLUTION:Explanation: Assume the length of the bridge = x meter Total distance covered = 135+x meter total time taken = 30s speed = Total distance covered /total time taken = (135+x)/30 m/s => 45 Ã— (10/36) = (135+x)/30 => 45 Ã— 10 Ã— 30 /36 = 135+x => 45 Ã— 10 Ã— 10 / 12 = 135+x => 15 Ã— 10 Ã— 10 / 4 = 135+x => 15 Ã— 25 = 135+x = 375 => x = 375-135 =240 Answer: Option E #### E QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue? options: A)no change B)decreases by 6.5% C)increases by 6.5% D)increases by 5.6% E)None of these SOLUTION:Explanation : Reduction of price = (100 -15)% = 85% = 0.85 Increase of sale = (100+15)% = 115% = 1.15 Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5% Answer :B #### B QUESTION:If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days? options: A)127 B)237 C)360 D)450 E)281 SOLUTION:Explanation: Let the required no of hectares be x. Then Men --- Hectares---Days 10---------80---------24 36---------x---------30 More men, More hectares (Direct proportion) More days, More hectares (Direct proportion) x=36/1030/2480 x= 360 Answer: C #### C QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^327 + 26^5. Answer: D. #### D QUESTION:When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? options: A)32 B)36 C)40 D)45 E)50 SOLUTION:A = 9k+3 = 5j+4 B = 9m+3 = 5n+4 A-B = 9(k-m) = 5(j-n) Thus A-B is a multiple of 9 and 5, so it is multiple of 45. The answer is D. #### D QUESTION:The cost of raw material of a product increases by 30, the manufacturing cost increases by 20 and the selling price of the product increases by 60. The raw material and the manufacturing cost, originally, formed 40 and 60 of the total cost respectively. If the original profit was one-fourth the original manufacturing cost, find the approximation new profit percentage. options: A)48.38% B)54.68% C)62.48% D)42.36% E)None of these SOLUTION:Explanation : Let, the total initial cost of the product be Rs 100. Manufacturing cost = Rs 60 Raw materials cost = Rs 40 Also, original selling price => Rs100+(60/4)= Rs 115. New raw material cost =>Rs 40+30% of 40= Rs 52. New manufacturing cost =>Rs 60+20% of 60= Rs 72 New cost of the product = Rs124 New selling price =>115+60% of 115=Rs 184 New profit percentage =>60/124×100 =>48.38%. Answer : A #### A QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:B and C started a business investing Rs. 72,000 and Rs. 45,000 respectively. In what ratio the profit earned after 7 years be divided between B and C respectively? options: A)7:5 B)5:8 C)5:7 D)8:5 E)None of these SOLUTION:B:C = 72000 : 45000 = 8:5. ANSWER:D #### D QUESTION:You roll two six sided dices together. Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5? options: A)2/23 B)1/33 C)1/36 D)3/54 E)6/35 SOLUTION:C 1/36 The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36. Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5. Therefore, the probability will be 1 on 36 or 1/36. #### C QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:One day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at which point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each subsequent turn, Connie wins 1 6 of the amount she would have won the previous turn. What is Connie's expected earnings from the game? options: A)32/31 B)33/31 C)34/31 D)36/31 E)0/31 SOLUTION:Connie has a 1 6 chance of winning 6 dollars her first turn. She has a 5/6 1/6 chance of winning 1 dollar her second turn. Next, she has a 25 36 1/6 chance of winning 1/6 dollars her third turn. Generalizing, Connie's expected earnings form a geometric series with initial term 1/6 6 = 1 and common ratio 5/6 1/6 = 5/36 . Hence, Connie's expected earnings are 1/1- 5/36 = 36/31 correct answer D #### D QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105. options: A)18 B)8 C)12 D)16 E)None of these SOLUTION:105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 The H.C.F of 32, 48 and 80 is 16. ANSWER:D #### D QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE SOLUTION:Solution: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000. => 3x = 36000. => x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. So A's share = Rs. (35000 x 21/50) = Rs. 14,700. Answer: Option D #### D QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton? options: A)330 B)300 C)252 D)225 E)210 SOLUTION:Baker Ram is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5. To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210. Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210. #### E QUESTION:Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Sandy walks 12 km in the first two hours so there are 40 km remaining. When Ed starts walking, they complete a total of 10 km per hour. They will meet four hours after Ed starts walking. Since Sandy walks for 6 hours, she walks 36 km. The answer is D. #### D QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? options: A)E982 B)27 C)12 D)14.6 E)28 SOLUTION:Explanation: T = 11/45 * 60 = 14.6 Answer: Option D #### D QUESTION:The average of 11 numbers is 11. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is options: A)10.4 B)11.5 C)81.5 D)11.5 E)21.5 SOLUTION:Explanation: Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4. Answer: A #### A QUESTION:What is the value of x if (64^2)-(36^2)=20x? options: A)120 B)100 C)140 D)130 E)115 SOLUTION:20x=(64+36)(64-36) 20x=10028 x=(10028)/20 x=528 x=140 Option C #### C QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=5015/85=8.82 ANSWER:E #### E QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year? options: A)5% B)6% C)7% D)2% E)8% SOLUTION:increase = 262500 - 175000 = 87500 % increase in 10 yrs = 87500/175000100 = 50% avg = 50/10 = 5% ANSWER A #### A QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.450 B)Rs.500 C)Rs.550 D)Rs.640 E)Rs.650 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent? options: A)16% B)17% C)18% D)58% E)23% SOLUTION:Total CP = Rs. 36000 + Rs. 15000 = Rs. 51000 and SP = Rs. 62900 Profit(%) = (62900 - 51000)/51000 * 100 = 23% Answer: E #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:990.35=34.65 approx. 35 Answer : B #### B QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has? options: A)102 B)60 C)75 D)90 E)95 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 544 16x = 544 x = 34. Hence, total number of notes = 3x = 102 Answer: Option A #### A QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 11 = (5,6)(6,5)= 2 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 11 in any attempt =2/36=1/18 Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18 Probability of losing game =(17/18)(17/18)(17/18)=139/165 I.e. Probability of wining game = 1-(139/165) =26/165 Answer : Option C #### C QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? options: A)116 B)132 C)148 D)164 E)180 SOLUTION:3/10P are ponies with horseshoes, so P is a multiple of 10. 5/83/10P = 3/16P are Icelandic ponies with horseshoes, so P is a multiple of 16. The minimum value of P is 80. Then H = P+4 = 84. The minimum number of horses and ponies is 164. The answer is D. #### D QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:139 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 93+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:√[200√[200√[200……..∞]]] = ? options: A)200 B)10 C)1 D)20 E)2 SOLUTION:Let √[200√[200√[200……..∞]]] = x ; Hence √200x = x Squaring both sides 200x = x² Þ x (x – 200) = 0 Þ x = 0 or x – 200 = 0 i.e. x = 200 As x cannot be 0, x = 200. ANSWER:A #### A QUESTION:In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)33% D)40% E)52% SOLUTION:Total employed people 12%, out of which 80 are employed males, hence 40% are employed females. (employed females)/(total employed people)=40/120=1/3=33% Answer: C. #### C QUESTION:The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is: options: A)91 B)910 C)1001 D)1911 E)None of these SOLUTION:Explanation: Required number of students = H.C.F of 1001 and 910 = 91. Answer: A #### A QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:A company recently conducted a survey and found that 40,000 of its customers live in rural areas. If the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas, how many customers live in urban areas? options: A)90,000 B)91,200 C)92,400 D)93,600 E)94,800 SOLUTION:The number of customers in urban areas is 40,000+1.3740,000=94,800. The answer is E. #### E QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 999998 = 472392 Hence option (A). #### A QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? options: A)18° B)36° C)54° D)72° E)90° SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20% 100% of the circle is 360 degrees. Then (20%/100%)360 = 72 degrees The answer is D. #### D QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in? options: A)3 days B)5 days C)7 days D)11 days E)12 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. A) #### A QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? options: A)4328 B)5382 C)6174 D)7690 E)8436 SOLUTION:The number of ways for the ships to go to the ports is 3! = 6. At Port A, the number of ways to choose two winners is 7C2 = 21. At Port B, the number of ways to choose one winner is 7. At Port C, the number of ways to choose one winner is 7. The total number of ways to give out gift certificates is 62177 = 6174 The answer is C. #### C QUESTION:The average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)14 years B)16 years C)18 years D)12 years E)11 years SOLUTION:2 2 = 16 Answer:B #### B QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.151.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)1800 C)2100 D)1950 E)2200 SOLUTION:P = 15(100/10)2 => P = 1500 ANSWER:A #### A QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed against the current will be options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these SOLUTION:Explanation: Speed with current is 20, speed of the man + It is speed of the current Speed in sƟll water = 20 - 5 = 15 Now speed against the current will be speed of the man - speed of the current = 15 - 5 = 10 kmph Answer: B #### B QUESTION:The daytime telephone rate between two cities is 50 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is: options: A) 0.4(0.60) + 35c B) 0.4(0.50 + 0.32c) C) 0.4(0.60 + 9c) D) 0.6(0.60 + 32c) E) 0.6(0.60 + 0.35c) SOLUTION:For first three minutes = 50 cents Remaining minutes = 35 -3 = 32 charge for 32 minutes = 32c total cost (if the call was made in daytime) = 0.50 + 32c 60% chargereducedon night calls => 40% charge =>0.4(0.50 + 32c) Hence, Answer is B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 40 =20 hours Answer is D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (512/5)/100] P= 1500.Answer:A #### A QUESTION:A man sells a horse for Rs.920 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? options: A)287 B)279 C)267 D)860 E)940 SOLUTION:CP = SP + 1CP = SP - g 920 + x = 980 - 2x 3x = 60 => x =20 CP = 920 + 20 = 940 Answer:E #### E QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 13579...99 g(97) = 13579...97 g(99) - g(97) = 13579...99 - 13579...97 = 13579...97(99 - 1) = 13579...9798 hence:A. #### A QUESTION:A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate? options: A)480 B)580 C)680 D)280 E)380 SOLUTION:Let the total no of mangoes in the crate be x Then the no of bruised mango = 1/30 x Let the no of unsalable mangoes =3/4 (1/30 x) 1/40 x =12 x=480 Answer is A. #### A QUESTION:A train 330 m long passed a pole in 11 sec. How long will it take to pass a platform 760 m long? options: A)76 sec B)89 sec C)87 sec D)35 sec E)36 sec SOLUTION:Speed = 330/11 = 30 m/sec. Required time = (330 + 760)/30 = 36 sec. Answer:E #### E QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years? options: A)5:8 B)7:5 C)3:8 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8 Answer A #### A QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is: options: A)51:52 B)52:53 C)51:53 D)52:55 E)53:54 SOLUTION:Explanation: Let C.P. of the article be Rs. x. Then, required ratio = 104% of x / 106% of x = 104/106 = 52/53 = 52:53 ANSWER IS B #### B QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = t 5a2 + 7b2 = t 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D <<<Examples ends QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n? options: A)8/7 B)8 C)9/8 D)7 E)5 SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 9x+xn and we are told that it equals to 9xn: 9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9 n = 9/8 Answer: C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5 SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x). Now the sum of greatest three would be 7+8+9=24 so the answer has to be 8x....that is option A #### A QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =âˆšb : âˆša = âˆš25 : âˆš36 = 5 : 6 Answer D #### D QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green? options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220 SOLUTION:Prob of selecting one blue and two green is (487/121110) one blue and two green can be arranged in 3!/2! ways hence the prob becomes 3487/121110=28/55 Correct answer is B #### B QUESTION:If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average R (arithmetic mean) annual increase in the index over this period? options: A) (x + 100)/18 B) x/18 C) (100 − x)/18 D) (x − 100)/18 E) 100x/18 SOLUTION:CPI in end of 1967 = 100 CPI in end of 1985 = x Number of years = 18 Average annual increase in CPI R= (x-100)/18 Answer D #### D QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:1395 x 1395 options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these SOLUTION:1395 x 1395 = (1398)2 = (1400 - 2)2 = (1400)2 + (5)2 - (5 x 1400 x 5) = 1946025. Answer: Option A #### A QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work? options: A)30 days B)60 days C)18 days D)80 days E)90 days SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9 Amount of work done by JOHN and ANDREW in 6 days = 6 Ã— (1/9) = 2/3 Remaining work â€“ 1 â€“ 2/3 = 1/3 JOHN completes 1/3 work in 6 days Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18 => JOHN can complete the work in 18 days Answer : C #### C QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely? options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec SOLUTION:Explanation: D = 250 m + 250 m = 500 m RS = 80 + 40 = 120 5/18 = 100/3 T = 500 * 3/100 = 15 sec Answer: Option A #### A QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:How many positive integers less than 254 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)43 E)64 SOLUTION:252/4=63 Multiples of 4 which are a multiple of 6 will be of the form 223=12n where n>0 240/12=20 63-20=43 Answer: D #### D QUESTION:A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? options: A)5 B)6 C)10 D)13 E)28 SOLUTION:Suppose there are c columns and there are r rows Original Situation So, Number of tiles = cr = 48 Also. Reach column has r tiles and each row has c tiles New Situation Number of tiles in each column is r-2 and number of tiles in each row is c+4 So, number of rows = r-2 and number of columns is c+4 So, Number of tiles = (r-2)(c+4) = 48 Comparing both of them we get cr = (r-2)(c+4) => 4r -2c = 8 c = 2r - 4 Putting it in cr=48 (2r-4)r = 48 2r^2 - 4r - 48=0 r cannot be negative so r = 6 and c = 8 So, Answer will be B #### B QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 312=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 851 is 0. The answer is A. #### A QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was. options: A)Rs 10000 B)Rs 15000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=Pâˆ—Râˆ—T/100 =>P=S.I.âˆ—100/Râˆ—T =>P=3600âˆ—100/12âˆ—3=Rs10000 Option A #### A QUESTION:The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again? options: A)16:00. B)18:00. C)20:00. D)22:00. E)24:00. SOLUTION:Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10 If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours Answer A #### A QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)1/2 B)1/2 C)8/15 D)9/20 E)9/24 SOLUTION:Explanation : Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20 Answer : D #### D QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ? options: A)A)63.3% B)B)52.4% C)C)81.2% D)D)75.4% E)E)72.11% SOLUTION:Total number of students = 1100+700 = 1800 Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502 number of failures = 1298100/1800= 72.11% Answer is E #### E QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream. options: A)7 kmph B)8 kmph C)9 kmph D)7 kmph E)6 kmph SOLUTION:Speed in still water = (10 + 4)1/2 kmph = 7 kmph. answer :A #### A QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:A sum of Rs. 12500 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (16500 - 12500) = Rs. 4000/- Rate = (100 4000) / (12500 * 4) = 8% ANSWER:D #### D QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D QUESTION:The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? options: A)4/19 B)1/9 C)2/3 D)1 1/9 E)2 1/9 SOLUTION:Total bought = 4/19+2/13 left part 4/26--->2/13 so used part 4/19+2/13-2/13=4/19 ANSWER:A #### A QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)36 years C)32 years D)44 years E)None of these SOLUTION:The total age of 10 students with average 24 = 240 The total age of 12 students with average 26 = 312 The total age of 2 new students = 72 Their average =36 Correct Option B #### B QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price? options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these SOLUTION:Explanation : CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140 100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12 Answer : Option A #### A QUESTION:Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls. options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7% SOLUTION:Let the cost price of 1 balls be Rs 1 Cost of 14 balls= Rs 14 Selling price of 14 balls = 9 Gain/loss = 14 - 9 = 5 %=5/14âˆ—100= 35.7 Answer: A #### A QUESTION:What is the sum of all even numbers from 1 to 401? options: A)122821 B)281228 C)281199 D)122850 E)40200 SOLUTION:Explanation: 400/2 = 200 200 * 201 = 40200 Answer: E #### E QUESTION:Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? options: A)4328 B)5382 C)6174 D)7690 E)8436 SOLUTION:The number of ways for the ships to go to the ports is 3! = 6. At Port A, the number of ways to choose two winners is 7C2 = 21. At Port B, the number of ways to choose one winner is 7. At Port C, the number of ways to choose one winner is 7. The total number of ways to give out gift certificates is 62177 = 6174 The answer is C. #### C QUESTION:If points A and B are (8-3) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 812=96 five-minute intervals, thus total of 9630 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=9630 --> x=2430 and 3x=3(2430)=2490. Therefore, the total revenue from ticket sales that day was 24306+249010=$25,920. Answer: B. #### B QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (120R)/100 R = 40% Answer:D #### D QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ? options: A)1/26 B)1/20 C)1/25 D)1/29 E)1/23 SOLUTION:Let E1 be the event of drawing a red card. Let E2 be the event of drawing a king . P(E1 ∩ E2) = P(E1) . P(E2) (As E1 and E2 are independent) = 1/2 * 1/13 = 1/26.Answer: A #### A QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations T could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:T=4C1 * 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 3a = b = 3c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)131 B)292 C)394 D)424 E)969 SOLUTION:Ratio of a:b:c= 1:3:1 Two possible greatest single digit values for b are 9 and 6 if b is 9, then x= 393 if b is 6, then x= 262 difference= 393-262= 131 A is the answer #### A QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50* 9/10 x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:4 E)1:2 SOLUTION:He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33) Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters) Hence the water added would be .1 liter. Therefore the ratio of water to milk is .1/1 = 1/10 ANSWER:B #### B QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N? options: A)107 B)331 C)511 D)691 E)871 SOLUTION:N/P=10 7/P= 20P+7 N/(P+2)=15 2/(P+2)=15P+30+2 solving these two equations we get P=5 N= 107 answer is A. #### A QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 800018 : (80004) + (400014) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: options: A)30 B)28 C)24 D)20 E)35 SOLUTION:Product of two nos = product of HCF and LCM Let one number = x => 25 * x = 5 * 150 x=5150/25=30 ANSWER A #### A QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)298 m B)888 m C)120 m D)217 m E)166 m SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? options: A)12km B)15km C)18km D)24km E)Data Inadequate SOLUTION:time=distance/speed so, let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so, (x/4+y/3)+(y/6+x/4)=6 x+y=12 km. ANSWER:A #### A QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 45!. Answer: C. #### C QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 172+37+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L4 => L = 36/4 = 9 Answer D #### D QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours Answer: Option D #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:Tough and Tricky questions: Exponents. If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy? options: A)4, 2, 8, 6 B)4 and 2 C)2 and 8 only D)6 and 4 E)8 and 6 SOLUTION:Only Units digit of X and Y contribute to the Units digit of XY. Finding all values of X for positive values of a When, a=1; X=2 a=2; X=4 a=3; X=8 a=4; X=16 a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4...... Similarly, Finding all values of Y for positive values of b When, b=1; Y=3 b=2; Y= 9 b=3; Y= 27 b=4; Y=81 b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=2 and Y=3: Units digit of XY = 6 When X=2 and Y=9: Units digit of XY = 18 When X=2 and Y=7: Units digit of XY = 14 When X=2 and Y=1: Units digit of XY = 2 When X=4 and Y=3: Units digit of XY = 12 When X=4 and Y=9: Units digit of XY = 36 When X=4 and Y=7: Units digit of XY = 28 When X=4 and Y=1: Units digit of XY = 4 When X=8 and Y=3: Units digit of XY = 24 When X=8 and Y=9: Units digit of XY = 72 When X=8 and Y=7: Units digit of XY = 56 When X=8 and Y=1: Units digit of XY = 8 When X=6 and Y=3: Units digit of XY = 18 When X=6 and Y=9: Units digit of XY = 54 When X=6 and Y=7: Units digit of XY = 42 When X=6 and Y=1: Units digit of XY = 6 There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6 Ans: A #### A QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball? options: A)5⁄7 B)10⁄21 C)2⁄7 D)11⁄21 E)None of these SOLUTION:Reqd probability = 5C2/7C2=5×4/7×6=10/21 Answer B #### B QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=23322 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:Find HCF of 4/5, 8/35, 2/15, 6/25 ? options: A)2/125 B)6/360 C)2/525 D)2/720 E)3/680 SOLUTION:We know that the HCF for fraction can be calculated as: HCF = (HCF of numerators) / (LCM of denominators) = (HCF of 4, 8, 2, 6) / (LCM of 5, 35, 15, 25) = 2 / (5 x 7 x 3 x 5) = 2 /525 Ans - C #### C QUESTION:By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%? options: A)6.54 B)9.45 C)7.34 D)6.67 E)5.09 SOLUTION:90% --- 8 110% --- ? 90/110 * 8 = 6.54 Answer: A #### A QUESTION:Find the base K of the number system, if (524)8 = (664)K ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:58^2 + 28^1 + 48^0 = 6K^2 + 6K^1 + 4K^0 320 + 16 + 4 = 6(K^2) + 6K + 4 340 = 6(K^2) + 6K + 4 6(K^2) + 6K + 4 - 340 = 0 6(K^2) + 6K - 336 = 0 dividing by 6; (K^2) + K - 56 = 0 solving this quadratic equation we get, K=7 and K=-8 thus K=7 ANSWER:D #### D QUESTION:Helen went to the stationers and bought things worth Euro 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Euro 15 B)Euro 15.7 C)Euro 19.7 D)Euro 20 E)None SOLUTION:Explanation: Let the amount taxable purchases be Euro x. Then, 6% of x = 30/100 x = (30/100 x 100/6) = 5. Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70 Answer: Option C #### C QUESTION:Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The total number in the three clubs is 17+24+22=63. All 50 students signed up for at least one club. 3 of those students signed up for exactly one more club. 63 - 53 = 10 so 5 students must have signed up for exactly three clubs. The answer is A. #### A QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July? options: A)$4 B)$0.1 C)$1 D)$3 E)$1.65 SOLUTION:Lets assume price of Coffee in June =100x Price of green Tea in June =100x Price of Coffee in July = 200x (because of 100% increase in price) Price of green Tea in July = 10x (because of 90% Decrease in price) Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x As per question 315x= 3.15$ x = 0.01S So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound Answer B #### B QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? options: A)62% B)69.45% C)70% D)71% E)72% SOLUTION:Required percentage = [ (288 + 98 + 3.00 + 23.4 + 83) x 100 ] % (420 + 142 + 3.96 + 49.4 + 98) = [ 495.4 x 100 ] % 713.36 ~= 69.45%. B) #### B QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)115 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 25 : x => x = {\color{Blue} \frac{25\times 1}{0.128}} => x = 195.31 So time will be approx 195 seconds Answer: B #### B QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:An oratorical society consists of six members, and at an upcoming meeting, the members will present a total of four speeches. If no member presents more than two of the four speeches, in how many different orders could the members give speeches? options: A)720 B)1080 C)1170 D)1470 E)1560 SOLUTION:You need to remember that of the 3 people, 1 is going twice and two are going once. Since one of the 3 is going once, there are 3C1 possibilities for the double speaker. So, to convert your work to the correct answer, you need to multiply: 240 * 3C1 = 240 * 3 = 720. ANS:A #### A QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 412=48 6 dozens of bananas cost is rs8 then 68=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? options: A)12.0 B)13.5 C)14.5 D)23.5 E)26.5 SOLUTION:The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C. #### C QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length? options: A)48.29 B)50 C)26.8 D)45.29 E)30 SOLUTION:Speed = 29 Km/hr = 29(5/18) m/sec = 145/18 m/sec Total distance = 288+101 = 389 meter Time = Distance/speed = 389 (18/145) = 48.29 seconds. Answer: A #### A QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2pir. The perimeter of a semicircle is 2pir/2 + 2r = pir + 2r The perimeter is pi9 + 29 which is about 46. The answer is D. #### D QUESTION:In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? options: A)18 B)36 C)42 D)52 E)56 SOLUTION:All options other than 'D' are factors of 2013. Hence, 'D' is the answer #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:A man purchased 3 blankets @ Rs.100 each, 2 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)278 B)900 C)278 D)450 E)772 SOLUTION:10 150 = 1500 3 * 100 + 2 * 150 = 600 1500 – 600= 900 Answer:B #### B QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions. Hence, the number of all possible selections is 3 10 – 1. Answer C #### C QUESTION:Solve x^2 – 7x = 0 options: A)(0,7) B)(0,3) C)(0,2) D)(0,5) E)(0,6) SOLUTION:This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x^2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 Ans: A #### A QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1â„7 hours B)6 2â„7 hours C)8 2â„7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 Ã— 2 = 16 km Distance covered in next two hours = 10 Ã— 2 = 20 km Distance covered in next two hours = 12 Ã— 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 â€“ 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. âˆ´ Time taken = 4â„12 = 1â„3 hour. Total time= 6 + 1â„3 = 6 1â„3 hour Answer E #### E QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:The value of (34.310.4731.5)/(0.067323.257.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.310.4731.5)/(0.067323.257.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:A CAN FINISH A WORK IN 12 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK? options: A)4 B)5 1/2 C)6 D)8 E)NONE OF THESE SOLUTION:B'S 10 DAY'S WORK=(1/1510)=2/3 REMAINING WORK = (1-2/3)=1/3 NOW, 1/18 WORK IS DONE BY A IN 1 DAY 1/3 WORK IS DONE BY A IN (121/3)=4 DAYS. CORRECT OPTION:A #### A QUESTION:Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is? options: A)109 B)106 C)104 D)108 E)101 SOLUTION:Let the present ages of the father and son be 2x and x years respectively. Then, (2x - 18) = 3(x - 18) => x = 36 Required sum = (2x + x) = 108 years.Answer: D #### D QUESTION:A train 120 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)16 kmph B)88 kmph C)54 kmph D)18 kmph E)27 kmph SOLUTION:S = 120/16 * 18/5 = 27 kmph Answer: E #### E QUESTION:A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings? options: A)$390 B)$520 C)$1080 D)$1170 E)$630 SOLUTION:Explanatory Answer A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them. As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day. Similarly, B will complete 1/8th and C will complete 1/12th of the work. So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12 Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values. We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2. i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2. Hence, B's share will be 31170/9 = 390. correct choice is (A) #### A QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:20, 19, 17, ?, 10, 5 options: A)14 B)15 C)13 D)18 E)17 SOLUTION:A 14 The Pattern is - 1, - 2, -3, ... #### A QUESTION:Vijay bought 160 shirts at the rate of Rs. 255 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)Rs. 321 B)Rs. 270 C)Rs. 277.5 D)Rs. 285 E)None of these SOLUTION:Total CP per shirt = 255 + 1400/160 + 1.75 + 320/160 = Rs. 267.5 SP = CP[(100 + profit%)/100] = 267.5 * [(100 + 20)/100] = Rs. 321. ANSWER:A #### A QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is options: A)42 B)36 C)28 D)20 E)24 SOLUTION:Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10×36/10 km/hr = 36 km/hr Answer: Option B #### B QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L? options: A)6 B)-1 C)-2 D)-6 E)-10 SOLUTION:We need to find out the value of p and L to get to the slope. Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving 5 = -p2 +9 p2 = 4 p = + or - 2 simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7. -7 = -t2+9 t = +or - 4 considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1 IMO option B is correct answer. #### B QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = t 5a2 + 7b2 = t 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26 SOLUTION:Explanation: Let the present age of P and Q be 3x and 4x respectively. Eight years ago, P was half of Q in age => 2(3x – 8) = (4x – 8) => 6x – 16 = 4x – 8 => 2x = 8 => x = 4 7x=74=28 Answer: Option B #### B QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 321/4 = 8 mins. ANSWER:A #### A QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 242=48 Answer(B) #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is? options: A)1/9 B)1/3 C)1/5 D)1/1 E)1/2 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A <<<Examples ends QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was. options: A)Rs 14000 B)Rs 25000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=Pâˆ—Râˆ—T/100 =>P=S.I.âˆ—100/Râˆ—T =>P=9000âˆ—100/12âˆ—3=Rs25000 Option B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 6840 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)868.6 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 6840/18 + 6840/14 = 380 + 488.6 = 868.6 hours Answer: Option D #### D QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)a^2 = (3/2)a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to bsqrt2 so, b sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)a^2 so, a^2 = (2/3)b^2 = (2/3)18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)228 B)480 C)267 D)288 E)276 SOLUTION:SP = 800 Profit = 25% CP = (SP)[100/(100+P)] = 800 * [100/125] = 640 Loss = 25% = 25% of 640 = Rs.160 SP = CP - Loss = 640 - 160 = Rs.480 Answer: B #### B QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:62467 × 9998 = ? options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211 SOLUTION:D 624545066 62467 × 9998 = 62467 × (10000 - 2) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066 #### D QUESTION:By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is? options: A)50 B)25 C)400 D)200 E)150 SOLUTION:Marked price = Rs. 300 C.P. = 100/300 * 300 = Rs. 100 Sale price = 90% of Rs. 300 = Rs. 270 Required gain % = 200/100 * 100 = 200%. Answer:D #### D QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:If 3log(45^2) = x, find x options: A)5 B)6 C)7 D)8 E)9 SOLUTION:3(log2^25^2)=x 3log(52)^2=x 32log(52)=x 6log10=x log10 base 10=1 so 61=x x=6 ANSWER:B #### B QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)6 months B)8 months C)10 months D)7 months E)12 months SOLUTION:Explanation: 7 8 : 9 * x = 8:9 => x= 7 ANSWER IS D #### D QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? options: A)8000 B)8077 C)2776 D)2976 E)2971 SOLUTION:8820 ---- 441 100 ---- ? => 5% x 105/100 105/100 = 8820 x1.1025=8820 x=8820/1.1025 => 8000.Answer: A #### A QUESTION:A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre options: A)s510 B)s780 C)s880 D)s480 E)s980 SOLUTION:area of the plot=110m65m=7150sq.m area of plot excluding gravel=105m60m=6300sq.m area of gravel =7150sq.m-6300sq.m =850sq.m cost of building it = 850sq.m60 = 51000p in Rs =51000/100=Rs510 ANSWER:A #### A QUESTION:Find the base K of the number system, if (524)8 = (664)K ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:58^2 + 28^1 + 48^0 = 6K^2 + 6K^1 + 4K^0 320 + 16 + 4 = 6(K^2) + 6K + 4 340 = 6(K^2) + 6K + 4 6(K^2) + 6K + 4 - 340 = 0 6(K^2) + 6K - 336 = 0 dividing by 6; (K^2) + K - 56 = 0 solving this quadratic equation we get, K=7 and K=-8 thus K=7 ANSWER:D #### D QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32900+83000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650 SOLUTION:Explanation: P - 340 = (P48)/100 P = 500 ANSWER IS D #### D QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ? options: A)64 B)1/8 C)1 D)4 E)1/64 SOLUTION:Say r=2 => V1 = 1/16 when r=1; V2 = 1/4 V2 = 4V1. Answer : D #### D QUESTION:A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,000 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether? options: A)60000 B)60100 C)60500 D)50000 E)70000 SOLUTION:80% parts used of subsidary company, so 20% parts used of other companies. Now, 20% parts = 10,000 computers So, 1% parts = 10,000/20 Or, 100% parts = 50,000 computers. Hence answer is (D) #### D QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps. options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s SOLUTION:Explanation: Distance = Speed x Time Speed = (1080/10) = 108 kmph Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps. Answer: Option E #### E QUESTION:A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make? options: A)100% B)90% C)140% D)115% E)120% SOLUTION:The total CP = Rs. 18000 + Rs. 5000 = Rs. 2300 and SP = Rs. 46000 Profit(%) = (46000 - 23000)/23000 100 = 100% Answer:A #### A QUESTION:The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 1/5. The probability that none of them will be alive for 10 more yrs, is options: A)1/2 B)1 C)2/3 D)1/5 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/5 Ans.(D) #### D QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000 SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? for first 5000 , 8% tax then we get 400$ as tax. Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount. A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount) 550+400 = 950$...hence this is the option. ANSWER :option A. #### A QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c311c3)+(5c411c2)+(5c511c1) 1936 ANSWER:E #### E QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000 SOLUTION:Equation is correct, so math must be a problem. 0.1240,000+0.2(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000. Answer: B. #### B QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam? options: A)2. B)4. C)X=5. D)X=6. E)8. SOLUTION:C. 5 hrs If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C QUESTION:Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in? options: A)8 min B)7 min C)5 min D)9 min E)4 min SOLUTION:1/10 + 1/15 - 1/x = 1/42 x = 7 Answer: B #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score? options: A)662 B)672 C)654 D)642 E)721 SOLUTION:8 83 = 664 – 10 = 654 ANSWER:C #### C QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ? options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29 SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways. Hence the probability is 6/216 = 1/36 Answer: B #### B QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 â€¦. (i) A + B = (25 x 2) = 50 â€¦. (ii) B + C = (28 x 2) = 56 â€¦.(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 â€¦. (iv) Subtracting (i) from (iv), we get : B = 16. Bâ€™s weight = 16 kg. Answer E #### E QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4100=3/4100=75%. Answer: B. #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)(5 choose 2) = 410 = 40 Jaune X = (4 choose 2)(5 choose 1) + (4 choose 3) = 65 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/84=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m. Answer: B. #### B QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48. options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512 SOLUTION:P : 2/13 = 5/34 : 7/48 As the product of the means is equal to the product of the extremes. P7/48 = 2/13 * 5/34 P7/48 = 10/442 P = 480/3094 => P = 240/1547 Answer: C #### C QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? options: A)20 B)60 C)100 D)120 E)150 SOLUTION:y = 0.50.5x = x/4 y%x = 9 (y/100)x = 9 (x/400)x = 9 x^2 = 9400 x = 60 The answer is B. #### B QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ? options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr SOLUTION:given upstream(u) =29km/hr down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr Answer is (D) #### D QUESTION:What approximate value should come in place of the question mark (?) in the following equation? 1.542 × 2408.69 + 5134.632 = ? options: A)4600 B)4800 C)5200 D)6400 E)8800 SOLUTION:Explanation 3700 + 5100 = 8800 Answer E #### E QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning? options: A)292 B)180 C)276 D)144 E)168 SOLUTION:Let no of passengers in the beginning be X After first station no passengers=(X-X/3)+280=2X/3 +280 After second station no passengers =1/2(2X/3+280)+12 1/2(2X/3+280)+12=244 2X/3+280=2232 = 464 - 280 = 184 2X/3=184 X=276. So the answer is option C) 276. #### C QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price 100/(100+profit) C.P. = 100100/130 = $77(approximately) Answer is D #### D QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π10 = 20 π cm Answer: A #### A QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 66 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6? options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720 SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6 Seeing the Options After Dividing an Finding the Reminder of 2 My Answer was A #### A QUESTION:30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed? options: A)165 B)170 C)175 D)180 E)185 SOLUTION:27200=5400. The other 3 carrots weigh a total of 540 grams. The average weight is 540/3 = 180 grams. The answer is D. #### D QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 > b^2 > c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=1, b=2, and c=3. None of the options must be true. Answer: A. #### A QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 12 coconut doughnuts, and 10 jam-filled doughnuts. How many doughnuts did Anne buy in all? options: A)25 B)34 C)39 D)21 E)11 SOLUTION:Add the numbers of doughnuts. 12 + 12 + 10 =34. Answer is B. #### B QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? options: A)17603 B)17608 C)17628 D)17600 E)176023 SOLUTION:Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 * 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600 Answer: D #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%? options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5% SOLUTION:Let marked price = $100. Then, C.P. = $64, S.P. = $87 Gain % = 23/64 * 100 = 35.9%. B #### B QUESTION:A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours? options: A)125 miles B)225 miles C)520 miles D)425 miles E)525 miles SOLUTION:During each hour, the car travels 65 miles. For 8 hours it will travel 65 + 65 + 65 + 65 + 65+ 65 + 65 + 65 = 8 × 65 = 520 miles correct answer is C) 520 miles #### C QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/1001000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2all three + neither 21+18+19-x-25=40 solving for x you get 8 Answer C #### C QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ? options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms SOLUTION:Solution Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor? options: A)6!/6^6 B)6^6/6! C)6/6! D)6/6^6 E)1/6^6 SOLUTION:Each person out of 6 has 6 options, hence total # of outcomes is 6^6; Favorable outcomes will be 6!, which is # of ways to assign 6 different buttons to 6 people: 1-2-3-4-5-6 (floors) A-B-C-D-E-F (persons) B-A-C-D-E-F (persons) B-C-A-D-E-F (persons) ... So basically # of arrangements of 6 distinct objects: 6!. P=favorable/total=6!/6^6 Answer: A. #### A QUESTION:If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches? options: A)Rs 900 B)Rs 800 C)Rs 1,800 D)Rs 2,800 E)None of these SOLUTION:Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425 Profit = Rs (425 - 200) = Rs 225 Profit of 8 watches = Rs 225 x 8 = Rs 1,800 ANSWER:B #### B QUESTION:Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in options: A)1 13/17 hours B)2 8/11 hours C)3 9/17 hours D)5 5/11 hours E)None SOLUTION:Solution Net part filled in 1 hour = (1/10 + 1/6 -1/12) = 11/60. Therefore, the tank will be full in 60/11 hrs. â€¹=â€º 5 5/11 hrs. Answer D #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 27 ? options: A)6 B)7 C)8 D)9 E)11 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 27; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E #### E QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him? options: A)2000 B)3000 C)4000 D)1000 E)5000 SOLUTION:Let the money he took for shopping be m. Money he spent = 30 % of m = 30/100 × m = 3/10 m Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10 But money left with him = $ 2100 Therefore 7m/10 = $ 2100 m = $ 2100× 10/7 m = $ 21000/7 m = $ 3000 Therefore, the money he took for shopping is $ 3000. Answer:B #### B QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) * 15 = 45 Answer is C #### C QUESTION:{3, 5, 8, y} For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y options: A)16/5, 28/3 B)4, 16/5 C)4, 16/5, 28/3 D)4, 28/3 E)3, 4, 5 SOLUTION:The set can have the following forms: 1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3 2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4 3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4 4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case. Thus the possible values are 4 and 28/3. D is the correct answer. #### D QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20100)/36) %=120% Answer E)120 #### E QUESTION:50% of a number is 10 less than 3/5th of that number. What is the number? options: A)100 B)50 C)150 D)200 E)75 SOLUTION:Let the number be x Then, 3x/5 - (50% of x) = 10 3x/5-50x/100 = 10 x = 100 Answer is A #### A QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length? options: A)87 B)69 C)40 D)72 E)24 SOLUTION:Speed = 75 Km/hr = 75(5/18) m/sec = 125/6 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (6/125) = 24 seconds Answer: E #### E QUESTION:Mary and John can do a piece of work in 24 day; John and Vino in 30 days;Vino and Mary in 40 days. If Mary, John and Vino work together they will complete work in ? options: A)77 B)20 C)27 D)19 E)17 SOLUTION:Explanation: Given that Mary and John take 24 days; i.e., (Mary + John)'s 1 day's work = 124124 John and Vino take 30 days; i.e., (John + Vino)'s 1 day's work = 130130 Vino and Mary take 40 days; i.e., (Vino + Mary)'s 1 day's work = 140140 Adding above 3 equations, we get, [(Mary + John) + (John + Vino) + (John + Vino)]'s 1 day's work = 124+130+140124+130+140 2((Mary + John + Vino)'s 1 days work = 124+130+140124+130+140 2(Mary + John + Vino)'s 1 days work = 5+4+31205+4+3120 = 110110 Therefore, (Mary + John + Vino)'s 1 days work = 120120 i.e., Mary, John and Vino together can complete the work in 20 days. Answer: B #### B QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is options: A)8/17 B)7/15 C)3/15 D)5/12 E)1/4 SOLUTION:Person ( A ) ( B ) ( A+B ) Time - ( 15 ) ( 20 ) (-) Rate - ( 20 ) ( 15 ) ( 35 ) Work -(300) (300) (300) therefore A+B requires (300/35) days to complete entire work For 1st 5 days they work 35 * 5 = 175 Remaining work is 300 - 175 = 125 Remaining fraction of work is = 125/300 = 5/12 Answer D #### D QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages? options: A)25 years B)28 years C)32 years D)26 years E)28 years SOLUTION:let rhea age be x rick age be y given x-8=1/2(y-8)......a also given x/y=(3/4) =>x=3/4(y).......b by solving a and b we get y=16 x=12 then x+y=12+16=28 ANSWER:B #### B QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)45% C)32% D)40% E)28% SOLUTION:answer b male-employed - 64% female-employed-19% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 19/64 =28 E #### E QUESTION:If 80% of 90 is greater than 70% of a number by 30, what is the number? options: A)70 B)60 C)10 D)75 E)85 SOLUTION:Explanation: 80/100 * 90 - 70/100 * x = 30 72 - 70/100 * x = 30 72 - 30 = 70/100 x 42 = 70/100 x 42 * 100 / 70 = x 60 = x Answer: Option B #### B QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat? options: A)3! B)8! C)11! D)12! E)14! SOLUTION:Ans.(A) Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122 SOLUTION:Explanation: Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 Answer: B #### B QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 1000, what is the least possible value of n? options: A)12 B)11 C)14 D)13 E)15 SOLUTION:1000 = 222555, so we need 3 factors of 2 and 3 factors of 5. Therefore, the smallest value of n is 15, so the answer is E. #### E QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 17/100 = 119 The answer is B. #### B QUESTION:Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21 options: A)1 B)-1 C)2 D)-2 E)3 SOLUTION:B -1 19x + 19y + 17 = -19x + 19y - 21 38x = -38 => x = -1 #### B QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? options: A)48 B)99 C)266 D)28 E)17 SOLUTION:Explanation: If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48. Answer: A) 48 #### A QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =250=100m ANSWER:D #### D QUESTION:Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer. options: A)115 × 8 ÷ 10 + 8 B)425 ÷ 17 × 4 C)36 × 5 ÷ 6 + 17 × 4 D)2(6) + √256 + 20 E)35 × 12 ÷ 14 + 14 × 5 SOLUTION:All others are equal to 100. But option (c) gives a value equal to 98. Answer C #### C QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =316250/20 =600 Answer : C #### C QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:0.[u]225[/u = 0.225225225..... Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5. Answer E #### E QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 18/5 = 8 sec ANSWER:C #### C QUESTION:Two dice are rolled. The probability of getting a sum of at least 9 is options: A)13/36 B)5/18 C)35/36 D)11/36 E)15/36 SOLUTION:Sum of 9 = {(3,6) (6,3)} = 2ways. Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways. Sum of 11 = {(6,5) (5,6)} = 2 ways. Sum of 12 = {(6,6) (6,6)} = 2 ways. Therefore, Favourable cases = 10 Total cases = 6 x 6 = 36. Therefore, Probability = 10/36 = 5/18. ANSWER:B #### B QUESTION:An plane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of ? options: A)100 B)720 C)1100 D)940 E)860 SOLUTION:We know Distance = speed * time = 240 * 5 = 1200 km Now to cover 1200 km in 5/3 hrs , speed = distance / time = 1200 / (5/3) = 720 KMPH Ans- B #### B QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100100 = 132 10% discount Then price = 132 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:In track last week, the boys ran 15 laps. The girls ran 5 more laps. Each lap is a one-fifth of a mile. How many miles did the girls run? options: A)2 miles B)3 miles C)4 miles D)5 miles E)6 miles SOLUTION:The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4. The girls ran 4 miles correct answer C #### C QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? options: A)126 B)120 C)101 D)112 E)115 SOLUTION:8 shirts 9 pants we can combine 2 shirts with (12-3) pants 29=18 we can combine the other shirts (6) with any pants (9) 912=54 Thus total :108+18=126 ANS:A #### A QUESTION:40, 45, 50, 55, 60, 70, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.3, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 70, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.3 = 47.2. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:The greatest number of four digits which is divisible by 7, 10, 40 and 60 is: options: A)9200 B)9300 C)9400 D)8400 E)7400 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 7, 10, 40 and 60 is 4200. On dividing 9999 by 4200, the remainder is 1599. Required number (9999 - 1599) = 8400. ANSWER :D #### D QUESTION:Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done? options: A)4!5! B)6!6! C)5!7! D)6!7! E)7!7! SOLUTION:The number of arrangements of n distinct objects in a row is given by n!. The number of arrangements of n distinct objects in a circle is given by (n-1)!. The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)! Now, 5 men in a circle can be arranged in (5-1)! ways and if we place 5 women in empty slots between them then no two women will be together. The # of arrangement of these 5 women will be 5! and not 4! because if we shift them by one position we'll get different arrangement because of the neighboring men. So the answer is indeed 4!5!. A #### A QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book? options: A)20 B)18 C)16 D)15 E)15.39 SOLUTION:Actually u can set up 2 equation P--stands for the pages D--stands for the days 1) PD=480 (we want to find the Days, soP=480/D) 2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000 as the 1) stated u can put 1) into 2) => 1000-5P+15D-75=1000 => 15D-5P=75 put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16) => D^2-5D-160=0 so D=15.39days. Ans: (E) #### E QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^ba^c=a^(b+c). Answer: C #### C QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 2006 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)A)Rs.7000 B)B)Rs.8000 C)C)Rs.8571 D)D)Rs.8600 E)E)Rs.8700 SOLUTION:The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571. C) #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:If 4a = 16b and 9b = 14c, Find a:b:c? options: A)52:13:7 B)13:7:52 C)7:13:52 D)64:14:9 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (9b = 14c ==> b/c = 14/9) ==> a:b = 16:4 and b:c = 14:9 a:b:c = 64:14:9 Answer: Option D #### D QUESTION:A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate? options: A)480 B)580 C)680 D)280 E)380 SOLUTION:Let the total no of mangoes in the crate be x Then the no of bruised mango = 1/30 x Let the no of unsalable mangoes =3/4 (1/30 x) 1/40 x =12 x=480 Answer is A. #### A QUESTION:Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? options: A)9 B)12 C)14 D)16 E)18 SOLUTION:Explanation: We have, 2/3 * 2/5 * 3/4 * X = 36 X = 180 Now, 4/5 * X ===> 4/5 * 180 = 144 √144 = 12 ANSWER: B #### B QUESTION:In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr options: A)8.5 seconds B)2.86 seconds C)3.5 seconds D)2.5 seconds E)2.6 seconds SOLUTION:First convert speed into m/sec Speed = 126(5/18) = 35 m/sec Time = Distance/speed = 100/35 = 2.86 seconds Answer: B #### B QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)Rs. 750 B)Rs. 800 C)Rs. 850 D)Rs. 900 E)None of these SOLUTION:Explanation: Let the cost of Production = Rs. P Then, as per question, =>(125/100∗115/100∗110/100∗P)=1265 =>253/160P=1265 =>P=800 Option B #### B <<<Examples ends QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents? options: A)17 years B)11 years C)6 years D)5 years E)8 years SOLUTION:When age of Son=0 ,Mother=23 After 6 years, Son=6 ,Mother=23+6=29 ,Father=34 So difference between ages of Mother & Father=34-29=5 ANSWER:D #### D QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min SOLUTION:1/20 + 1/40 - 1/80 = 5/80 80/5 = 16 ANSWER:E #### E QUESTION:At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? options: A)404 B)452 C)444 D)468 E)422 SOLUTION:312 + 222 - 112 (since 112 is counted twice )= 422 E is the answer #### E QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these SOLUTION:The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer : B #### B QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)5 B)4 C)6 D)8 E)3 SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4%.Answer:B #### B QUESTION:A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)500m C)C)650m D)D)750m E)E)1200m SOLUTION:Relative speed of the policeman = 20-16 = 4 km/hr time taken by policeman to cover 300m = (300/1000)(1/4) = 3/40 hr In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m Answer is E #### E QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.9281.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible? options: A)5 B)6 C)9 D)24 E)26 SOLUTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 01 + 11 + 21 + 11 + 11 + 01 = 5 cases...A #### A QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:28=16.Answer is A. #### A QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4332211 = 144 ways E #### E QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. options: A)None B)I only C)II only D)III only E)I and II SOLUTION:given 2x/y is prime and greater than 2. => 2x/y could be any of the following 3,5,7.... => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set) 1. x = y , can't be true if x=y , 2x/y = 2 which is not odd and prime. 2. y=1. can't be true. if y=1,2x/y = 2x = even which is not odd & prime. 3. x and y are prime integers, need not be true. lets say 2x/y = 3 and say y=2 prime =>x = 6/2 = 3 prime satisfies the given condition here. but when 2x/y = 3 and y=5 prime => x = 15/2 not prime My Answer is A #### A QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: options: A)42 B)43 C)46 D)47 E)49 SOLUTION:A 42 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) 125 : 150 :: 35 : x 125 x x = 150 x 35 x = (150 x 35)/125 x = 42 #### A QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? options: A)2 B)4 C)6 D)8 E)12 SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less. Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter ANSWER:D #### D QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts. options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22 SOLUTION:Solution : Given SI1 = SI 2 P1 : P2 = 1/R1T1 : 1/R2T2 = 1/(105) : 1/(9:6) 27:25 B #### B QUESTION:What is the remainder when 1014104710501053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24242730 break them into pairs 2424/33 gives remainder 15 and 2730/33 gives remainder 18 so 1518/33 gives remainder 6. B #### B QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is- options: A)42 B)32 C)48 D)28 E)38 SOLUTION:X/63 = 24. X = 24 63. So correct answer would be, (24 63) /36 = 42. ANSWER : A #### A QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted? options: A)72% B)47% C)42% D)34% E)28% SOLUTION:Town A is 40%, therefore town B must be 60% Town A registered voters:0.70∗0.40=0.28 Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent ANSWER:B #### B QUESTION:Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is: options: A)18 B)19 C)20 D)21 E)22 SOLUTION:Explanation: Let first number be x. So,2nd no. = 4x & 3rd no.=8x. So,x+4x+8x=78 × 3 = 234. 13x = 234 x = 234/13 Hence,smallest Number x=18. Answer: A #### A QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 66 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr SOLUTION:still in water=1/2(98+10)km/hr =54km/hr correct option is :B #### B QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage? options: A)33 B)50 C)99 D)87 E)71 SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 4) SP of 60 articles = Rs. 150 (30 * 5) Profit percentage = (150 - 100)/100 * 100 = 50% Answer: B #### B QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)2388 B)2380 C)2888 D)2663 E)2922 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs. 2380. Answer: B #### B QUESTION:The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)22 seconds B)65 seconds C)78 seconds D)12 seconds E)21 seconds SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer:D #### D QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) * 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)18 cm B)20 cm C)22 cm D)24 cm E)26 cm SOLUTION:2(l + b) = 5 b 1 2l + 2b = 5b 3b = 2l b = 2 l 3 Then, Area = 216 cm2 l x b = 216 l x 2 l = 216 3 l2 = 324 l = 18 cm. A) #### A QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 420=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) 15 = 45 Answer is C #### C QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 6300 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 17500 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×6300 / 12×3) => Rs. 17500. Answer : B #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? options: A)525 B)665 C)412 D)235 E)856 SOLUTION:Answer: Option B 8 * 84 = 672 â€“ 7 = 665 #### B QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? options: A)Rs.16003 B)Rs.16029 C)Rs.1288 D)Rs.16108 E)Rs.12000 SOLUTION:Explanation: Manager's monthly salary Rs. (2000 * 21 - 1500 * 20) = Rs.12000. Answer: E #### E QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 68.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 505/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 50018/250 = 36sec Answer is C #### C QUESTION:A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 375,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes? options: A)a) 500 B)b) 750 C)c) 1,000 D)d) 1,250 E)e) 1,500 SOLUTION:Since N = 2F, no of Florida zip codes (F) will be N/2. Since N = 4A, no of Arizona zip codes (A) will be N/4 Since N = (4/3)C, no of California zip codes (C) will be 3N/4 N + N/2 + N/4 + 3N/4 = 5N/2 = 250 N = 100 C = 3N/4 = 75 No of orders is 25% of 375,000 = 93,750 So required ratio = 93,750/75 =1,250 Answer D #### D QUESTION:If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence? options: A)8 B)-9 C)-8 D)9 E)6 SOLUTION:if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence. 7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence. 4th - 2nd = 2 numbers away. -10 + 2= -8 Answer: C #### C QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.8 C)4 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1X2X3 = (1/3)^3 XX1X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? options: A)25 B)37 C)36 D)29 E)21 SOLUTION:Explanation: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get 4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60. We know that SI = , where p is the principal, n the number of years and r the rate percent of interest. In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60. Therefore, 60 =(60n4)/100 => n = 100/4 = 25 years. Answer: A) 25years #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is? options: A)Rs. 3900 B)Rs. 4900 C)Rs. 4980 D)Rs. 5000 E)Rs. 5900 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. A) #### A QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? options: A)30% B)30.77% C)36% D)37% E)38% SOLUTION:Pick numbers. Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100; This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77 Increase in the number of computers purchased = 30.77%. Answer: B. #### B QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now? options: A)8 B)12 C)16 D)20 E)24 SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with: 1) Today, Jim is TWICE as old as Fred 2) Today, Sam is 2 years younger than Fred 3) Six years ago, Jim was 7 times as old as Sam. let's TEST Answer D: 20 IF....Jim is currently 20 years old.... Fred is 10 years old Sam is 8 years old 6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer. D #### D QUESTION:A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.46 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.54 In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:45 E)6:11 SOLUTION:water = w (liter) Milk = m (liter) ==> Cost = Price x Quantity = 0.46m ==> Revenue = Price x Quantity = 0.54(m + w) ==> Profit =0.54(m+w) - 0.46m = 0.2(0.46m)[20% of cost] ==> 0.54m + 0.54w - 0.46m = 0.092m ==> 0.012m = 0.54w ==> m/w = 0.54/0.012 = 45 --OR-- w/m = 1/45 D is correct. #### D QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning. options: A)36 B)39 C)42 D)45 E)None of the above SOLUTION:Let the average after 17th inning = x. Then, average after 16th inning = (x – 2). ∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55. Answer E #### E QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:A group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary. options: A)24 B)36 C)48 D)60 E)64 SOLUTION:The number of ways to choose three cities is 4C3=4. The number of itineraries for each group of 3 cities is 3!. So the number of itineraries to three cities is 43!=24. The number of ways to choose four cities is 4C4=1. The number of itineraries for the group of 4 cities is 4!. So the number of itineraries to four cities is 4!=24. The total number of itineraries is 24+24=48. The answer is C. #### C QUESTION:If -1 < x < 0, which of the following must be true? I. x^4 < x^3 II. x^6 < 1 – x III. x^5 < x^2 options: A)I only B)II only C)III only D)II,III only E)I,II,III only SOLUTION:Answer : E #### E QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:Find the missing in the series: 70, 56, 45, 41,___ options: A)22 B)287 C)2679 D)276 E)2771 SOLUTION:Answer:D #### D QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)1110! B)98! C)87! D)76! E)65! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=1110! Ans:A #### A QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget? options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430 SOLUTION:Difficulty level: 600 Each month's budget = 12000/12 = 1000 Budget for 4 months = 41000 = 4000 Actual amount spent = 4540 Amount spent over the budget = 4540 - 4000 = 540 Answer (B), Regards, #### B QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)? options: A)8 B)22 C)10 D)14 E)12 SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2 = 12 Answer: E #### E QUESTION:The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? options: A)55 B)56 C)57 D)58 E)59 SOLUTION:20x + 50 = 21(x – 5) X=55 ANSWER:A #### A QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)100 =66 2/3% Ans C #### C QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ? options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 19 x 13 ) / (19 +13 ) km/hr. = 15 km/hr. Correct Option: A #### A QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? options: A)4 B)16 C)8 D)1 E)2 SOLUTION:Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B #### B QUESTION:Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)). options: A)1/50 B)3/50 C)4/50 D)6/50 E)9/50 SOLUTION:Answer is A. #### A QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time S will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank S= 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z? options: A)21 B)15 C)14 D)10 E)6 SOLUTION:The smallest possible product is 21 which is 37. All other products are too big. The answer is A. #### A QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)6 D)5 E)1 SOLUTION:2x * x = 128 => x = 8 Answer:A #### A QUESTION:Which of the statements is true for 3111 & 1714 options: A)11 B)88 C)66 D)17 E)16 SOLUTION:Answer:B #### B QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 1642.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:In Hockey game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:In Hockey game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1: P(win) = 1- P(not win) = 1 - 4/64/6 = 5/9. Answer: C. #### C QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1x5)/100 + (1600-x)6/100 = 16005.67/100 Simplifying we get x= 528 B #### B QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 12 (1!)^3=1 2!=2, therefore (2!)^3=222=8 3!=6, therefore (3!)^3=666=216 4!=24 therefore (4!)^3= 242424 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 2600 = Rs.1200 Answer: A #### A QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are: options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186 SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62. The numbers are 62, 124, 186. ANSWER:A #### A QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:Mary and John can do a piece of work in 24 day; John and Vino in 30 days;Vino and Mary in 40 days. If Mary, John and Vino work together they will complete work in ? options: A)77 B)20 C)27 D)19 E)17 SOLUTION:Explanation: Given that Mary and John take 24 days; i.e., (Mary + John)'s 1 day's work = 124124 John and Vino take 30 days; i.e., (John + Vino)'s 1 day's work = 130130 Vino and Mary take 40 days; i.e., (Vino + Mary)'s 1 day's work = 140140 Adding above 3 equations, we get, [(Mary + John) + (John + Vino) + (John + Vino)]'s 1 day's work = 124+130+140124+130+140 2((Mary + John + Vino)'s 1 days work = 124+130+140124+130+140 2(Mary + John + Vino)'s 1 days work = 5+4+31205+4+3120 = 110110 Therefore, (Mary + John + Vino)'s 1 days work = 120120 i.e., Mary, John and Vino together can complete the work in 20 days. Answer: B #### B QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell? options: A) 140 B) 103 C) 105 D) 115 E) 120 SOLUTION:First 100 machines = 3% commission = 0.0310010000 = 30000 Commission from sale of next machines = 46000 - 30000 = 16000 So 40 more machines.. Total = 140 machines IMO A.. #### A QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 60 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ? options: A)2hrs, 48mins B)7hrs, C)7hrs, 12mins D)13hrs, 4mins E)14hrs, 24mins SOLUTION:The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/60 --> x=1/420--> (time) = (reciprocal of rate) = 392 minutes = 7 hours Answer: B. #### B QUESTION:What is the 9th term in this sequence? 2,4,6,13,22,35,60 options: A)138 B)148 C)158 D)168 E)178 SOLUTION:2+4 =6 +0 =6 6+4 =10+3 =13 13+6 =19+3 =22 22+13=35+0 =35 35+22=57+3 =60 60+35=95+3 =98 98+60=158+0=158 so 9th term is 158 ANSWER:C #### C QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None SOLUTION:Formula = S1S2/S2-S1 T1+T2/60 = 46/2 17/6 = 24/2 * 17/60 = 17/5 = 3 2/5 Km A #### A QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? options: A)39 B)88 C)3 D)7 E)62 SOLUTION:Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Answer:A #### A QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669 SOLUTION:they invested in the ratio 1:2 a's share =1/35000=1666 b's share=2/35000=3333 ANSWER:C #### C QUESTION:If the simple interest on a certain sum of money for 2 years is one–fifth of the sum, then the rate of interest per annum is options: A)14% B)7% C)10% D)15% E)3% SOLUTION:Explanation: Let the Principal(P) be x Then, Simple Interest(SI) = x/5 Time(T) = 2 years Rate of interest per annum(R) = (100×SI)/PT = (100 × (x/5)/(x × 2) = 20/2 = 10% Answer: Option C #### C QUESTION:Jeni has 7 flavors of cake in his bakery. How many options are there for Sheera to pick a one-flavor, two-flavor,three-flavor, four-flavor, five-flavor, six-flavor or seven-flavor order? options: A)423 B)325 C)142 D)171 E)127 SOLUTION:7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 . Answer: E #### E QUESTION:Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had? options: A)A)5 B)B)11 C)C)19 D)D)3 E)E)4 SOLUTION:13-10=3. Answer is D #### D QUESTION:If a^x = b^y, then options: A)log a/b= x/y B)log a/ log b = x/y C)log a/ log b = y/x D)log b/a = x/y E)log b/a = y/x SOLUTION:a^x = b^y => log a^x = log b^y => x log a = y log b => log a/ log b = y/x ANSWER:C #### C QUESTION:Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool? options: A)4 2/3 B)9 1/4 C)9 1/3 D)8 3/4 E)10 1/2 SOLUTION:The answer is D 7 pumps take 5 hours. 1 Pump will take 57 hours . Hence 4 pumps will take (57)/4 = 8 75/100 = 8 3/4 hours #### D QUESTION:Which of the number is the odd one out? options: A)21165 B)17642 C)81002 D)52832 E)72927 SOLUTION:D 52832 All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27. Answer is D #### D QUESTION:The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas. options: A)5:25 B)4:25 C)3:15 D)7:15 E)6:15 SOLUTION:Let the diagonals of the squares be 2x and 5x respectively. Ratio of their areas = (1/2)(2x) 2:(1/2)(5x) 2 = 4x2: 25x2 = 4 : 25. ANSWER B 4:25 #### B QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4 and 5). Make the 4 number as large as possible and make the 5 number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6 and 7). Make the 6 number as large as possible and make the 7 number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? options: A)39:40 B)39:45 C)39:40 D)39:41 E)39:42 SOLUTION:3: 4 A = 3/7210 = 90 390: 400 39:40 Answer: A #### A QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:If y is an integer, then the least possible value of \|23 - 4y\| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. \|23-4(5)\| \|23-20\| \|3\| = 3 Next, let’s let y equal 5. \|23-4(6)\| \|23-24\| \|-1\| = 1 We see that the smallest possible value of \|23-4y\| is 1. Answer A. #### A QUESTION:A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? options: A)38 sec B)35 sec C)44 sec D)40 sec E)50 sec SOLUTION:Explanation: Speed = 45 km/hr = 45×(10/36) m/s = 150/12 = 50/4 = 25/2 m/s Total distance = length of the train + length of the platform = 360 + 140 = 500 meter Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds Answer: Option D #### D QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10% options: A)36 B)40 C)32 D)42 E)45 SOLUTION:Let the weight of tea(25 per kg) to be used - X The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30) total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit) The equation follows like this 25X + 900 + (10 % of (25X + 900)) = 30( X + 30) 25X + 900 +2.5 X + 90 = 30 X + 900 27.5 X + 990 = 30 X + 900 2.5 X = 90 X= 90/2.5 = 36 ANSWER:A #### A QUESTION:If a, b, and c are positive numbers such that (a/(a+b))(10) + (b/(a+b))(20)=c and if a<b which of the following could be the value of c? options: A)10 B)12 C)15 D)18 E)30 SOLUTION:The answer is D. For any positive a and b, c is a number between 10 and 20. Since a < b, weight of 10 is inferior of weight of 20 -> c is > 15 -> 18 is the answer. #### D QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica? options: A)48 B)47 C)46 D)49 E)52 SOLUTION:let their ages are 9x,15x and 25x respectively. difference between the ages of Patrick and Monica = 25x-9x=16x where 49x=147 or x=3 so diff in ages = 16x=163=48 yrs ANSWER:A #### A QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:14 To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible. 75-yes 72 -yes 69 and 66 -no 63 - yes 60 -no 57, 54, and 51 -yes 48 - no 45 and 42 - yes 39 - no 36 - yes 33 and 30 - no 27, 24, and 21 - yes 18 -no 15 and 12 yes Correct answer is E. #### E QUESTION:If n = 2.0254 and n is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153 SOLUTION:n=2.03 n-n=2.03-2.0254 0.0046 Answer: D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 45, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)A)19.7 B)B)19.9 C)C)20.9 D)D)21.9 E)E)39.7 SOLUTION:Total cost of the items he purchased = Rs.45 Given that out of this Rs.45, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (45−30/100−x)6/100 = 30/100 ⇒ 6(45 −0.3 −x) = 30 ⇒ (45 − 0.3 − x) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 E) #### E QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue? options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17 SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/189/17 = 12/17. Answer: E. #### E QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L options: A)1/3. B)1/2. C)3. D)2. E)6. SOLUTION:Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2 C #### C QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:How many 0's are there in the binary form of 61024 + 464 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:61024 + 464 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is options: A)25% B)35% C)20% D)23% E)30% SOLUTION:Suppose S.P of 50 mangoes = Rs 50 Therefore, Gain = Rs 10 => C.P = Rs 40 Gain % = 10/40 x 100 = 25% Gain = 25% ANSWER:A #### A QUESTION:Two numbers N and 16 have LCM = 48 and GCF = 8. Find N. options: A)11 B)32 C)24 D)48 E)50 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 16 N = 48 * 8 N = 48 * 8 / 16 = 24 correct answer C #### C QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket? options: A) $60 B) $80 C) $90 D) $120 E) $180 SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T. We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have: (1/2)T + (1/3)T + (1/10)T + 8 = T To get rid of the fractions we can multiply the entire equation by 30, and we obtain: 15T + 10T + 3T + 240 = 30T 28T + 240 = 30T 240 = 2T T = 120 John spent $90 at the supermarket. Answer: D #### D QUESTION:Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $12.00 each, what was Company C’s gross profit? options: A) $2,250 B) $2,500 C) $4,100 D) $3,250 E) $4,500 SOLUTION:Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900 Revenue : 500 * 12 = $6000 Profit: 6000 - 1900 = $ 4100 Option C is correct #### C QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train? options: A)230 m B)250m C)643m D)832m E)270m SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then, x + 270/26 = 20 x + 270 = 520 x = 250. Answer:B #### B QUESTION:Which of the following number is divisible by 24 ? options: A)22 B)24 C)26 D)27 E)28 SOLUTION:24 = 3 x8, where 3 and 8 co-prime. Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8. Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8. Consider option (D), Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3. Also, 736 is divisible by 8. 3125736 is divisible by (3 x 8), i.e., 24. B #### B <<<Examples ends QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following points is symmetric with y=x at (2,3)? options: A)(-2,-1) B)(-2,1) C)(2,1) D)(3,2) E)(-1,2) SOLUTION:We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x. (2,3) would become (3,2). Answer (D). #### D QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket? options: A) $60 B) $80 C) $90 D) $120 E) $180 SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T. We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have: (1/2)T + (1/3)T + (1/10)T + 8 = T To get rid of the fractions we can multiply the entire equation by 30, and we obtain: 15T + 10T + 3T + 240 = 30T 28T + 240 = 30T 240 = 2T T = 120 John spent $90 at the supermarket. Answer: D #### D QUESTION:A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have? options: A)200 B)125 C)180 D)152 E)250 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 45% % of of employees other than secretaries and salespeople = 100 - 60 = 40% But this number is given as 50 so 40% of x = 50 x = 125 Therefore there a total of 125 employees in the company D Correct answer - B #### B QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 Ã— 9 Ã— 9 Ã— 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month? options: A)x/(y - r) B)x/(r - y) C)x D)x/r E)x/y SOLUTION:Two ways... 1) let t be the total number, so cost = ty+x and selling price=tr.. No profit no loss....ty+x=tr.....T=x/(r-y)... B #### B QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? options: A)129 B)128 C)189 D)187 E)112 SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135 SP = CP[(100 + profit%)/100] = 135 * [(100 + 40)/100] = Rs. 189. Answer: C #### C QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b? options: A)-512 B)-257 C)-256 D)-513 E)128 SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation. For the quadratic equation is in the form of ax^2+bx+c=0, The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b 512 can be expressed as product of two numbers in the following ways: 1 * 512 2 * 256 4 * 128 8 * 64 16 32 The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513. The least value possible for b is therefore -513. D #### D QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)877m B)180m C)786m D)165m E)456m SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B #### B QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.052400+x+0.08x = 2400+x+0.08(2400+x) 0.052400+0.08x = 0.06x+0.082400 0.02x = 2400(0.08-0.05) x = 24000.03/0.02 = 3600 Ans:D #### D QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)364 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter? options: A)15 B)25 C)30 D)45 E)60 SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach... We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats. Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as... 15X/7X When we add the 16 cats and factor in the 'ending ratio', we have an equation.... 15X/(7X+16) = 15/11 Here we have 1 variable and 1 equation, so we can solve for X.... (15X)(11) = (7X+16)(15) (X)(11) = (7X+16)(1) 11X = 7X + 16 4X = 16 X = 4 With this X, we can figure out the initial number of dogs and cats... Initial dogs = 15X = 15(4) = 60 Final Answer: D #### D QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x4x=900 x^2= 225 x= 15 Length= 415= 60 difference= 60-15= 45 E is the answer #### E QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered? options: A)60 B)72 C)84 D)90 E)216 SOLUTION:E is the answer.... D = TS where D=distance, T=Time and S=Speed To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes Difference, 216 minutes E #### E QUESTION:one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is? options: A)150 B)133 C)175.5 D)178 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. So, their average price = Rs. 126 + 135 = Rs. 130.50 2 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price Rs. 153 Rs. x (x - 153) 22.50 x - 153 = 1 22.50 x - 153 = 22.50 x = 175.50 C #### C QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails? options: A)a. 4 B)b. 5/2 C)c. 2 D)d. 3/2 E)e. 5/4 SOLUTION:let the weight of nail be n and that of screw be s.. so s+w=1/2 * (6s+1n)... or 1n = 4s.. lets see the weight of 3 s and 3n= 3s+34s=15s.. and weight of 2s and 4n= 2s+42s=10s.. ratio= 15s/10s=15/10=3/2 D #### D QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec SOLUTION:Answer : D. Speed of the train relative to man = (58 - 8) kmph = (50* 5/18) m/sec = (125/9)m/sec Time taken by the train to cross the man = Time taken by It to cover 250 m at 125/9 m / sec = 250 9/ 125 sec = 18sec #### D QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:There are 100 wine glasses. I offered my servant to 3 paise for every broken glass to be delivered safely and forfeit 9 paisa for every glass broken at the end of day. He recieved Rs.2.40 .how many glass did he break. a. 20 b. 73 c. 5 d. 8 options: A)22 B)281 C)29 D)28 E)191 SOLUTION:Answer:B #### B QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:How many positive integers less than 254 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)43 E)64 SOLUTION:252/4=63 Multiples of 4 which are a multiple of 6 will be of the form 223=12n where n>0 240/12=20 63-20=43 Answer: D #### D QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs SOLUTION:Part filled by A in 1 hour = 1/50 part filled by B in 1 hour = 1/75 Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30 Both the pipes will together will fill the tank in 30 hours. Answer is D #### D QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next? options: A)52 B)56 C)96 D)128 E)None SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8. Answer: Option B #### B QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15 ANSWER:D #### D QUESTION:If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca options: A)50 B)30 C)20 D)94 E)25 SOLUTION:(a+b+c)2= a2+b2+c2+2(ab+bc+ca) 2(ab+bc+ca)= (a+b+c)2- a2+b2+c2 =169-69 =100 ab+bc+ca=50 ANSWER A 50 #### A QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)38 B)2767 C)245 D)277 E)232 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in : options: A)15 days B)20 days C)25 days D)30 days E)None of these SOLUTION:Solution (A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50 (A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i) Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii) From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25 ⇒ A’s 1 day’s work = 3/50 ∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50 So, B alone could do the work in 25 days. Answer C #### C QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m options: A)II,III only B)I,III only C)I only D)III only E)II only SOLUTION:n > 1. So, option II, III is not possible. So, Option I is correct. Answer : C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score? options: A)662 B)672 C)652 D)646 E)721 SOLUTION:8 82 = 656 – 10 = 646 ANSWER:D #### D QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday? options: A)X. B)X/2. C)2X/3 D)X/3 E)X/4. SOLUTION:Given the value of stock is X dollars. Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value) Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6 Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value) Ans: A is correct option.. #### A QUESTION:How many digits are in (12×10^14)(10×10^15)? options: A)24 B)25 C)26 D)27 E)32 SOLUTION:The question simplfies to (12×10^14)(10^16) => 1210^30 => Will contain 30 zeros +2 digit 12 =>32 Ans E #### E QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later? options: A) $8,000 B) $5,600 C) $3,200 D) $2,400 E) $4,800 SOLUTION:E. Market value in 1982= $ 8000 Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400 Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800 #### E QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(82003))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 5050 = 2500m = 2.5km Speed = 602.5=150km/hr Answer is D #### D QUESTION:A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? options: A)40.4 sec B)40.5 sec C)50.4 sec D)50.5 sec E)60.4 SOLUTION:Speed = 55 Km/hr (to convert km/hr in to M/s) = 55 x 5/18 M/s Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, ) = 770 m Time = Distance / Speed = 770 x 18 / (5 x 55) = 50.4 sec correct Answer: option a #### A QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26 SOLUTION:Explanation: Let the present age of P and Q be 3x and 4x respectively. Eight years ago, P was half of Q in age => 2(3x – 8) = (4x – 8) => 6x – 16 = 4x – 8 => 2x = 8 => x = 4 7x=74=28 Answer: Option B #### B QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:Two squares are chosen at random on a chessboard. What is the probability that they have a side in common? options: A)1/18 B)64/4032 C)63/64 D)1/9 E)1/4 SOLUTION:Explanation : No of ways of selecting two squares from 64 squares on the chess board is 64C2. Three cases arise: case 1: when first square is any of the four corner ones In this case second square can be chosen in 2 ways no of ways of selecting two squares: 42 = 8 case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones the second square can be chosen in 3 ways no of ways of selecting two squares: 243 = 72 case 3: the first square is any of the 36 remaining squares the second square can be chosen in 4 ways no of ways of selecting two squares: 364 = 144 Total no of ways of selecting two adjacent squares = 8 + 72 + 144 = 224 So required probability = 224/64C2 = 224/4032 = 1/18 Answer : A #### A QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] options: A)800 B)3200 C)900 D)1600 E)None SOLUTION:Answer 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 4 x [(36 x 48 x 250) / (12 x 9 x 5)] = 4 x 4 x 4 x 50 = 3200 Correct Option: B #### B QUESTION:An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested? options: A)99 B)112 C)118 D)124 E)130 SOLUTION:Let x be the number of green apples. There were 496 total apples; there are three times as many red apples as green apples. Therefore, x + 3x = 496 4x = 496 x = 124 Answer: D #### D QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:Find the one which does not belong to that group ? options: A)237 B)232 C)223 D)426 E)111 SOLUTION:Explanation: 525 => 5 52, 39 => 3 32, 24 => 2 22, 636 => 6 62. The above pattern is not followed in 426. Answer: D #### D QUESTION:A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? options: A)20 B)24 C)25 D)26 E)30 SOLUTION:Ans.(A) Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways #### A QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C 100 =50% Answer A #### A QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)2789 B)2772 C)1991 D)6725 E)2099 SOLUTION:CP = SP (100/(100 + profit%)) = 8339(100/124) = Rs. 6725. Answer: D #### D QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 12)/60 =12/47 Answer B #### B QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is: options: A)8 B)4 C)12 D)16 E)14 SOLUTION:Explanation : Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4. Number of Knives = 3x = 12. Answer : C #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 18/5 = 60 km/hr. Answer:C #### C QUESTION:A bike covers a certain distance at the speed of 65km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)86.66 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(C) Sol. Total distance = 65 × 8 = 520 km Now speed = 520/6 = 86.66 km/h #### C QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now? options: A)8 B)12 C)16 D)20 E)24 SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with: 1) Today, Jim is TWICE as old as Fred 2) Today, Sam is 2 years younger than Fred 3) Six years ago, Jim was 7 times as old as Sam. let's TEST Answer D: 20 IF....Jim is currently 20 years old.... Fred is 10 years old Sam is 8 years old 6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer. D #### D QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:In a throw of dice what is the probability of getting number greater than 5 options: A)1/7 B)1/6 C)1/11 D)1/13 E)2/9 SOLUTION:Number greater than 5 is 6, so only 1 number Total cases of dice = [1,2,3,4,5,6] So probability = 1/6 B) #### B QUESTION:Divide Rs.32000 in the ratio 3:3? options: A)12000, 20000 B)12000, 200098 C)16000, 16000 D)12000, 20006 E)12000, 20001 SOLUTION:3/6 * 32000 = 16000 5/6 * 32000 = 16000 Answer: C #### C QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 52 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:In a business Ram invests Rs.60,000. After 6 months his uncle invests Rs.40,000. After one year they got a profit of Rs.12,000. Then uncle gets his share as options: A)Rs.2500 B)Rs.2000 C)Rs.1000 D)Rs.3000 E)Rs.4000 SOLUTION:ram=60,000(12months) uncle=(40000)(6months) 6000012 : 400006 3 : 1 uncle share= (1/3+1)(12000)=3000 ANSWER:D #### D QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 520 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(104)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following? options: A)1 B)10 C)10^2 D)10^3 E)10^4 SOLUTION:Because the question asks for what value isclosestthe question invites approximation. Let's look at the numerator: 10^9 - 10^2 10^9 is HUGE compared to 10^2. So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself). Likewise, 10^7 is HUGE compared to 10^3. So 10^7 - 10^3 is very close to 10^7. So we have: 10^9/10^7 or 10^(9-7) = 10^2. Choose C. #### C QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5700 = Rs.3500 ANSWER:D #### D QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)200 B)300 C)600 D)700 E)100 SOLUTION:E 100 Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100x = 80 x = 100. #### E QUESTION:Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP? options: A)430 B)450 C)550 D)590 E)660 SOLUTION:Cost price = 540/90 x 100 = 600 To gain 10% = 600 x 10/100 = 60 SP = CP + gain = 600 + 60 = 660 Answer :E #### E QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)123 B)143 C)166 D)190 E)210 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions. Hence, the number of all possible selections is 3 10 – 1. Answer C #### C QUESTION:A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond? options: A)5/43 B)8/32 C)6/26 D)4/13 E)2/31 SOLUTION:Total number of cards = 52 Total Number of King Cards = 4 P(King) = 4/52 P(Diamond) = 13/52 P(King and Diamond) = 1/52 P(King or a Diamond) = P(King) + P(Diamond) â€“ P(King and Diamond) =4/52+13/52â€“1/52=16/52=4/13 Answer D #### D QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14Ã—30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—14) Ratio of the capacity of a man and woman =1/(15Ã—14) : 1/(14Ã—30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: options: A)50 m B)150 m C)200 m D)data inadequate E)None of these SOLUTION:Explanation: Let the length of the train be x metres and its speed be y m/sec. Then, (x/y)= 15 y =(x/15) =x+100/25=x/15 => 15(x + 100) = 25x => 15x + 1500 = 25x => 1500 = 10x => x = 150 m. Answer: B #### B QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears? options: A)300 B)250 C)130 D)303 E)111 SOLUTION:830-527=303. Answer is D. #### D QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed Ã— time =9Ã—4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=520=100 Total price of 3 packet milk=312=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector? options: A)1/120 B)1/100 C)1/80 D)1/60 E)1/40 SOLUTION:The largest angle is 87. Let d be the difference between any two angles in the progression. The sum of all the angles will be: 87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d The sum of all the central angles in a circle = 360 696 - 28d = 360 d = 336/28 = 12 The smallest sector is (87-7d) = 87-712 = 3 3/360 = 1/120 The answer is A. #### A QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? options: A)17% B)18% C)30% D)17% E)12% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C #### C QUESTION:If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is: options: A)3:4:5 B)12:15:20 C)20:15:12 D)6:8:10 E)8:4:12 SOLUTION:Explanation: 6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12 ANSWER IS C #### C QUESTION:If d<0, which of the following represents a positive number? options: A)d\|d\| B)\|d\|d C)\|d\|/d D)-d\|d\| E)d/ \|d\| SOLUTION:Answer : D #### D QUESTION:If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? options: A)12.0 B)13.5 C)14.5 D)23.5 E)26.5 SOLUTION:The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C. #### C QUESTION:If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)? options: A)85/365∗84/364 B)13/65∗13/64 C)1 - 85!/365! D)1 - {365!}/{280!(365^8^5)} E)1 - 85!/(365^8^5) SOLUTION:Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays) total ways to pick 85 birthdays = 365^85 Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)85! Hence Probability = 1−365!/280!36585 ANswer is D #### D QUESTION:The triplicate ratio of 1:3 is? options: A)1:27 B)1:8 C)1:3 D)1:1 E)1:2 SOLUTION:1^3: 3^3 = 1:27 Answer: A #### A QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? options: A)28% B)25% C)11.11% D)28% E)55% SOLUTION:900 --- 100 100 --- ? => 11.11% Answer: C #### C QUESTION:If a positive integer n is divisible by both 2 and 3, then n must also be divisible by which of the following? I. 6 II. 5 III. 18 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:A multiple of 2 and 3 is also a multiple of 6, but not necessarily a multiple of 5 or 18. The answer is B. #### B QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 â€¦. (i) A + B = (25 x 2) = 50 â€¦. (ii) B + C = (28 x 2) = 56 â€¦.(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 â€¦. (iv) Subtracting (i) from (iv), we get : B = 16. Bâ€™s weight = 16 kg. Answer E #### E QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)66/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-6 = 1/3 (B+6) ----> 3A-18 =B+6 Scenario 2 B-6 = 1/2 (A+6) -----> 2B-12 = A+6 From Scenario 1, B = 3A-24 Substitute B with this information in Stmt 2 2 (3A-24) -12 = A+6 ------> 6A -48-12 = A+6 ------> 6A- A = 60+6 ---> 5A= 66 A= 66/5, Answer choice A #### A QUESTION:The price of 10 bat is equal to that of 4 balls. The price of 15 balls and 2 bats together is Rs. 4000. The total price of 12 chairs and 3 balls is: options: A)Rs. 3200 B)Rs. 3500 C)Rs. 3700 D)Rs. 3900 E)Rs. 4000 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. D) #### D QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/42/3 = 1/6 of the attendees. Females who did not arrive on time are 1/61/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay? options: A)270 B)360 C)276 D)271 E)272 SOLUTION:128 :169 = 186 8: 12: 9 12/29 870 = 360 Answer: B #### B QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 * 75 = 20.93 ANSWER:D #### D QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:Positive Integer A gives the remainder of 9 when divided by another positive Integer B. If A/B = 47.45, what is the value of B? options: A)96 B)75 C)48 D)20 E)12 SOLUTION:I think the answer should be 25. This is how i solved. .45 of B = Remainder .45 of B = 9 B = (9 100) / 45 = 20. D #### D QUESTION:In how many ways can 6 apples (identical) be distributed among 5 children? (Some children may get no apples.) options: A)124 B)210 C)128 D)130 E)132 SOLUTION:Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1. n=6 r= 5 10C4 =210 Answer : B #### B QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible? options: A)100 B)90 C)80 D)70 E)60 SOLUTION:Secretary can sit in 2C2 ways = 1 Near the gate we can have 6C2 combinations (2 secretaries are already having a place) In the center we can have 4 C2 employees as 4 already have a place Near coffee machine we can have 2C2 employees as all other place are taken Number of selection = 2C2 6C2 * 4C2 * 2C2 = 90 Ans: B #### B QUESTION:By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 20%? options: A)228 B)480 C)512 D)288 E)276 SOLUTION:SP = 800 Profit = 25% CP = (SP)[100/(100+P)] = 800 [100/125] = 640 Loss = 25% = 25% of 640 = Rs.128 SP = CP - Loss = 640 - 128 = Rs.512 Answer: C #### C QUESTION:Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)14 E)16 SOLUTION:The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: D. #### D QUESTION:A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 3/ 50 sec = 12sec Answer : C #### C QUESTION:How many figures are required to number the pages the pages of a book containing 365 pages? options: A)987 B)977 C)967 D)897 E)997 SOLUTION:1 to 9 = 9 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 ----------- 987 ANSWER:A #### A QUESTION:If the complement of a certain angle is five times the measure of that certain angle, then what is the measure of that certain angle? options: A)45° B)30° C)22.5° D)18° E)15° SOLUTION:Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example. The original angle is x, so the complement is 5x, and together, these add up to 90 degrees. x + 5x = 90 6x = 90 x = 15° Answer = (E) #### E QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x â€“ 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.? options: A)A)12PM B)B)4PM C)C)1PM D)D)3PM E)E)5PM SOLUTION:Let x hours be they will meet together distance covered by 1st person+distance covered by 2nd person = 450km 70x+80x = 450 x= 3 hr They will meet = 9AM +3hr = 12PM Answer is A #### A <<<Examples ends QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? options: A)30% B)40% C)50% D)60% E)65% SOLUTION:Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? options: A)Rs.70 B)Rs.75 C)Rs.50 D)Rs.60 E)None of these SOLUTION:2C + 3T = 1300 --- (1) 3C + 3T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 100 => T - C = 100 ANSWER:E #### E QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:219C2 = 2171 = 342 The answer is B. #### B QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x))) 2=5%(15+x)-------->x=25 Ans A #### A QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)100}=4% Answer is A. #### A QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:The triplicate ratio of 1:3 is? options: A)1:0 B)1:8 C)1:27 D)1:2 E)1:1 SOLUTION:13: 33 = 1:27 Answer: C #### C QUESTION:What is the HCF of 2/3, 4/15 and 6/5 options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15 Answer: Option E #### E QUESTION:A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days? options: A)4 B)4/5 C)7/9 D)10 E)24/7 SOLUTION:A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4 A,B,C together will complete the job in 4 days Answer is A #### A QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)30% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 45 are employed males, hence 19% are employed females. (employed females)/(total employed people)=19/64=30% Answer: C. #### C QUESTION:Solve 8x – 4 = 4x + 11 options: A)5(1/3) B)6(1/3) C)7(1/3) D)3(3/4) E)9(1/3) SOLUTION:Sol. 8x – 4 = 4x + 11 => 8x – 4x = 11 + 4 => 4x = 15 => x = 15/3 = 3(3/4). Answer D #### D QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8) options: A)6/k B)8/k C)83k D)2/k E)1/k SOLUTION:Part of the book he can read in 1 minute = 1/k Part of the book he can read in 8 minutes =8/k. Answer: B #### B QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher. options: A)40 yrs B)42 yrs C)45 yrs D)46 yrs E)47 yrs SOLUTION:The average age of 30 boys of a class is equal to 14 yrs: i.e Sum of all boys:3014 include class teacher:31 candidates in a class & avg age is:15 yr i.e. sum of all:3115(include class teacher)=465 so,the age of the class teacher:465-420=45yr answer will be 45 yrs ANSWER:C #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)201 SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111 Answer : Option C #### C QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:In the simple subtraction problem below, some single digits (not necessarily distinct) are replaced by letters. Find the value of 2A + 2B + 4CD. A9C5 - 2B79 -------------- 633D options: A)50 B)52 C)66 D)48 E)46 SOLUTION:A9C5 -2B79 ---------- 6336 since,15-9=6. from there,D=6 and solving all,we get A=8,B=5,C=1. So 28+25+416=50 ANSWER:A #### A QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students? options: A)17 years B)16 years C)15 years D)14 years E)13 years SOLUTION:Sum of the ages of 14 students = (18 * 35) - (20 * 25) = 630 - 500 = 130 Required average = (130/10) = 13 years. Answer:E #### E QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^327 + 26^5. Answer: D. #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 2006 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree? options: A)16 hours. B)19 hours. C)12 hours. D)18 hours. E)13 hours. SOLUTION:The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet. Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet. In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours. Answer D #### D QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46 options: A)16 B)46 C)24 D)11 E)7 SOLUTION:Explanation : 7 is the only odd number in the given series Answer : Option E #### E QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7. options: A)18 B)20 C)17.5 D)30 E)32 SOLUTION:Solution Average = (7+14+21+28)/4) = 70 / 4 = 17.5. Answer C #### C QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: A)4! B)5! C)7! D)8! E)9! SOLUTION:There are seven positions to be filled. The first position can be filled using any of the 7 letters contained in PROBLEM. The second position can be filled by the remaining 6 letters as the letters should not repeat. The third position can be filled by the remaining 5 letters only and so on. 758 Therefore, the total number of ways of rearranging the 7 letter word = 7654321 = 7! Ways. C #### C QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 1045 900 = 2045 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch? options: A)51% B)52% C)53% D)54% E)55% SOLUTION:let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16 so total 52 students takes lunch out of 100 students..so required % is 52% ANSWER:B #### B QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y? options: A)96 B)75 C)50 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 6.12 and remainder is 6 So .12 X y = 6 hence y= 50 Ans C #### C QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream. options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs. SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long? options: A)30 B)40 C)50 D)60 E)70 SOLUTION:Number of pieces = 42.5/0.85 = 42.50/0.85 = 4250/85 = 50. ANSWER:C #### C QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2. #### B QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A #### A QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed? options: A)36 B)64 C)72 D)80 E)100 SOLUTION:you count up combinations twice. 498... and let me name 6 with students A,B,C,..,F after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same. I don't think that's the only mistake. 64 is a factor of = 2^24^2 144 is a factor of = 2^43^2. These are very different numbers and you cannot divide 144 with something to get to 64. #### B QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Let number of pounds of 5$ candy to be used be w 6 = (158 + 5w)/(15 +w) =>90 + 6w = 120 + 5w => w = 30 Answer B #### B QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? options: A)18° B)36° C)54° D)72° E)90° SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20% 100% of the circle is 360 degrees. Then (20%/100%)360 = 72 degrees The answer is D. #### D QUESTION:Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank? options: A)IX B)XXIII C)XV D)XI E)None SOLUTION:Explanation: This is a simple addition series; each number is 3 more than the previous number. Answer: D #### D QUESTION:In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had? options: A)10.7% B)20% C)25% D)33 1/3 E)58 1/3 SOLUTION:No of bank customers in 1985 = 60 x .45 = 27 No of bank customers in 1987 = 144 x .25 = 36 increase in % = 100 X 9/27 = 100/3 or 33 1/3 D is the correct answer #### D QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt? options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36 SOLUTION:The total number of ways the dice can land is 666=216. Bob must get a score of 18=6+6+6. There is only 1 way to do this. P(Bob wins)=1/216 The answer is A. #### A QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? options: A)299 B)277 C)276 D)370 E)281 SOLUTION:Speed = 72 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 150)/26 = 20 x = 370 m. Answer: D #### D QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction? options: A) 49 B) 9 C) 28 D) 26 E) 21 SOLUTION:x/y = 2/5 -> 1 (x+4)/2y = 1/3 -> 2 Divide 1 by 2 : => 2x/(x+4) = 6/5 => 5x = 3x + 12 => x = 6 => y = 5/2 * 6 = 15 so x - y = 9 The answer is B #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.03 B)0.04 C)0.048 D)0.05 E)0.12 SOLUTION:Probability of Brand A defective is x Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12 Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25 Total = 40 + 25 + 25 = 100 Probability of having defective piece in a lot of 100 ( All brands ) = 0.053 Hence 5.3 defective piece out 100 lot. So 40x + 2.12 + 2 = 5.3 x = 0.03 ANSWER :Opt A. #### A QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positivenegative = negative. Thus option C is always negative. #### C QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) options: A)6 B)35 C)41 D)30 E)23 SOLUTION:Under root (32pi/4) ~ 25 Under root (25) = 5 Hence, 25+5 = 30 is the approx answer. D is the correct answer. #### D QUESTION:A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? options: A)15% B)20% C)25% D)29% E)80% SOLUTION:Listed selling price of chair = 84.95 $ Discounted selling price of chair = 59.95 $ Discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = (25/84.95) 100% = 29 % approx Answer D #### D QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? options: A)903 B)2209 C)2878 D)1210 E)1560 SOLUTION:As expected, this question boils down to 2 equation, Consider total number of Balls in Triangle = T and number of balls in last row = x. 1+2+3+...+x = T x(x+1)/2 = T ----(a) As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253) (x-8)^2 = T+253 -----(b) Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk. We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42. Cross check by putting in eq (a) = x(x+1)/2 = T = > 4243/2=903 Hence, answer is A. #### A QUESTION:A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:M = 20 S = 12 US = 20 - 12 = 8 D = 40 T = 40/8 = 5 Answer:C #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. options: A)1 hour and 59 minutes B)2 hour and 59 minutes C)4 hour and 59 minutes D)4 hour and 59 minutes E)5 hour and 59 minutes SOLUTION:Solution: The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half. So, it will take 1 hour and 59 minutes for it to be filled half. Answer A #### A QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.50.5x = x/4 y%x = 36 (y/100)x = 36 (x/400)x = 36 x^2 = 36400 x = 120 The answer is E. #### E QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? options: A)126 B)120 C)101 D)112 E)115 SOLUTION:8 shirts 9 pants we can combine 2 shirts with (12-3) pants 29=18 we can combine the other shirts (6) with any pants (9) 912=54 Thus total :108+18=126 ANS:A #### A QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x10 = 185016 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd. options: A)8/16 B)9/16 C)10/16 D)11/16 E)7/16 SOLUTION:since, p(odd)=3p(even) and p(odd)+p(even)=1 hence p(odd)=3/4 now only oddodd=odd hence two odd i s p(odd)=3/43/4=9/16 ANSWER:B #### B QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (120R)/100 R = 40% Answer:D #### D QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-? options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these SOLUTION:Explanation: 112% of CP = Rs.42750 :. CP = Rs.42750x100/112 = Rs.38169. Answer: Option B #### B QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2PD or m - 2PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is? options: A)1/2 B)1 C)-1/2 D)-1 E)0 SOLUTION:When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero. Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p => x = (p + q - r + p - q + r + q + r - p) / (r + q + p) => x = (r + q + p) / (r + q + p) = 1 p + q + r is non-zero. ANSWER:B #### B QUESTION:E and F have a data plan which gives them 200 GB every month. If E uses 7 GB every 9 days and F uses 5 GB every 4 days, how many GB will be unused after a 30 day month? Answer in fractions. options: A)365/6 B)73/6 C)35/6 D)835/6 E)200/6 SOLUTION:Number of GB that E uses every day: 7/9 Number of GB that F uses every day: 5/4 Number of GB that E and F use every day: 7/9+5/4=73/36 Number of GB that E and F use in 30 days: 30x(73/36)=365/6 Number of GB remaining: 200-365/6=835/6 Answer is D #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is options: A)276 B)299 C)312 D)322 E)None SOLUTION:Solution Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. Answer D #### D QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:The calendar for the year 2007 will be the same for the year: options: A)2014 B)2016 C)2017 D)2018 E)2019 SOLUTION:Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day. Year : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Odd day : 1 2 1 1 1 2 1 1 1 2 1 Sum = 14 odd days 0 odd days. Calendar for the year 2018 will be the same as for the year 2007. Answer: Option D #### D QUESTION:Three seventh of a number is 12 more than 40% of that number. What will be the 10% of that number? options: A)A)148 B)B)210 C)C)21 D)D)248 E)E)258 SOLUTION:3/7 x – 40/100 x = 12 x = 35 * 12 35 * 12 * 10/100 = 42/2 = 21 ANSWER:C #### C QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person? options: A)400 B)410 C)420 D)430 E)440 SOLUTION:Largest 3 digit number divisible by 24= 984 So their shares are (9843/12=246) , (9844/12=328) , (9845/12=410) ANSWER:B #### B QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:In track last week, the boys ran 15 laps. The girls ran 5 more laps. Each lap is a one-fifth of a mile. How many miles did the girls run? options: A)2 miles B)3 miles C)4 miles D)5 miles E)6 miles SOLUTION:The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4. The girls ran 4 miles correct answer C #### C QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K? options: A)30 B)4 C)5 D)66 E)All of these SOLUTION:The first term divisible by 3, so any term could be the third term. Answer =(E) #### E QUESTION:Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? options: A) 20% B) 42% C) 44% D) 66% E) 84% SOLUTION:You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 \Answer:C #### C QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally? options: A)475 B)700 C)220 D)400 E)None of these SOLUTION:Explanation : He sells 20% of oranges and still there are 380 oranges remaining => 80% of oranges = 380 ⇒ (80 × Total Oranges)/100 = 380 ⇒ Total Oranges/100 = 4.75 ⇒ Total Oranges = 4.75 × 100 = 475 Answer : Option A #### A QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 5002/25 =40sec ANSWER:A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black? options: A)4/7 B)3/5 C)5/8 D)2/3 E)3/4 SOLUTION:Each ball has an equal chance (1/9) of being selected fourth. The probability that a black ball is selected fourth is 6/9 = 2/3. The answer is D. #### D QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+3366=448c =>c=3366/112=18 Answer B. #### B QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 109876 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 109876 / 5! = 109876 5! / (5!5!) = 10! / (5!5!) Answer: Option B #### B QUESTION:If there are 30 cans out of them one is poisoned. If a person tastes very little he will die within 14 hours. So if there are mice to test in 24 hours, how many mice’s are required to find the poisoned can? options: A)5 B)4 C)1 D)2 E)3 SOLUTION:first we drink one cane to every rat... after one hour again drink one cane to every rat... and so on till 10 hour... In 10 hour every rat drink 10 cans so all rat drink 30 cans... if A OR B OR C died from poison in 14th hour so they died from 1st cane OR 2nd cane OR 3rd cane respectively if died in 15th hour they died from 4th,5th,6th cans respectively....so on In 24th hour they died from 28th,29th,30th cans respectively... so we can determine which cane is poisoned.. ANSWER:E #### E QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12 SOLUTION:Let the two numbers be x and y. 60/100 * x + y = 5/4y => 3/5 x = 1/4 y => x/y = 5/12 E) #### E QUESTION:If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is? options: A)238 B)150 C)988 D)210 E)171 SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 140)/25 = x/15 => x = 210 m. Answer: D #### D QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 5%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.15% C)14.95% D)13.33% E)12.52% SOLUTION:(100%+5%)(100%-19%) = 1.05.81 = 0.8505. 1-0.8505 = 14.95% lost = -14.95% The Answer is C The organization has lost 14.95% of its total volunteers from fall to spring. #### C QUESTION:The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number? options: A)A)188 B)B)65 C)C)58 D)D)62 E)E)48 SOLUTION:6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s answer = 658+665-1150= 188 Answer is A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages? options: A)(12/x)y B)(5/x)y C)(10/x)y D)(10x)y E)(13/x)y SOLUTION:x page in 10 mins i.e. 1 page in 10/x mins i.e. y pages in (10/x)y Answer: option C #### C QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to options: A)22 B)14 C)6 D)8 E)16 SOLUTION:Given J > P J + P = 7, only options are (6, 1), (5, 2), (4, 3) From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14 Answer:B #### B QUESTION:The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is? options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9 SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B #### B QUESTION:A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%? options: A)Rs.21.81 B)Rs.12 C)Rs.12.25 D)Rs.12.31 E)None SOLUTION:Solution 88 : 16 = 120 : x x= (16Ã—120/88) = Rs.21.81 Hence, S.p per Kg = Rs.21.81 Answer A #### A QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=66 = 36 (6^3)= 366 = .16 (6^4)= .166 = ..96 (6^5) = ..966 = ..76 (6^6) = ..766 = ...56 (6^7) = ....566 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2(3)^2 = 1009 = 900 Vehicles inspected within 3 hours = 603/9 = 19 P = 19/900 Ans:D #### D QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(13651.89+7201.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:A rectangular grass field is 75 m 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:In a throw of dice what is the probability of getting number greater than 5 options: A)1/7 B)1/6 C)1/11 D)1/13 E)2/9 SOLUTION:Number greater than 5 is 6, so only 1 number Total cases of dice = [1,2,3,4,5,6] So probability = 1/6 B) #### B QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. options: A)276 B)552 C)414 D)1104 E)2202 SOLUTION:Let x be the divisor. N1 = xa + 238 N2 = xb + 362 N1 + N2 = x(a+b) + 600 = xc + 68 x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1. The answer is B. #### B QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 68.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)4 Km C)4 1/5 Km D)3 2/5 Km E)3 3/5 Km SOLUTION:Formula = S1S2/S2-S1 * T1+T2/60 = 46/2 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A <<<Examples ends QUESTION:Find the missing in the series: 70, 56, 45, 41,___ options: A)22 B)287 C)2679 D)276 E)2771 SOLUTION:Answer:D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c311c3)+(5c411c2)+(5c511c1) 1936 ANSWER:E #### E QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is: options: A)180 B)1800 C)18 D)18000 E)1350 SOLUTION:Area of the hall= 36001500 Area of each stone= (8050) Therefore, number of stones= (36001500/ 8050)= 1350 ANSWER:E #### E QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each? options: A)96 cm B)108 cm C)120 cm D)132 cm E)154.28 cm SOLUTION:Sum of all interior angles is given by: 180(n-2) = n is number of sides 180(n-2) = 145n from here n = 10.28 So perimeter becomes 1510.28= 154.28 Answer: E #### E QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3 5 7 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen? options: A)1.34 B)2.84 C)3.84 D)4.34 E)5 SOLUTION:40(40/100) = 16 --- 50 ? --- 12 => Rs.3.84 Answer: C #### C QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 43!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C33!=60 total S=84 outcomes D #### D QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold? options: A)2 B)5 C)9 D)12 E)15 SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b) => 3(10 + r) + 5(10 + b) = 120 => 30 + 3r + 50 + 5b = 120 => 3r + 5b = 120 - 30 - 50 = 40 => 5b = 40 - 3r => b = 8 - (3/5)r To minimize b, we need to maximize r and it will be a multiple of 5. r = 5, b = 8 - (3/5)5 = 5 r = 10, b = 8 - (3/5)10 = 2 Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets. Answer: D #### D QUESTION:he L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is: options: A)30 B)40 C)38 D)36 E)39 SOLUTION:Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 48 or x = 8 The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40. Answer: Option B #### B QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y? options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5 SOLUTION:Explanation: 30 x = 50 y x: y = 30: 50 = 3 : 5 Answer:B #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)(C-20)+20=(3/4)C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:How many different subset of the set of the 12 Calendar Month will not have the Month of March. options: A)1951 B)1948 C)1953 D)1947 E)1949 SOLUTION:This is a combination solution Since we have 11 different Month other than the Month of March we can take any Month from the set of 11 Months to make a subset. 11C1 +11C2 + 11C3 + 11C4 + 11C5 + 11C6 + 11C7 + 11C8 + 11C9 + 11C10 + 11C11 = 1948 Plus the one set that is null that is the Set having no element in it which is 11C0 =1 = 1948 + 1 = 1949 E = 1949 #### E QUESTION:The HCF of two numbers is 42 and the other two factors of their LCM are 11 and 12. What is the largest number. options: A)462 B)450 C)480 D)504 E)555 SOLUTION:Explanation: HCF of the two numbers = 42 HCF will be always a factor of LCM 42 is factor of LCM other two factors are 11 & 12 Then the numbers are (42 11) and (42 x 12) = 462 and 504 Answer: Option D #### D QUESTION:At what rate percent per annum will a sum of money double in 16years? options: A)10.6% B)3.65% C)6.25% D)8.32% E)11% SOLUTION:Let principle = P S.I. = P T = 16yrs Rate = 100P/P16 = 25/4% = 6.25% Answer is C #### C QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be? options: A)20 B)40 C)80 D)160 E)180 SOLUTION:3 kg costs $30 1 kg costs $10 8 kg costs $80 The answer is C. #### C QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double (5,5)? options: A)1/24 B)1/36 C)1/12 D)1/18 E)1/3! SOLUTION:total no. in two dice (1,1) ,(2,2) .....(6,) Total number of events= 66 Total events of getting same pair(5,5) = 6 Probability= 6/66= 1/6=1/3! E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? options: A)33 B)77 C)26 D)12 E)99 SOLUTION:Let the required number of working hours per day be x. More pumps, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8 x = (3 x 2 x 8) (4) x = 12. Answer:D #### D QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The product of 2 integers is negative Thus an odd number of integers need to be negative to have a negative product We are asked at most how many are required. So, the highest odd integer before 6,i.e. 1 Correct Option : A #### A QUESTION:For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/7, what are the odds of it burning out during the period from 6months to 1 year following its purchase? options: A)5/27 B)2/9 C)1/2 D)4/9 E)2/3 SOLUTION:P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period) P(of burning out in 1st 6 mnth)= 2/7 --->P( of not burning out in 1st 6 mnth)=1-2/7=5/7 ---->P(of not burning out in a six mnth period)=1/2 5/7=1/3 --->P(of burning out in a six mnth period)=1-1/3=2/3 now P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)P(of burning out in a six mnth) =5/7 * 2/3=1/2 Ans C #### C QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9300 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7500 Ã— 100/90 Ã— 100/90 = 9259 A) #### A QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus? options: A)52 B)92 C)95 D)88 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 11 Total People can seat= 81+11=92 ANSWER:B #### B QUESTION:what is the least number by which 15,625 must be divided to get a number perfect square options: A)21 B)25 C)24 D)40 E)45 SOLUTION:15,625/25=625 625=(25)^2 Ans-25 ANSWER:B #### B QUESTION:What was the day of the week on, 18th July, 1776? options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days. 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days) Total number of odd days = (0 + 4) = 4. Required day was 'Thursday'. Answer:A #### A QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)5/18 = 45 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) options: A)200π B)240π C)300π D)480π E)1,200π SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280 Revolutions in one second= 1320 Revolutions in 60 seconds (one minute)= 132060 Total distance traveled= total revolutions distance traveled in one revolution 132060 2π10/5280= 300π C is the answer #### C QUESTION:Find the unit's digit in the product 2467 153 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 17=7.Also 172 gives 1 Hence unit's digit in the product =71=7. Option A #### A QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 * 100 = 700 #### C QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell? options: A)69 B)72 C)75 D)78 E)81 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.2x. Then she canned 1.40.2x=0.28x. The total amount of pears is x+0.2x+0.28x=1.48x The fraction of pears that she sold is 1/1.48=100/148=25/37. The number of pears she sold is (25/37)111=75. The answer is C. #### C QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged? options: A)6 B)48 C)36 D)24 E)12 SOLUTION:Dhoni have to sit at either of the ends. If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24 David can also sit on the other end, then another 4! ways we can arrange. So total number of ways = 24+24 = 48 Answer : B #### B QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 3200 = 400 Answer: D #### D QUESTION:Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals options: A)1 B)2 C)3 D)4 E)None of these SOLUTION:Explanation : Arithmetic mean is more by 1.8 means sum is more by 18. So, ba – ab = 18. b > a because sum has gone up, e.g. 31 – 13 = 18. Hence, b – a = 2. Answer : B #### B QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4 a:b:c = 5:9:63/4 =20:36:63. Answer is D. #### D QUESTION:Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)1 years B)7 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) = 42 years. Required difference = (42 - 36) = 6 years. Answer: C #### C QUESTION:A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be options: A)7744 B)2388 C)3778 D)2992 E)2888 SOLUTION:Explanation: length of wire = {\color{Blue}2 \Pi r}= 2 (22/7 )56 = 352 cm side of the square = 352/4 = 88cm area of the square = 8888 = 7744sq cm Answer: A) 7744 #### A QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green? options: A)13% B)14% C)15% D)16% E)17% SOLUTION:Number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks Number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks Total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12/80 100 = 15% Answer: C #### C QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 600 = 80/100 * 600 = 480 Option A #### A QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number? options: A)20 B)22 C)27 D)28 E)30 SOLUTION:Given Ratio => 2:3 2x - 10 : 3x - 10 = 2 : 4 4[2x - 10] = 2[3x - 10] 8x - 40 = 6x - 20 8x - 6x = 40 - 20 x = 10 Then biggest number is = 3x 3x = 30 Ans = E #### E QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7 SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively. Then, (4.5x - 4)/(3x + 4) = 1/1 1.5x = 8 => x = 5.33 Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? options: A)65 B)44 C)86 D)29 E)26 SOLUTION:Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Answer: B #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? options: A)5/16 B)5/12 C)5/19 D)5/17 E)5/15 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 Answer: B #### B QUESTION:If f(x)=x^2 and x is a natural number, what CANNOT be the solution to f(f(f(x)))? options: A)16384 B)65536 C)6561 D)256 E)1 SOLUTION:Answer A is equal to 4^7 and cannot be a solution because f(f(f(x)) is equivalent to x^8 and 4^7 cannot equal to anything to the power of 8. #### A QUESTION:A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? options: A)2% B)6% C)14% D)28% E)63% SOLUTION:case 1: (7/90)=x/100 x=8% case 2: (9/63)=y/100 y=14% So percent increase is =(y-x)=(14-8)%=6% Answer is B #### B QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected? options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14 SOLUTION:1- (4c3/8c3) = 13/14 Answer : C #### C QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr? options: A)12 km/hr B)14 km/hr C)10 km/hr D)8 km/hr E)9 km/hr SOLUTION:Explanation: The person needs to cover 6 km in 45 minutes Given that he covers one-half of the distance in two-thirds of the total time => He covers half of 6 km in two-thirds of 45 minutes => He covers 3 km in 30 minutes Hence, now heneed to cover the remaining 3 km in the remaining 15 minutes Distance = 3 km Time = 15 minutes = 1/4 hour Required Speed=Distance/Time = 3/(1/4) = 12 km/hr Answer: Option A #### A QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:Which of the following is not divisible by 6? options: A)10032 B)21192 C)47816 D)91232 E)72031 SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3 Option A: 10032, Divisible by 2. Hence divisible by 6 Option B: 21192, Divisible by 2 & 3. Hence divisible by 6 Option C: 47816, Divisible by 2. Hence divisible by 6 Option D: 91232, Divisible by 2. Hence divisible by 6 Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")(Number of ways the vocalist can sing "new songs")= 1510=150 Answer: C #### C QUESTION:There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg. options: A)29.23 kg B)32.56 kg C)35.66 kg D)37.25 kg E)NONE OF THE ABOVE SOLUTION:Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg 1) First find the total weight of all students - Weight of batch A = (36 x 40) = 1440 - Weight of batch B = (44 x 35) = 1540 Total weight of all students = (1440 + 1540) = 2980 kg 2) Find average weight of whole class (Batch A + Batch B) students = (36 + 44) = 80 students Average Weight = Total weight of all the students / No. of Students = 2980 / 80 = 37.25 kg ANSWER IS D #### D QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)4% B)4.65% C)6.125% D)7.24% E)7.45% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year. options: A)140 B)141 C)142 D)143 E)146 SOLUTION:next year total population=[150^2+90^2]^.5=174.92=175 man decreased by 5% so total man =150.95=142.5 women will be= 175-142.5=32.5 so population after two years= [135^2+32.5^2]^.5=146.15=146 so population after two year= 146 ANSWER:E #### E QUESTION:There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? options: A)8300 B)14500 C)7700 D)13000 E)5900 SOLUTION:Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 #### C QUESTION:For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ? a) 4 b) -3 c) -6 options: A)a only, B)b only, C)c only, D)a and b only E)b and c only SOLUTION:Notice that the question asks which of the following MUST be in the set, not COULD be in the set. Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure. Answer: E. Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set. #### E QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77x=45 --> x=4577/87=677/17=~40. Answer: C. #### C QUESTION:In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together? options: A)6!/2! B)3!3! C)4!/2! D)4! (3!/2!) E)3!3!/2 SOLUTION:In the word ABROAD , there are 3 vowels - 2 A's and O Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together = (4! * 3! )/2! We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! . The entire vowel group is considered as a single group . Answer D #### D QUESTION:he average of 15 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)14 D)19 E)8 SOLUTION:Average of 15 numbers = 0. Sum of 15 numbers (0 x 15) = 0. It is quite possible that 14 of these numbers may be positive and if their sum is a the 15th number is (-a). Answer: Option C #### C QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 6 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15 So, T=15-5 = 10.C #### C QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 Ã— 16 = 368 m2 Area of the inner rectangle = 19 Ã— 12 = 228 m2 Required area = (368 â€“ 228) = 140 m2 Answer B #### B QUESTION:If x and y are even integers, which of the following is an odd integer? options: A)x+y B)xy C)xy+2 D)x^2+y^2 E)None of these SOLUTION:even+even = even even * even = even even+even =even Answer : E #### E QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips? options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32 SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(5251)/(21)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(2625)/(21)=325, N(B)=4C2=(43)/(21)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. options: A)15 B)30 C)35 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 90(x - 5) 80x - (5 * 30) = 90(x - 5) 300 = 10x => x = 30 ANSWER:B #### B QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:One half of the people at the game wore the team colors. Two thirds of those people wore team hats as well. One fourth of those with team colors and team hats had banners to wave. Twenty five people had team colors and banners, but no hats. One hundred people had only banners. If there were 1824 people at the game, how many had banners? options: A)177 B)277 C)377 D)477 E)577 SOLUTION:1/2 x 1824 = 912 with team colors 2/3 x 912 = 608 with hats and colors 1/4 x 608 = 152 with hats, colors, and banners 152 + 100 + 25 = 277 with banners correct answer B #### B QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres? options: A)20 B)200 C)300 D)90 E)140 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 8480 [4L - 40] = 8480 / 26.50 = 320 4L = 360 L = 360/4= 90 meters. Answer: D #### D QUESTION:If the product of the integers r, s, t and u is 770, and if 1 < r< s< t< u, what is the value of r+ u? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 * 5 * 7 * 11 So r= 2, s= 5, t= 7, u= 11 r+ u= 2 + 11 = 13 Answer - B #### B QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:In how many different ways can change be provided for a one dollar bill using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents), if at least two of each type of coin must be included? options: A)0 B)6 C)8 D)10 E)15 SOLUTION:I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any other coins. We cannot have all four coins represented if we have four quarters. Case I does not allow any ways. II. Case II = Three Quarters (75 cents) This does not allow for two each of the other coins. Case II does not allow any ways. III. Case III = Two Quarters (50 cents) This allows for 2-3 dimes. Subcase 1 = 2 Q, 3 D (80 cents) (2 ways) we could have 2-3 nickels Subcase 2 = 2 Q, 2 D (70 cents) (4 ways) we could have 2-5 nickels Case III allows for a total of 6 ways There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals Total = 0 + 0+ 6 =6 ways. OA =(B) #### B QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? options: A) 400 B) 625 C) 1,250 D) 2,500 E) 312 SOLUTION:total fish = x percentage of second catch = (8/50)100 = 16% so, x 16% = 50 x = 312 ans.E #### E QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 312012 = M21209 M2 = 312012/1209 = 4 ANSWER:A #### A QUESTION:Obra drove 140π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive? options: A)6.67% B)12.5% C)18.75% D)29.16% E)33.3% SOLUTION:area enclosed by the circular track on which she drove is 57,600π square meters So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240 Circumference of the circular track = 2πr = 480π Therefore, part of circumference covered = 140π/480π =29.16% Hence, answer is D. #### D QUESTION:The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)11:00 am B)12:00 noon C)1:00 pm D)2:00 pm E)3:00 pm SOLUTION:In ninety minutes, the first train travels 90 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train in 4.5 hours. The second train will catch the first train at 1:00 pm. The answer is C. #### C QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52(15/60) =13m sum of length and breadth = 68(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2120 = 60 sq meter Answer: B) 60 #### B QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph? options: A)32 mph B)34 mph C)36 mph D)35 mph E)31 mph SOLUTION:Explanation : Average speed=Total Distance/Time. Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours. Distance covered in the first 9 hours = 9Ã—40=360 miles Distance covered in the next 6 hours= 6Ã—30=180 miles Therefore, total distance travelled = 360+180=540 miles. The total time taken = 9+6=15hours. Hence, the average speed =540/15= 36 mph. Answer : C #### C QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:I. j; k; m; n; p II. j - 10; m; m; m; p + 15 III. j + 2; k + 1; m; n - 1; p - 2 If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following? options: A) I, III, II B) II, I, III C) II, III, I D) III, I, II E) III, II, I SOLUTION:Range of 1st Set = (p-j) Range of 2nd Set = P+15 - j +10 = (p-j) +25 Range of 3rd Set = P -2 - j - 2 = (p-j) - 4 R2 > R1 > R3 ==> SD2 > SD1 > SD3 Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B #### B QUESTION:Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)14 E)16 SOLUTION:The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: D. #### D QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files? options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr SOLUTION:Server J processes 480/4 files per hour = 120 per hour Server Y processes 180/8 files per hour = 60 per hour Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour 480/180 = 2 2/3 hours=C #### C QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? options: A)7 B)7.5 C)8 D)8.5 E)9 SOLUTION:The sum of the numbers is 69 = 54 K+M = 54 - 13 - 8 - 8 - 7 = 18 Since K ≠ M, K and M do not equal 9. Thus one of the two numbers is 8 or less and one is 10 or more. Then middle two numbers in the set are 8 and 8. The median is 8. The answer is C. #### C QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true? I. ab is even II. ab > 0 III. c is even options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6 lets see III option where C is even as per our assumption C can be even and odd, hence it is out. lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out So options B,C,D,E are gone and ans is A #### A QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:The time on a clock is 20 minutes past 5. What is the angle between the hands of the clock? options: A)60 degrees B)20 degrees C)30 degrees D)50 degrees E)40 degrees SOLUTION:The hour hand rotates 360 degrees in twelve hours. The hour hand rotates 30 degrees in one hour. The hour hand rotates 5 degrees in ten minutes. At this time, the hour hand has rotated 160 degrees. The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes. At this time, the minute hand has rotated 120 degrees. The difference is 160 - 120 = 40 degrees. The answer is E. #### E QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5729 B)5760 C)2889 D)3600 E)2799 SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 2.5 = 3600.Answer: D #### D QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 * Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(5044)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/360/55 = 40 min D #### D QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)364 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination options: A)14 years B)14 years 5 month C)14 years 8 month D)15 years E)15 years 5 month SOLUTION:(d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100 2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years 3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month C #### C QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:If the number 481673 is completely divisible by 9, what is the the smallest whole number in place of ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let x be the smallest whole number in place of * 481x673 is completely divisible by 9 => (4+8+1+x+6+7+3) is divisible by 9 => (29+x) is divisible by 9 x should be the smallest whole number. Hence, (29+x)=36 =>x=36−29=7 Answer is D. #### D QUESTION:When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 48) 4n = 4(6) =24, which leaves a remainder of 0 when divided by 8. Answer A #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:What percent of 200 is 55? options: A)0.25% B)4% C)25% D)27.5% E)250% SOLUTION:200x /100 = 55 x = 27.5 Ans: D #### D QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest .What is the rate of interest ? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:Solution S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100x3000/12500x4) = 6 %. Answer D #### D QUESTION:A man took loan from a bank at the rate of 10% p.a. simple interest. After 3 years he had to pay Rs. 3000 interest only for the period. The principal amount borrowed by him was: options: A)8000 B)10000 C)11000 D)12000 E)13000 SOLUTION:Principal = (100X3000)/(10X3)= Rs. 10000 answer : B #### B QUESTION:A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? options: A)5 B)6 C)10 D)13 E)28 SOLUTION:Suppose there are c columns and there are r rows Original Situation So, Number of tiles = cr = 48 Also. Reach column has r tiles and each row has c tiles New Situation Number of tiles in each column is r-2 and number of tiles in each row is c+4 So, number of rows = r-2 and number of columns is c+4 So, Number of tiles = (r-2)(c+4) = 48 Comparing both of them we get cr = (r-2)(c+4) => 4r -2c = 8 c = 2r - 4 Putting it in cr=48 (2r-4)r = 48 2r^2 - 4r - 48=0 r cannot be negative so r = 6 and c = 8 So, Answer will be B #### B QUESTION:If u r genius solve it:- 70 17 = 11 60 * 16 = 15 50 * 15 = ? options: A)2 B)12 C)6 D)8 E)10 SOLUTION:Logic: 7017=1190=1+1+9+0=11 6016=960=9+6+0=15 5015=750=7+5+0=? Answer : B #### B QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40 SOLUTION:SOL: Lets consider h(100): => 2468.........98100 => (21) (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50) => (2^50) * (1234........4950) => h(100) = (2^50) (50!) We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100). But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50; ANSWER:E #### E <<<Examples ends QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Evaluate:55- 1232 =? options: A)42 B)47 C)62 D)72 E)82 SOLUTION:According to order of operations, 12?3?2 (division and multiplication) is done first from left to right 12*2 = 4 2 = 8 Hence 55 - 1232 = 55- 8 = 47 correct answer B #### B QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5/18 = 10/3 m/s Hence time taken to cover 60 m = 603/10 = 18 seconds. Answer: D #### D QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 259x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:A sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest. What is the rate of interest? options: A)2% B)3% C)6% D)5% E)8% SOLUTION:B 3% S.I. = (13500 - 11500) = 2000. Rate = (100 x 2000)/(11500x5)% = 3% #### B QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in? options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec ANSWER: D #### D QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre. options: A)$10312.50 B)$13512.50 C)$16512.50 D)$14512.50 E)$18512.50 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $500 Hence, total cost =5.5×3.75×500= $10312.50 A #### A QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur? options: A)17 B)21.25 C)12.25 D)14.05 E)18 SOLUTION:radius=7mm. So dia= 14mm. putting D=14 in equation we can easily calculate t=21.25 ANSWER:B #### B QUESTION:A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it? options: A)(y+1)/2 B)(y-1)/2 C)y/(2+1) D)y/(2-1) E)y/2 SOLUTION:Lets put values for y, say y=8 since it's even and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms so putting y=8 in the options, option E = y/2 => 8/2 = 4 , the number of negative integers So, E is the answer #### E QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 105 ⇒ 1.75x = 105 ⇒ x = 60 coins Answer D #### D QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:If x is an integer, then x(x - 1)(x - k) must be evenly divisible by three when k is any of the following values except options: A)-4 B)-6 C)-1 D)2 E)5 SOLUTION:if we put k=-1 we get: X(x-1)(X+1) rearrange:(x-1)X(X+1) so it looks like a sequenc, if we assume that X =2 and put number from the answer then we get: (x – 1)x(x – k) k=5 =1.2.-3 k=2 =1.2.0 k=-1 =1.2.3 k=-4 =1.2.6 but when we put k=-6 =1.2.8 not satisfied so,answer is B #### B QUESTION:A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball? options: A)5⁄7 B)10⁄21 C)2⁄7 D)11⁄21 E)None of these SOLUTION:Reqd probability = 5C2/7C2=5×4/7×6=10/21 Answer B #### B QUESTION:Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$5200 B)$5408 C)$5208 D)$5608 E)$5808 SOLUTION:Interest for 1st year = 50004/100 = 200 Interest for 2nd year = 5200 4/100 = 208 Total =5000+200+208 = 5408 Answer : B #### B QUESTION:Evaluate: 20 - 12÷12×2 = options: A)A)4 B)B)8 C)C)12 D)D)16 E)E)20 SOLUTION:According to order of operations, 12÷12×2 (division and multiplication) is done first from left to right 12÷12×2 = 1 × 2 = 2 Hence 20 - 12÷12×2 = 20 - 12 = 8 correct answer is B) 8 #### B QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? options: A)12 years B)13 years C)15 years D)14 years E)18 years SOLUTION:Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) => 2x = 28 => x = 14 years. D #### D QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km. options: A)24 kmph B)22 kmph C)21 kmph D)28 kmph E)29 kmph SOLUTION:A 24 kmph Total time taken = x/40 + 2x/20 hours = 5x/40 = x/8 hours Average speed = 3x/(x/8) = 24 kmph #### A QUESTION:Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? options: A)2/33 B)4/33 C)2/165 D)4/165 E)7/165 SOLUTION:The number of ways to choose three people is 11C3=165. The number of ways to choose three girls is 5C3=10. P(only girls are chosen)=10/165=2/33 The answer is A. #### A QUESTION:Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 2/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? options: A)1/16 B)7/8 C)9/64 D)5/64 E)3/64 SOLUTION:P(Xavier will solve)=1/4 P(Yvonne will solve)=2/3 P(Zelda will NOT solve) = 1- 5/8 = 3/8. Now, we need to multiply all this Ps to find an answer: p= (1/4)(2/3)(3/8) = 1/16. Ans. A. #### A QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? options: A)150 B)750 C)1,250 D)1,500 E)2,500 SOLUTION:Given 150 deers were caught and they are tagged in the first slot. In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged. Given this 10% approximates the percentage of tagged deer in the forest..here number is 150.. then 100% is 1500.. is the number of deers population in the forest.. Answer: D is correct answer.. #### D QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D #### D QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? options: A)3 B)4 C)2 D)9 E)12 SOLUTION:Rate of machine R =1/8 Rate of machine S =1/4 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/8 +x/4 =1/2 3x/8=1/2 x=8/6=1.3=2 So no of machine R is 2 Answer C #### C QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 1110^e < 1/10 ? options: A) –4 B) –3 C) –2 D) –1 E) 0 SOLUTION:Just putting values, the LHS becomes e=0 --> 11 e=-1 --> 11/10 e=-2 --> 11/100 e=-3 --> 11/1000 Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3. Answer is B. #### B QUESTION:1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ? options: A)A)63.3% B)B)52.4% C)C)81.2% D)D)75.4% E)E)72.11% SOLUTION:Total number of students = 1100+700 = 1800 Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502 number of failures = 1298100/1800= 72.11% Answer is E #### E QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides. options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16 SOLUTION:CM=3 AREA=PMCM/2, thus PM=12 By Pythagorean Theorem, we can now find the value of PC. D is the correct option. #### D QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x 100)/ 4x = 25%. Answer: C #### C QUESTION:Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is options: A)Rs. 12500 B)Rs. 1000 C)Rs. 8000 D)Rs. 6000 E)Rs. 15000 SOLUTION:Sol. Saving = [100 - (40 + 20 + 10 + 10]% = 20%. Let the monthly salary be Rs. x. Then, 20% of x = 2500 â‡” 20 / 100x = 2500 â‡” x = 2500 Ã— 5 = 12500. Answer A #### A QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3p = (1.86^3)p. Similarly max value will be (2.1)^3p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 31.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these SOLUTION:The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer : B #### B QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is? options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1 SOLUTION:100(80/100)(85/100)(92/100) = 62.6 100 - 62.6 = 37.4 Answer:A #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 * 3200 = 400.Answer: D #### D QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 3001 = revenue (eq -1) if he reduced his price by 20% then , 240(customer) = 125/100revenue customer = 1.25300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:(469 + 174)(power 2) - (469 - 174)(power 2) / (469 x 174) = ? options: A)174 B)178 C)171 D)176 E)170 SOLUTION:Formula = (a + b)(power 2) - (a - b)(power 2) / ab = 4ab/ab = 4 (where a = 469, b = 174.) Answer is A. #### A QUESTION:A boat running up stram takes 6 hours to cover a certain distance, while it takes 9 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively? options: A)2 : 3 B)5 : 1 C)4 : 5 D)7 : 1 E)8 : 1 SOLUTION:Explanation: Let speed of boat is x km/h and speed stream is y km/hr 6(x+y) = 9(x-y) 6x+6y = 9x-9y 15y = 3x 5y = x x/y = 5/1 5 : 1 Answer: Option B #### B QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C? options: A)2250 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 75/247 7410 = 2250 Answer: A #### A QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs SOLUTION:Part filled by A in 1 hour = 1/50 part filled by B in 1 hour = 1/75 Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30 Both the pipes will together will fill the tank in 30 hours. Answer is D #### D QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.? options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None SOLUTION:Amount = [22000 * (1 + 12/100)3] = 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42 C.I. = (30908.42 - 22000) = Rs. 8908.42 ANSWER:A #### A QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 7:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/84=1/2, as it quadruples every hour then container was one-eighth full at 7:00 a.m -1 hour = 6:00 a.m. Answer: C. #### C QUESTION:A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set? options: A)1/7 B)1/4 C)5/14 D)11/28 E)27/28 SOLUTION:2/8 1/7 = 2/56 1-(2/56) = 54/56 = 27/28 Answer E #### E QUESTION:Annie has 100 cards numbered 1 through 100. If she deals four cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers? options: A)95!/100! B)96!/100! C)(95! X 5!)/100! D)(96! X 5!)/100! E)(97! X 4!)/100! SOLUTION:Alex to get 4 consecutive cards in ascending order, to have 4 consecutive at the end is good enough. There are 97 consecutive numbers in 100: {1, 2, 3, 4, }, {2, 3, 4, 5}, ..., { 97, 98, 99, 100};{4!97!}{100!}. Answer: E. #### E QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle. options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110° SOLUTION:Solution If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence x + 3x + 8x = 180 Solve for x 12x = 180 x = 15 The measures of the three angles are x = 15° 3x = 3 × 15 = 45° 8x = 8 × 15 = 120° ANSWER IS C #### C QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r? options: A)2 B)3 C)4 D)5 E)Cannot be determined SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y (15^r . 4^2 ) / 4^y = 15^y. 4^0 15^r . 4^(2-y) = 15^y. 4^0 Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A QUESTION:A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)250 B)350 C)450 D)550 E)525 SOLUTION:The number of chocolate bars is equal to 21 * 25 = 525 correct answer E #### E QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|a\| = -a, \|b-3\| + \|ab-b\| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: \|ab\| = ab and \|a\| = -a Question: \|b-3\| + \|ab-b\| = ? ** Looking at \|ab\| = ab tells us that a and b are either both positive or negative Looking at \|a\| = -a tells us that a must be negative ** Combine two observations: a and b are both negative values Let a=-1 and b=-1 \|b-4\| + \|ab-b\| = \|-1-3\| + \|1-(-1)\| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint? options: A)10 B)20 C)28 D)14 E)19 SOLUTION:number of statues=all the paint÷amount used per statue =7/8 ÷ 1/16 =7/816/1 =112/8 =14. Answer is D. #### D QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be? options: A)1 B)2 C)3 D)5 E)7 SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number. If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum. Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3. The correct answer is choice (C). Note:1 is not a prime number. #### C QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15. How many flies did her frog eat on Thursday? options: A)12 B)14 C)10 D)11 E)13 SOLUTION:A) 12. The frog started eating 3 more flies each day. 3 +3 =6 6+3=9 9+3=12 12+3=15 #### A QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = xx is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:What is the largest 4 digit number exactly divisible by 88? options: A)9944 B)9999 C)9988 D)9900 E)9987 SOLUTION:Largest 4 digit number = 9999 9999 ÷ 88 = 113, remainder = 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 Answer: Option A #### A QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)96 C)100 D)125 E)250 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 5.6 , so radius is 2.8 New area = 7.84π Increase in area is 3.84π % increase in area = 3.84/4100 So, % increase is 96% Answer will be (B) #### B QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years, The age of the 15th student is options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Explanation: Age of the 15th student = [15 15 - (14 * 7 + 16 * 7)] = 15 years. Answer: E #### E QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 1110^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10100/((100-10 )5) = Rs. 2(2/9) B #### B QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is : options: A)22 B)40 C)88 D)27 E)11 SOLUTION:Explanation: Let the numbers are By Hypothesis , ......(i) Mean of new numbers = By (i) Answer: B) 40 #### B QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:rom the beginning; Initially milk to water is 12l : 8l remove half 6 - 4 add 10l milk 16 - 4 remove half 8 - 2 add 10l milk 18 - 2 18:2 = 9:1 ANSWER:B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement? K9D 2$M JUR ? options: A)Î´KW B)Î´K5 C)Î´56 D)Î´W6 E)None of these SOLUTION:Explanation: K +6 2 +6 J +6 Î´ 9 +6 S +6 U +6 5 D +6 M +6 R +6 W ANSWER IS E #### E QUESTION:The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July? options: A)$4 B)$0.1 C)$1 D)$3 E)$1.65 SOLUTION:Lets assume price of Coffee in June =100x Price of green Tea in June =100x Price of Coffee in July = 200x (because of 100% increase in price) Price of green Tea in July = 10x (because of 90% Decrease in price) Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x As per question 315x= 3.15$ x = 0.01S So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound Answer B #### B QUESTION:I. q-14, q, q, q, q+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of q or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 12)/60 =12/47 Answer B #### B QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 61/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. â€¹=â€º 61. Answer C #### C QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 B)67 C)108 D)26 E)27 SOLUTION:Length = Speed * time Speed = L/T S = 600/20 S = 30 M/Sec Speed= 3018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C #### C QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:A boat having a length 7 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: options: A)100 kg B)120 kg C)89 Kg D)80 Kg E)210 Kg SOLUTION:Volume of water displaced = (7 x 3 x 0.01) m3 = 0.21 m3. Mass of man = Volume of water displaced x Density of water = (0.21 x 1000) kg = 210 kg. Answer: E #### E QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes at 13 km/hr downstream and 4 km/hr upstream. options: A)4.5 kmph B)9.5 kmph C)7.5 kmph D)8.5 kmph E)5.5 kmph SOLUTION:Speed in still water = (13 + 4)1/2 kmph = 8.5 kmph. answer :D #### D QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 1500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100. => 200 + 2x/25 = (4000 + x) × 6 × 1/100. => 20000 + 8x = (4000 + x) × 6. => 20000 + 8x = 24000 + 6x. => 2x=4000. => x=2000. Answer : D #### D QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? options: A)17% B)18% C)30% D)17% E)12% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C #### C QUESTION:Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed? options: A)200 B)20000 C)25200 D)2500 E)2000 SOLUTION:Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = 7C3 4C2 = 210 Number of groups each having 3 consonants and 2 vowels = 210 Each group contains 5 letters Number of ways of arranging 5 letters among themselves = 5! = (5 * 4 * 3 * 2 * 1) = 210 Required number of words = (210 * 210) = 25200 ANSWER C #### C QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)% SOLUTION:100 – 12 = 88 88------12 100------? => 11 3/22% ANSWER:A #### A QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)35 kmph D)23 kmph E)14 kmph SOLUTION:S = (10 + 60)/2 = 35 kmph Answer:C #### C QUESTION:If a function f is defined by f(x)= (1-x)/x for all non zero numbers x. If f(a) = 1 and f(a/b) = 3 then b= ? options: A)3 B)1/3 C)2 D)1/2 E)-2 SOLUTION:Given that f(x)= (1-x)/x and f(a) = 1, then f(a) =(1-a)/a=1 ===> a=1/2, then backsolve using the answer choices: f(a/b) = f(1/2b) = 3 A) 3 ===> f(1/23) = f(1/6) = 5 B) 1/3 ===> f((1/2)/(1/3)) = f(3/2) = (-1/2)/(3/2) = -1/3 C) 2 ===> f(1/22) = f(1/4) =3 WINS D) 1/2 ===> f((1/2)/(1/2)) = f(1) = 0 E) -2 ===> f((1/2)/-2) = f(-1/4) = (5/4)/(-1/4) = -5 Answer: C #### C QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)32 E)40 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40. Thus E is the correct answer choice #### E QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers? options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9 SOLUTION:Let two numbers be x and y. Equation (i): x + y = 18 Equation (ii): x - y = 4 Solve system of equations: 2x=22 x=11 y=7 Answer C is correct. #### C QUESTION:9, 35, 91, 189, 341, ? options: A)502 B)521 C)559 D)611 E)712 SOLUTION:Explanation : 13 + 23 = 9 23 + 33 = 35 33 + 43 = 91 43 + 53 = 189 53 + 63 = 341 63 + 73 = 559 Answer : Option C #### C QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform? options: A)150 B)145 C)165 D)162 E)152 SOLUTION:D = 130 + x T = 20 S = 130+x/15 * 18/5 = 70 kmph. => (130+x) * 18 = 5250 => 130 + x = 292 => x= 162 m Answer: D #### D QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)1992 C)9921 D)2798 E)2789 SOLUTION:P = 15(100/10)2 => P = 1500 Answer: A #### A QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 2460 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000? options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000 SOLUTION:Saving = (45-30)% of 48000 = 7200. Answer:D #### D QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP? options: A)56% B)68% C)75% D)85% E)95% SOLUTION:Let the volume of sphere PP be 64 parts. Therefore volume of sphere QQ =64−3764%=64−3764% of 6464 =64−37=27=64−37=27 parts. The volume of RR =27−1927×27=27−1927×27 =27−19=8=27−19=8 parts. Volume ratio: =P:Q:R=64:27:8=P:Q:R=64:27:8 Radius ratio: =P:Q:R=4:3:2=P:Q:R=4:3:2 The surface area will be 16:9:516:9:5 Surface area of RR is less than the surface area of sphere PP 16k−4k=12k16k−4k=12k Now, =12k16k×100=12k16k×100 =75%=75% Thus surface area of sphere RR is less than the surface area of sphere P by 75% C #### C QUESTION:If log1087.5 = 5.9421, then the number of digits in (875)10 is? options: A)30 B)70 C)27 D)26 E)25 SOLUTION:X = (875)10 = (87.5 x 10)10 Therefore, log10X = 10(log1087.5 + 1) = 10(5.9421 + 1) = 10(6.9421) = 69.421 X = antilog(69.421) Therefore, number of digits in X = 70. ANSWER:B #### B QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)21 B)24 C)88 D)99 E)26 SOLUTION:(1618)/12 = 24 Answer: B #### B QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:Andy solves problems 78 to 125 inclusive in a Math exercise. How many problems does he solve? options: A)53 B)52 C)51 D)50 E)48 SOLUTION:125-78+1= 48 'E' is the answer #### E QUESTION:Find the value of a from (15)^2 x 8^3 Ã· 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 Ã· 256 = a = 225 x 512 Ã· 256 = 450 E #### E QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year? options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155 SOLUTION:cost of type A products next year = 1.3 * 3200 = 4160 cost of type B products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 ANSWER:C #### C QUESTION:Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? options: A)40 minutes. B)1 hour and 30 minutes. C)1 hour. D)1 hour and 40 minutes. E)2 hours and 15 minutes. SOLUTION:Rate =Output/Time Pomes Rate=25/20=5/4 Dylan Rate=25/60=5/12 Combined rate = 5/4+5/12= 20/12 CombinedRateCombinedTime= CombinedOutput 20/12t=150 t=90 mins => 1 hr 30 min #### C QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 2x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ? options: A)2 B)7 C)5 D)3 E)6 SOLUTION:Let n=3 (leaves a remainder of 3 when divided by 24) 9n = 9(3) =27, which leaves a remainder of 6 when divided by 7. difference = 6 - 3 = 3. Answer D #### D QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:Find the odd man out 4, 16, 25, 36, 42, 64 options: A)36 B)25 C)42 D)95 E)4 SOLUTION:2^2 = 4 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 ANSWER:C #### C QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen? options: A)35. B)45. C)40. D)30. E)25. SOLUTION:Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls. Now here 90% are Boys and 10% are Girls. Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%.. If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it. Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ). IMO option A is correct. #### A <<<Examples ends QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 55 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10? options: A)5 B)7 C)4 D)9 E)3 SOLUTION:30,40,50,60,70 total 5 Answer is A #### A QUESTION:A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)38.89 B)39.18 C)38.78 D)38.0 E)38.18 SOLUTION:Explanation : After 10 days : 300 women had food for 35 days. Suppose 275 women had food for x days. Now, Less women, More days (Indirect Proportion) 275 : 300 :: 35 : x => 275 x x = 300 x 35 => x = 300 x 35 / 275 => x = 38.18 Answer : E #### E QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:The simple interest on a sum of money will be Rs.1000 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)8981 B)3799 C)1200 D)2693 E)2000 SOLUTION:P --- 10 ---- 1000 P --- 5 ----- 500 3P --- 5 ----- 1500 ------ => 2000 Answer: E #### E QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4 Median = 4 Difference = 4-4 = 0 Option A #### A QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)60000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 10800 ( 18 × 600 = 10800) 100% -------> 60000 votes (100 × 600 = 60000) C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:A number is missing from the number series below. Can you find it ? 84, 155, ?, 399 , 584, 819. options: A)275 B)350 C)399 D)258 E)449 SOLUTION:D The missing number is 258. 84 = 4^3 + 3^2 + 4 155 = 5^3 + 5^2 + 5 399 = 7^3 + 7^2 + 7 584 = 8^3 + 8^2 + 8 819 = 9^3 + 9^2 + 9 Thus, 258 = 6^3 + 6^2 + 6 #### D QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is options: A)3Â° B)18Â° C)24Â° D)90Â° E)None of these SOLUTION:In a clock, each minute makes 6Â° âˆ´ 15 minutes will make 6 Ã— 15 = 90Â° Answer D #### D QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by options: A)12 % B)19 % C)25 % D)32 % E)36 % SOLUTION:Explanation: Let original consumption = 100 kg and consumption = y kg. So, 100 x 6 = y x 8 y = 75 kg Reduction in consumption = 25 %. ANSWER: C #### C QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour? options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2 SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same. Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of: R = (100 mi)/(1.5) = 66.67 mph That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars. One of the speeds is x, and let's call the other y. We want y. x + y = 66.67 y = 66.67 - x Answer =(A) #### A QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)20% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+44) i.e 144. Now, his consumption should be reduced to :- =(144−100)/144 ∗ 100. Hence, the consumption should be reduced to 30.6%. Answer : E #### E QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60? options: A)200 B)220 C)240 D)322 E)342 SOLUTION:Required Number = (LCM of 15, 30, 45 and 60) + 20 = 180 + 20 = 200 Option A #### A QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 27 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning options: A)20 B)10 C)30 D)50 E)40 SOLUTION:Assume the number of boys at present = x Then, the number of girls at present = 5x Before the boys left, the number of boys were (x+27) and number of girls were 5x Hence, 2(5x) = x + 27 => 10x = x + 27 => x = 3 Number of girls in the beginning = (5x + 15) = (5×3 + 15) = 30 Answer is C. #### C QUESTION:a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate? options: A)17% B)13% C)12% D)7% E)6% SOLUTION:for 0 years = (900,000- 800,000) = 100,000. for 2 years = (100,000 x 2)/2= 100,000 Principal = (800,000 - 100,000) = 700,000. Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: D #### D QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:The rate of the pump + leak = 5/14 1/2 - leak's rate = 5/14 leak's rate = 1/2 - 5/14 = 1/7 The leak will empty the tank in 7 hours. The answer is D. #### D QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 * 100 = 700 #### C QUESTION:What is the remainder when 1274 * 1275 * 1277 1285 is divided by 12? options: A) 0 B) 6 C) 11 D) 9 E) 7 SOLUTION:1271127512771285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1) Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6. Answer: B #### B QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them? options: A)21 B)24 C)27 D)33 E)45 SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6 Given, X + X+3 + X+6 = 90 3X = 81 X = 27 The numbers are 27, 30, 33 Therefore the largest number is 33 Answer D. #### D QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 1060 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is options: A)35.22 B)36.12 C)36.22 D)36.42 E)None SOLUTION:Solution Correct sum = (36x50+44-23) = 1821. âˆ´ Correct mean = 1821 / 50 = 36.42. Answer D #### D QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)9 B)10 C)11 D)12 E)14 SOLUTION:A number will be divisible by 3 if sum of all the digits of the number is divisible by 3 Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition If sum of Digits = 3, No. = 12, 21 --- 2 Cases If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases If sum of Digits = 12, No. = 57, 75 --- 2 Cases Total Cases = 2+4+6+2 = 14 cases Answer: option E #### E QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9124= 6D28 D2 = 9124/68 = 9 ANSWER:B #### B QUESTION:The sum of two consecutive number is 109. Which is the larger number? options: A)42 B)43 C)44 D)45 E)55 SOLUTION:Let consecutive number be x, x+1 Therefore sum of the consecutive number is x + x+1=109 2x+1=109 2x=108 x=54 Therefore larger number is x+1=55 ANSWER:E #### E QUESTION:How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? options: A)48 B)12 C)72 D)100 E)720 SOLUTION:So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 24!=48. Answer A. #### A QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/21/3=x/6 Platinum card unspent limit is= x-1/9x=8/9x So if gold card balance is transferred then the rest unspent will be 8/9x-x/6=13/18x So the ans is D #### D QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it? options: A)22 B)38 C)60 D)88 E)90 SOLUTION:Explanation: Let the required no of hours be x. Then Less men , More hours (Indirect Proportion) \inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90 Hence, 10 men can do it in 90 hours. Answer: E) 90 #### E QUESTION:40% of x is greater than 1/3rd of x by 110.what is x? options: A)1100 B)2100 C)1300 D)1650 E)1400 SOLUTION:4x/10-x/3=110 1x/15=110 x=1650 ANSWER:D #### D QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)197 C)278 D)270 E)279 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x50 = 200040 x=1600 2000 ------- 400 Answer: A #### A QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica? options: A)48 B)47 C)46 D)49 E)52 SOLUTION:let their ages are 9x,15x and 25x respectively. difference between the ages of Patrick and Monica = 25x-9x=16x where 49x=147 or x=3 so diff in ages = 16x=163=48 yrs ANSWER:A #### A QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails? options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16 SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin. Using the binary formula and defining a head as a success, P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2 t= 6/16 = 3/8 The answer is therefore (C) #### C QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x) SOLUTION:Ans B Plug some numbers Let y = 40 houses and x = 20 then they painted 20 houses per week as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week total time they took = (40/20) + (40/65) = 2.6 weeks Putting the values of x and y in equation B (y +220)/(5x) = (40+220)/520 = 260/100 = 2.6 #### B QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 5/18 = 40 m/sec Time taken = 150/40 = 3.75 sec. ANSWER:C #### C QUESTION:If x = 3^9 and x^x = 3^k, what is k? options: A)3^11 B)3^13 C)3^25 D)3^27 E)3^81 SOLUTION:Solution: We know that x=3^9 which implies x^x = (3^9)^(3^9) = 3^(9 * 3^9) [because (x^y)^z = x^(yz))] so 3^(3^2 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)] therefore x^x = 3^(3^11) Given that x^x=3^k so 3^(3^11) = 3^k Since the base is same the exponent will also be same therefore k = 3^11 Answer: A #### A QUESTION:What is the value of x if (64^2)-(36^2)=20x? options: A)120 B)100 C)140 D)130 E)115 SOLUTION:20x=(64+36)(64-36) 20x=10028 x=(10028)/20 x=528 x=140 Option C #### C QUESTION:A train 150 m long running at 72 kmph crosses a platform in 28 sec. What is the length of the platform? options: A)410 m B)354 m C)450 m D)350 m E)250 m SOLUTION:A 410 A = (72 * 5/18)28-150 = 410 #### A QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11 inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing may help you with this one.) options: A)100 B)130 C)120 D)110 E)101 SOLUTION:3 x 11 = 33 V = 33 x missing measure V is 330 330 ÷ 33 = 10 which is the missing measure of the side of the box top 10 x 11 = 110 sq. ft. which is area of the top of the box. correct answer D #### D QUESTION:In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk? options: A)1 B)40 C)20 D)26 E)30 SOLUTION:Explanation : One bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x For one cow = 20 days Answer : C #### C QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14 years B)18 years C)20 years D)22 years E)16 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 24) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :B #### B QUESTION:9, 35, 91, 189, 341, ? options: A)502 B)521 C)559 D)611 E)712 SOLUTION:Explanation : 13 + 23 = 9 23 + 33 = 35 33 + 43 = 91 43 + 53 = 189 53 + 63 = 341 63 + 73 = 559 Answer : Option C #### C QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged? options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200 SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}. 6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways. Therefore the final answer is 6!2!2!=2,880. Answer: C. #### C QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(22003))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places options: A)34 B)35 C)56 D)67 E)23.57 SOLUTION:Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places Answer: Option E #### E QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream? options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 51/3 = 17 kmph ANSWER:E #### E QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) * 1 + 1 = 15 1 + 1 = 16. 3rd term = (2nd term) 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) 3 + 3 = 34 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:How many 4-digit numbers can be formed from the digits 0,2, 3, 5, 6, 7 and 9, which are divisible by 5 and if the repetition is not allowed? options: A)200 B)240 C)300 D)360 E)120 SOLUTION:Since, each desired number is divisible by 5, so we must have either 0 or 5 at the unit place. So , the tens place can now be filled by any of the remaining 6 digits (2, 3, 6, 7, 9, 0 or 5) the hundreds place can now be filled by any of the remaining 5 digits therefore the 3-digit no can be formed by (4 * 5 * 6 * 2) = 240 ways Ans- B #### B QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)227 B)299 C)276 D)600 E)211 SOLUTION:Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600 Answer: D #### D QUESTION:P is 10% more efficient than Q. P can complete a work in 21 days. If P and Q work together, how many days will it take to complete the same work? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:The work done by P in 1 day = 1/21 Let work done by Q in 1 day = q q × (110/100) = 1/21 q = 100/(21×110) = 10/(21×11) The work done by P and Q in 1 day = 1/21 + 10/(21×11) = 21/(21×11)= 1/11 P and Q together can do the work in 11 days. The answer is C. #### C QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 25=55 35=57 GCF = 5 P.S you can make squares with side of 5 Answer : A #### A QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1 SOLUTION:From the wording in the prompt, we're essentially mixing two liquids: Liquid X is 40% concentrate Liquid Y is 25% concentrate We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra: X = # of ounces of liquid X Y = # of ounces of liquid Y (.4X + .25Y) / (X + Y) = .35 .4X + .25Y = .35X + .35Y .05X = .1Y 5X = 10Y From here, you have to be CAREFUL to answer the question that is ASKED. 5X = 10Y Y/X = 5/10 = 1/2 ANSWER:B #### B QUESTION:Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP? options: A)430 B)450 C)550 D)590 E)660 SOLUTION:Cost price = 540/90 x 100 = 600 To gain 10% = 600 x 10/100 = 60 SP = CP + gain = 600 + 60 = 660 Answer :E #### E QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:Find the odd man out 2, 5, 10, 17, 26, 37, 50, 64 options: A)50 B)26 C)64 D)27 E)17 SOLUTION:Difference is series of ODD numbers 2+3 = 5 5+5 =10 10+7=17 17+9=26 26+11=37 37+13=50 50+15=65 ANSWER:C #### C QUESTION:The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is options: A)5 B)10 C)12 D)40 E)50 SOLUTION:Solution Let the initial number of persons be x. Then 16x + 12 x 15 = 15.5(x+20) = 0.5x = 6 x = 12. Answer C #### C QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:Suppose there is a number 235 such that sum of first two digits is equal to the third digit. How many such 3 digits numbers are possible? options: A)42 B)43 C)44 D)45 E)46 SOLUTION:As we know that total digits are 0 ,1, 2, 3,4,5,6,7,8,9 if three digit no is xyz this means x+y=z must hold so we have to select two no out of 10 ans is 10 c 2=45 ANSWER:D #### D QUESTION:If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:a=105 = 3* 5 7 a^3 = 21 × 25 × 45 × q => a^3 = (73) x (55) x ( 3^2 5) x q => a^3 = 3^3 * 5^3 * 7 x q =>( 3* 5 7) ^3 = 3^3 5^3 * 7 x q q = 7^2 = 49 Answer D #### D QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.50.5x = x/4 y%x = 36 (y/100)x = 36 (x/400)x = 36 x^2 = 36400 x = 120 The answer is E. #### E QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)Total igneous rocks = 40 Total igneous rocks = 40 (3/2) = 60 Total sedimentary rocks = 2Total igneous rocks = 260 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ? options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these SOLUTION:Explanation: Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime =>800+x=65/3∗60 =>800+x=20∗65=1300 =>x=1300−800=500 So the length of the tunnel is 500 meters. Option C #### C QUESTION:Vijay bought 160 shirts at the rate of Rs. 255 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)Rs. 321 B)Rs. 270 C)Rs. 277.5 D)Rs. 285 E)None of these SOLUTION:Total CP per shirt = 255 + 1400/160 + 1.75 + 320/160 = Rs. 267.5 SP = CP[(100 + profit%)/100] = 267.5 * [(100 + 20)/100] = Rs. 321. ANSWER:A #### A QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it? options: A)10 B)15 C)77 D)55 E)21 SOLUTION:1/6 – 1/10 = 1/15 => 15 Answer: B #### B QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective? options: A)316/439 B)316/438 C)316/435 D)316/299 E)316/199 SOLUTION:Let A be the event of getting two oranges and B be the event of getting two non-defective fruits. and be the event of getting two non-defective oranges Answer: C) 316/435 #### C QUESTION:Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)70 m B)60 m C)80 m D)90 m E)100 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:How many ways are there to split a group of 10 students into two groups of 5 students each? (The order of the groups does not matter) options: A)104 B)126 C)148 D)172 E)216 SOLUTION:10C5 = 252 If we consider these groups, each group will be counted twice. The number of ways to choose 2 groups of 5 is 252/2 = 126 The answer is B. #### B QUESTION:18 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)153 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 17 people 2nd person will shake hand with 16 people 3rd person will shake hand with 15 people ...... total no. of handshakes = 17+...+3+2+1 = 17(17+1)/2 = 153 or, if there are n persons then no. of shakehands = nC2 = 18C2 = 153 ANSWER:B #### B QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)226 B)Rs.992 C)665 D)771 E)211 SOLUTION:(80033)/ 100 = 72 920 + 72 = 992 Answer: B #### B QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:Conversation between two mathematicians: First: I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor's door number on my left. The second mathematician verifies the door number and says that it is not sufficient. Then the first says "Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages? options: A)6,6, 1 B)6,6, 2 C)6,5, 1 D)6,5, 2 E)6,6, 3 SOLUTION:Possible options for same sum of ages ( 13 here)with product of ages as 36 are 2,2,9 and 6,6,1 but in case of 2,2,9 youngest is not really youngest as two children of age 2 years are twins. whereas in case of 6,6,1 youngest is really youngest. so 6,6, 1 is correct. ANSWER:A #### A QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 5/18 = 25 mps Answer:E #### E QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. options: A)300 B)T=400 C)T=500 D)600 E)None of these SOLUTION:{Managers} = {Female Managers} + {Male Managers}; We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively. Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200; Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500. Answer: C. #### C QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was: options: A)10 years. B)14 years. C)17 years. D)16 years. E)12 years. SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22 Son's age 10 years back (22 - 10) = 12 years. ANSWER :E #### E QUESTION:if a person cover 3/5 part of his journey by train,7/20 part of his journey by bus and rest 6.5 km. by walk.what is total distance of his journey? options: A)65 km B)100 km C)120 km D)130 km E)75 km SOLUTION:let total distance be=x km.then, 3x/5+7x/20+6.5=x;12x+7x+130=20x;x=130 hence total distance=130 km. answer D #### D QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? options: A)5/6 B)5/9 C)5/3 D)5/0 E)5/1 SOLUTION:No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4 = 120 favourable cases. The total cases are 6 * 6 * 6 = 216. The probability = 120/216 = 5/9. Answer: B #### B QUESTION:Calculate the circumference of a circular field whose radius is 6 centimeters. options: A)2 π cm B)1 π cm C)15 π cm D)12 π cm E)19 π cm SOLUTION:Circumference C is given by C = 2πr = 2π6 = 12 π cm Answer: D #### D QUESTION:If 20% of a number = 1000, then 120% of that number will be? options: A)20 B)120 C)360 D)6000 E)820 SOLUTION:Let the number x. Then, 20% of x = 1000 x = (1000 100)/20 = 5000 120% of x = (120/100 * 5000) = 6000. ANSWER:D #### D QUESTION:If 200!/10^n is an integer, what is the largest possible value of n? options: A)40 B)42 C)44 D)48 E)49 SOLUTION:We have to basically count the number of 5s withing 200 200/5 =40 200/5^2=8 200/5^3=1 We know for sure that there will be at least 49 even numbers(multiples of 2)within 200 So there are 49 10s in 200! ANSWER:E #### E QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.74 less, he could have gained 25%. What is the cost price? options: A)s.370 B)s.375 C)s.375 D)s.350 E)s.300 SOLUTION:CP1 = 100 SP1 = 120 CP2 = 80 SP2 = 80 * (125/100) = 100 20 ----- 100 74 ----- ? => 370 ANSWER:A #### A QUESTION:The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16? options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Given: x=16k (where k is a positive integer) and √x=√16k >16 --> x=16k>16^2 --> divide by 16. So as x/16=k=integer>16, then x/16 can be 17, 18, ... Answer: E. #### E QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 230 per month. What is his monthly salary? options: A)5000 B)5750 C)2878 D)2990 E)2771 SOLUTION:Income = Rs. 100 Expenditure = Rs. 80 Savings = Rs. 20 Present Expenditure 80(20/100) = Rs. 96 Present Savings = 100 â€“ 96 =Rs. 4 100 ------ 4 ? --------- 230 => 5750 Answer: B #### B QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is options: A)1/2 B)1 C)2 D)4 E)8 SOLUTION:Given: 5/w + 5/x = 5/ywx=y Find: (w+x)/2 = ? 5(1/w + 1/x) = 5(1/y) - divide both sides by 5 (1/w + 1/x) = 1/y (x+w)/wx = 1/wx - sub'd in y=wx x+w - 1 = 0 x+w = 1 Therefore (w+x)/2 = 1/2 Ans: A #### A QUESTION:(7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ? options: A)1 B)1 / 5 C)15 / 11 D)3 / 11 E)None SOLUTION:Answer Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = (14 + 1) / (10 + 1) =15 / 11 Option: C #### C QUESTION:Q=(429)^2 237 * (1243)^3 is thrice of ? options: A)33605 * 31960 * (1243)^2 B)33654 * 538219 * (1243)^2 C)33891 * 533247 * (1243)^2 D)34122 * 532004 * (1243)^2 E)34606 * 534572 * (1243)^2 SOLUTION:Q=(429)^2237(1243)^3 is an odd number. Among answer choices only C is an odd number, (so thrice C also will be an odd number). Answer: C. #### C QUESTION:Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip? options: A)48 B)42.5 C)44 D)50 E)52.5 SOLUTION:Total Time taken by jerry = (8/40)60 Minutes + 13 Minutes + (20/60)60 Minutes = 35 Minutes Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 2860 / 35 = 48 Miles per hour Answer: option A #### A QUESTION:How many C ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? options: A)3 B)16 C)28 D)32 E)56 SOLUTION:Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56 Ways to select 1 twin + 1 people = 4C16C1 = 24 Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen C = 56 - 24 = 32 Ans: D #### D <<<Examples ends QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9 SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E âˆ© H) = (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2 D #### D QUESTION:In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number? options: A)24 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=2x Therefore x + 2x = 6 ‹=›3x = 6 ‹=›x= 2. So, ten's digit = 2, unit's digit = 4. Hence, the required number is 24. Answer A #### A QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)18.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 36 Paise is given as tax => Total tax incurred = 36 Paise = Rs.36/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−36/100−x)6/100 = 36/100 ⇒ 6(25 −0.36 −x) = 36 ⇒ (25 − 0.36 − x) = 6 ⇒ x = 25 − 0.36 − 6 = 18.7 B) #### B QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)134 B)154 C)166 D)178 E)189 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was: options: A)2500 B)2520 C)3000 D)3100 E)None of these SOLUTION:Explanation : Number of valid votes = 70% of 9000 = 6300. Valid votes polled by other candidates = 40% of 6300 (40/1006300) = 2520. Harsh Mishra a year ago 0 upvotes Answer : B #### B QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price? options: A)s:1000 B)s:1067 C)s:1278 D)s:1028 E)s:1400 SOLUTION:90% 104% -------- 14% ---- 196 100% ---- ? => Rs:1400 Answer: E #### E QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by: options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800 SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6) = 147 : 189 : 126 = 7 : 9 : 6. Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22 = Rs.3600 ANSWER:C #### C QUESTION:A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:4C2=6. The answer is B. #### B QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together? options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2 SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min (1/30)+(1/20)-(1/90)=(1/x) 13/180=1/x => x=180/13 => x=13.85 minutes Answer: D #### D QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is- options: A)42 B)32 C)48 D)28 E)38 SOLUTION:X/63 = 24. X = 24 63. So correct answer would be, (24 63) /36 = 42. ANSWER : A #### A QUESTION:In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together. options: A)W8 B)789 C)279 D)277 E)191 SOLUTION:Answer:D #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:The perimeter of one face of a cube is 40 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)1000cm3 E)None of these SOLUTION:Explanation: Edge of cude = 40/4 = 10 cm Volume = aaa = 101010 = 1000 cm cube Option D #### D QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required? options: A)34 B)40 C)68 D)88 E)26 SOLUTION:We have: l = 20 ft and lb = 60 sq. ft. So, b = 3 ft. Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft. ANSWER:E #### E QUESTION:If (2/3)^n=(3/2)^3, what is the value of n? options: A)-3 B)-2 C)-1 D)0 E)1 SOLUTION:(2/3)^n = (3/2)^3 = (2/3)^-3 n = -3 (Answer = A) #### A QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)7 cm B)6 cm C)4 cm D)3 cm E)9 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: E #### E QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream? options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 51/3 = 17 kmph ANSWER:E #### E QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55800)/100 =>440 15% of his 440 marks is 440(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20? options: A)276 B)84 C)88 D)90 E)342 SOLUTION:Required Number = (LCM of 5, 10, 15 and 20) + 24 = 60 + 24 = 84 Option B #### B QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) options: A)9/(25xy) B)xy/225 C)225/(xy) D)225xy E)25xy/9 SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 25 / (xy/9) = 225/(xy). The answer is C. #### C QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Halfway between the multiples of 14, there will be another multiple of 7. The total number of multiples of 7 is 12+11 = 23. The answer is D. #### D QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is? options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3 SOLUTION:Correct sum = (36 * 50 + 48 - 23) = 1825. Correct mean = 1825/50 = 36.5 Answer:C #### C QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is options: A)2000 B)2200 C)2300 D)2400 E)None of these SOLUTION:Explanation : i) Given the total sum = Rs. 4000 If the sum given at 8% be Rs.a ie) P = a , n=1, R = 8% (aX18/100) = (8a/100) If the addition given at 10% be Rs. 4000 – a P = 4000-a , n=1, R = 10% (4000 – aX1X10)/(100) = (40000-10a)/100 Given Annual interest is Rs. 352 (8a/100) + (40000-10a)/100 = 352 8a – 10a = 35200 – 40000 -2a = -4800 X = (4800/2)= Rs.2400/- Answer : D #### D QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20. options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280 SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83. A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392; C's share = $ (1162 x (20/83))= $ 280. Option C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)288 B)165 C)881 D)1277 E)121 SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 25 = 375 m. Let the length of the platform be x m . Then, (x + 375)/36 = 15 => x = 165 m. Answer: B #### B QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A? options: A)2 B)3 C)5 D)6 E)8 SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize. 14n/60 If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have (27n)/(2^235) Simplifying 7n/(235) The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7. The number could be 235, or 2352, or 235..... However to be less than 200 we can not add any prime number. 235 = 120 If we added the next prime factor 7, we would have A=2357 = 840 Thus, answer B #### B QUESTION:Tough and Tricky questions: Word Problems. If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money Y would he earn per month? options: A)$700 B)$754 C)$770 D)$782 E)$893 SOLUTION:OFFICIAL SOLUTION: (C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as: $812 = 1.16S, where S is his current salary. Then S = $812/1.16 = $700. Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be: Y=$700 + $70 = $770. The correct answer is choice (C). #### C QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged? options: A)6 B)48 C)36 D)24 E)12 SOLUTION:Dhoni have to sit at either of the ends. If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24 David can also sit on the other end, then another 4! ways we can arrange. So total number of ways = 24+24 = 48 Answer : B #### B QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green? options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220 SOLUTION:Prob of selecting one blue and two green is (487/121110) one blue and two green can be arranged in 3!/2! ways hence the prob becomes 3487/121110=28/55 Correct answer is B #### B QUESTION:Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is? options: A)8 days B)10 days C)20/3 days D)14 days E)16 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 Ã— 20/30 = 20/3 days C) #### C QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. options: A)300 B)T=400 C)T=500 D)600 E)None of these SOLUTION:{Managers} = {Female Managers} + {Male Managers}; We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively. Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200; Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500. Answer: C. #### C QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits? options: A)36 B)77 C)88 D)99 E)22 SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1) Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2) Multiplying equation (1) by 2 and subtracting it from equation (2), we get => 2r = 72 => r = 36. Answer: A #### A QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 40 pints of Perfect Pink paint? options: A)9 B)16 C)21 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 40 pints will require 9/17 * 40= 21 pints.. C #### C QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is options: A)112 B)22 C)56 D)27 E)35 SOLUTION:Explanation: Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 28. L.C.M. of 16 and 28 = 112. Answer: Option A #### A QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr SOLUTION:still in water=1/2(98+10)km/hr =54km/hr correct option is :B #### B QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 541=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 Ã— 110/100 Ã— 110/100 = 12100 C #### C QUESTION:John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have? options: A)65 B)68 C)70 D)77 E)80 SOLUTION:Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60. Step 2: Then pencil are distributed in ratio among friends, Rakesh = ( 1 / 2 x 60 ) = 30. Rahul = ( 1 / 3 x 60 ) = 20. Ranjan = ( 1 / 4 x 60 ) = 15. Rohit = ( 1 / 5 x 60 ) = 12. Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x. For minimum number of pencils x = 1 . The person should have atleast 77 pencils. D) #### D QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? options: A)11 B)44 C)24 D)25 E)22 SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, A=236 and B=25 Ans - D #### D QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C26C2=150 Answer E #### E QUESTION:21 goats eat as much as 15 cows. How many goats eat as much as 35 cows? options: A)49 B)32 C)36 D)41 E)45 SOLUTION:Explanation: 15 cows ≡ 21 goats 1 cow ≡ 21/15 goats 35 cows ≡ 21×35/15 goats ≡ 21×7/3 goats ≡ 7 × 7 goats ≡ 49 goats Answer: Option A #### A QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 18/5 = 180 kmph Answer:D #### D QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)P(B) = 2/5 4/7 = 8/35 ANSWER IS A #### A QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 231 is 6. The answer is C. #### C QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/52/52/5 =36/125 A is the answer . #### A QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 Ã— 120/100 = 12000 C #### C QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? options: A)22 B)28 C)25 D)82 E)34 SOLUTION:M = 20 S = 5 DS = 20 + 5 = 20.Answer:C #### C QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. options: A)220. B)205. C)250 D)105 E)225 SOLUTION:different ways.. 1) EASIEST approach.. lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220... Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15.. total = 220-15 = 205 ANSWER:B #### B QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 * 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.2 per box per month for the record storage, what is the total amount that the company pays each month for record storage? options: A)a. 150 B)b. 300 C)c. 600 D)d. 120 E)e. 200 SOLUTION:Volume Per Box: 15x12x10 = 1,800 Total Volume: 1,080,000 Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600 Price Per Month: Number of Boxes * Price Per Box = 600 * 0.2 = 120 Answer: D #### D QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:P and Q are the only two applicants qualified for a short-term research project that pays 300 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? options: A)$5 B)$10 C)$15 D)$20 E)$25 SOLUTION:Let Q's hourly wage be x, then P's hourly wage is 1.5x Let T be the number of hours that Q needs, then P needs T-10 hours to do the job. Since they both are paid an equal total amount of $300: xT=1.5x(T-10) T = 30 hours and Q's hourly wage is 300/30 = $10 P's hourly wage is 300/(T-10) = $15 which is $5 per hour more. The answer is A. #### A QUESTION:A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? options: A)2.5π B)3π C)5π D)4π E)10π SOLUTION:If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle. In this case, diagonal = (9 + 16)^(1/2) = 5 Hence the radius = 2.5 Circumference = 2πr = 2π2.5 = 5π Correct Option: C #### C QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. options: A)None B)I only C)II only D)III only E)I and II SOLUTION:given 2x/y is prime and greater than 2. => 2x/y could be any of the following 3,5,7.... => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set) 1. x = y , can't be true if x=y , 2x/y = 2 which is not odd and prime. 2. y=1. can't be true. if y=1,2x/y = 2x = even which is not odd & prime. 3. x and y are prime integers, need not be true. lets say 2x/y = 3 and say y=2 prime =>x = 6/2 = 3 prime satisfies the given condition here. but when 2x/y = 3 and y=5 prime => x = 15/2 not prime My Answer is A #### A QUESTION:If one-third of one-fourth of a number is 15, then three-tenth of that number is options: A)35 B)15 C)60 D)54 E)57 SOLUTION:Let the number be x. then 1/3 of ¼ of x=15 X=15x12=180 The required number=(3/10)180=54 ANSWER D 54 #### D QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price? options: A)40% B)8% C)25% D)16.66% E)9% SOLUTION:Original cost before weight adjustment: X Cost after 90% weight adjustment: 9/10 X 20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100 Mark up on original cost of X: (108X/100)/X-1 = 8/100 ANSWER:B #### B QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area? options: A)158 B)129 C)150 D)123 E)60 SOLUTION:1/2 * 12 * 10 = 60 Answer:E #### E QUESTION:Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? options: A)2/5 B)1/4 C)1/3 D)1/2 E)2/3 SOLUTION:Let P be the capacity of Jar X. The amount of water in Jar Y is 1/2P/2=P/4 Then the total amount in Jar X is P/4+P/4=P/2 The answer is D. #### D QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)50 m B)60 m C)65 m D)75 m E)80 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 = options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 22^7 we would have: sum=9(22^7)=182^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C. Answer: C #### C QUESTION:A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? options: A)Rs. 375 B)Rs. 400 C)Rs. 600 D)Rs. 800 E)Rs. 850 SOLUTION:C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24 A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1 C's share (for 3 days) = Rs. (3 1/24 * 3200) =Rs.400 Answer = B #### B QUESTION:how many prime no. are there from 0 to 50? options: A)14 B)15 C)16 D)17 E)19 SOLUTION:we calculate it manually.we know the definition of prime no.prime no. should only have two distinctâ€‹ natural no. divisor 1 and itself. note:1 is not a prime no. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 total no.=15 answer B #### B QUESTION:A part-time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? options: A)9 B)13 C)17 D)20 E)33.33 SOLUTION:Let original hourly wage be x and let the no of hours worked be y Total wage will be =xy After the increment the wage will be=1.5 x Now we need to find number of hours worked so that xy=1.5xz i.e z=1/1.5 y = 2/3y %decrease = (y-2/3y)/y 100=100/3=33.33%. Thus my answer is E. #### E QUESTION:How many terminating zeroes T does 200! have? options: A) 40 B) 48 C) 49 D) 55 E) 64 SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:A river 7m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is? options: A)54996.5 B)32296.5 C)34996.5 D)34996.5 E)31255.5 SOLUTION:Rate of water flow-4kmph--4000/60--66.66 m/min depth of river--7m width of river--75m vol of water per min--66.66 775---34996.5 Answer C #### C QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour? options: A)73 B)83 C)12 D)83 E)11 SOLUTION:Explanation: T = 8/45 * 60 = 11 Answer: Option E #### E QUESTION:A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)350 B)250 C)450 D)550 E)650 SOLUTION:The number of chocolate bars is equal to 18 ? 25 = 450 correct answer C #### C QUESTION:If the cost price is 96% of sp then what is the profit % options: A)4.07% B)4% C)4.7% D)4.17% E)4.27% SOLUTION:Sol. sp=Rs100 : then cp=Rs 96:profit =Rs 4. Profit={(4/96)100}%=4.17% Answer is D. #### D QUESTION:Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996? options: A) $24 million B) $120 million C) $144 million D) $240 million E) $888 million SOLUTION:Convert units to millions as answer is in millions 1996 Imports = $1.44 bill = $1440 mill i.e. 1440/12 = $120 mill/month 1997 Imports = $388 mill/2 month i.e. $194 mill/month Difference/month = 194-120 = 74 Difference/year = $74 mill 12 = $988 mill ANSWER: E #### E QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack? options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13 SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits. Probability of getting spade or a jack: = (13 + 3)/52 = 16/52 = 4/13 Therefore, the probability of getting neither a spade nor a jack: = 1 − 4/13 = 9/13 ANSWER:A #### A QUESTION:The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is options: A)1008 B)1015 C)1022 D)1032 E)1043 SOLUTION:Required Number = (L.C.M of 12, 16, 18,21,28)+7 = 1008 + 7 = 1015 Answer: B #### B QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 119 = 99 Answer B #### B QUESTION:Sum of 53 odd numbers is? options: A)2709 B)2809 C)2909 D)3009 E)3109 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 53 odd numbers = 53^2 = 2809 ANSWER:B #### B QUESTION:By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 20%? options: A)228 B)480 C)512 D)288 E)276 SOLUTION:SP = 800 Profit = 25% CP = (SP)[100/(100+P)] = 800 * [100/125] = 640 Loss = 25% = 25% of 640 = Rs.128 SP = CP - Loss = 640 - 128 = Rs.512 Answer: C #### C QUESTION:If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true? options: A)x^2 + Px + A = 0 B)x^2 - Px - 2A = 0 C)2x^2 + Px + 2A = 0 D)2x^2 - Px - 2A = 0 E)2x^2 - Px + 2A = 0 SOLUTION:Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0. Now, assume: Length =x = 1 inchand width = 1 inch; Perimeter =P = 4 inches; Area =A = 1 square inches. Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px + 2A = 2 - 4 + 2 = 0. Answer: E. #### E QUESTION:Pipes A and B can fill a cistern in 10 and 90 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full? options: A)13 B)12 C)16 D)18 E)19 SOLUTION:: 1/10 + 1/90 = 1/9 9 * 2 = 18.Answer:D #### D QUESTION:In an election between two political leaders 10% of the voters did not cast their vote. 10% of the votes polled were found invalid. The successful political leader got 54% of the valid, votes and won by a majority of 3240 votes. The number of voters enrolled on the voters list was : options: A)30000 B)50000 C)33000 D)40000 E)45000 SOLUTION:Explanation : Solution: Let the number of voters be x. then, votes polled = 90% of x. Valid votes = 90% of(90% of x) .'. 54% of[90% of(90% of x)] - 46% of[90% of(90% of x)] = 3240. 8% of[90% of(90% of x)] = 3240. 8/100 * 90/100 * 90/100 * x = 3240 x = (3240100100100)/(89090) = 50000 Answer : B #### B QUESTION:In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? options: A)0.44 B)0.55 C)0.65 D)0.75 E)0.85 SOLUTION:Number of people whose age is less than 20 is given by 160 - 90 = 70 Probability P that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer A #### A QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E QUESTION:An office supply store stocks two sizes of notebooks, each in six colors: orange, blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)20 B)24 C)32 D)36 E)42 SOLUTION:First let's consider the small notebooks. There are 6 ways to choose notebooks of the same color. The number of ways to choose four notebooks with different colors is 6C4=15. There are 21 different packages we can make with the small notebooks. We can use the same process to find 21 different packages with large notebooks. The total number of different packages is 42. The answer is E. #### E QUESTION:What is the range of all the roots of \|x^2 - 5\| = x ? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:we get 2 quadratic equations here .. 1) x^2-x-5=0 ....... roots 2 , -1 2) x^2+x-5=0 ........ roots -2, 1 Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations . So value of x for given equation .... x=5 or x=1 I guess range is 5-1 =4 A #### A QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:What is the area of a square field whose diagonal of length 12 m? options: A)288 B)72 C)200 D)112 E)178 SOLUTION:d2/2 = (12 12)/2 = 72 Answer: B #### B QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 22=2^2=4. Total # of ways: 4C22^2=24. Answer: A #### A QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true. Therefore, the correct answer is (D). #### D QUESTION:18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place? options: A)144 B)131 C)279 D)90 E)45 SOLUTION:there are 18 business exec and in each handshake 2 business execs are involved. hence 18C2=153 Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake. total=153+126=279 ANS: C #### C QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (7505R)/100 R = 4% Answer :C #### C QUESTION:A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)35 hours B)25 hours C)20 hours D)Cannot be determined E)None of these SOLUTION:Suppose the efficiencies of pipes C, B and A are 4K, 2K and K. Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours Answer A #### A QUESTION:Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page? options: A)6:26 B)6:56 C)7:26 D)7:56 E)8:26 SOLUTION:Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom. The answer is C. #### C QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:If the cost price of 12 pens is equal to the selling price of 11 pens, the gain percent is: options: A)80% B)90% C)9% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 11 pens = Rs. 11; S.P. of 11 pens = Rs. 12. Gain % = 1/11 * 100 = 9% Answer:C #### C QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year? options: A)1:2:1 B)2:3:6 C)3:2:1 D)1:2:3 E)1:4:3 SOLUTION:Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively. 3b = 2b = c. a = c/3. b = c/2. Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments = 2:3:6. ANSWER:B #### B QUESTION:Solution for 4.75+.303+.432 options: A)2.91 B)5.911 C)5.485 D)5.986 E)2.999 SOLUTION:4.75+.303+.432=0 0=0-4.75-0.303-0.432 0=-5.485 answer :C #### C QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,15 = 15/100 x= 8015/100 x= 12 12/10 = 1,2 = 120%, Answer C #### C QUESTION:One train is traveling 72 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)2:1 D)5:4 E)5:1 SOLUTION:72 5/18 = 10 20:10 => 2:1 Answer: C #### C QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:What percentage of numbers from 1 to 20 have squares that end in the digit 9? options: A)1 B)14 C)20 D)21 E)22 SOLUTION:Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 18 are 3,7,13,17. Number of such numbers = 4. Required percentage = (4/18 * 100) = 22% ANSWER:E #### E <<<Examples ends QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 * 672 = 256 Answer: A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/85/74/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate * Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 344 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales? options: A)8% B)15% C)35% D)42% E)56% SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%. Answer D #### D QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5? options: A)180 B)245 C)320 D)260 E)270 SOLUTION:reduce to 1 - 80 5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320 C #### C QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)650 SOLUTION:Explanation: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters =5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120 All the 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves =3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6 Hence, required number of ways =120Ã—6=720 ANSWER IS B #### B QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3) options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69 SOLUTION:=> root 5/ root 3 = (root 5/ root 3)(root 3/ root 3) = root 15/ root 9 = 3.87/3 = 1.29 ANSWER:A #### A QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ? options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29 SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 6 * 6 = 216 ways. Hence the probability is 6/216 = 1/36 Answer: B #### B QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)1/10=80.5+7.51/10 80.5+0.75=81.25 E #### E QUESTION:Find the greatest number which on dividing 6215 and 7373, leaves a reminder of 23 and 29 respectively options: A)125 B)127 C)129 D)131 E)144 SOLUTION:Explanation: In this type of question, its obvious we need to calculate the HCF, trick is HCF of (6215 - 23) and (7373 -29) = HCF (6192, 7344) = 144 Option E #### E QUESTION:A certain Maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight. A certain green paint contains 10 percent blue pigment and 90 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5.3 =1.5 Grams of red pigment #### A QUESTION:If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be options: A) 478,823 B) 511,913 C) 531,875 D) 538,424 E) 569,114 SOLUTION:To know the unit digit you can multiply both digit number: 5 x 5 = 25 This eliminates A, B, D, and E, because the number must end with a 5 So the answer is C #### C QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these SOLUTION:Explanation : Total numbers = 70 Total numbers in 1 to 70 which has 1 in the unit digit = 7 Total numbers in 1 to 70 which has 9 in the unit digit = 7 Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14 Required percentage = (14/70) × 100 = 140/7 = 20% Answer : Option B #### B QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)150 B)152 C)154 D)158 E)144 SOLUTION:D = d Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 2460 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:What is the area of a square field whose diagonal of length 12 m? options: A)288 B)72 C)200 D)112 E)178 SOLUTION:d2/2 = (12 * 12)/2 = 72 Answer: B #### B QUESTION:A machine P completes a certain amount of work in 12 hrs and machine Q completes the same work in x hrs if both machines works together to complete the same work in 8 hrs then what is x? options: A)12 hrs B)18 hrs C)24 hrs D)32 hrs E)34 hrs SOLUTION:Explanation: P’s 1hr work = 1/12 Q’s 1 hr work = 1/x (A+B)’s 1 hr work = 1/8 = 1/12+1/x => x = 24 hrs Answer: Option C #### C QUESTION:Convert 50miles into yards? options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards SOLUTION:1 mile = 1760 yards 50 miles = 501760 = 88000 yards Answer is C #### C QUESTION:Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? options: A)40 minutes. B)1 hour and 30 minutes. C)1 hour. D)1 hour and 40 minutes. E)2 hours and 15 minutes. SOLUTION:Rate =Output/Time Pomes Rate=25/20=5/4 Dylan Rate=25/60=5/12 Combined rate = 5/4+5/12= 20/12 CombinedRateCombinedTime= CombinedOutput 20/12t=150 t=90 mins => 1 hr 30 min #### C QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours 1 choices = 1C11C1 = 11=1=D #### D QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)6 D)5 E)1 SOLUTION:2x * x = 128 => x = 8 Answer:A #### A QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages. options: A)20,35,45 B)8,20,28 C)16,28,36 D)16,28,46 E)None of these SOLUTION:Let the present ages of three persons be 4K,7K and 9K respectively. (4K - 8) + (7K - 8) + (9K - 8) = 76 20K = 100 K = 5 Therefore, then present ages are 20,35,45. ANSWER:A #### A QUESTION:The number 0.8 is how much greater than 1/2 ? options: A)½ B)3/10 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .8-1/2=x 8/10-1/2=x x= 3/10 ans B #### B QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? options: A)32 B)55 C)6 D)78 E)81 SOLUTION:S = (100 + 300)/45 = 400/45 * 18/5 = 32 Answer: A #### A QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:One type of liquid contains 10% of water and the second type of liquid contains 15% of water. A glass is filled with 5 parts of 1st liquid and 2 parts of 2nd liquid. The percentage of water in the new mixture in the glass is? options: A)5.6% B)11.4% C)15.6% D)21.3% E)18.9% SOLUTION:Required percentage = (10% of 5 + 15% of 2)/5+2 100 = 0.8/7 100 = 11.4% Answer is B #### B QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years. Total profit is Rs.1000/-. Find the C's share? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 800 E)Rs. 900 SOLUTION:Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6. So C's share = Rs. (1000 * 6/15) = Rs. 400. Answer: Option C #### C QUESTION:Which of the following is satisfied with \|x-4\|+\|x-3\|<6? options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4 SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, \|x-4\|+\|x-3\|<6 -> \|x-4+x-3\|<6 -> \|2x-7\|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. #### C QUESTION:If Aaron is now twice as old as Bailey was 5 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now? options: A)3B B)3B-1 C)3B-21 D)3B-11 E)3B-2 SOLUTION:B is Bailey's current age. Let Aaron's current age be A. given A = 2(B-5). four years from now Aaron's age will be = 2(B-5) + 4 = 2B-6 four years from now Bailey's age will be = B+4 Sum of ages of Mason and Gunther's after 4 years = 2B-6+B+4 = 3B-2 Ans : E #### E QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:In a throw of dice what is the probability of getting number greater than 5 options: A)1/7 B)1/6 C)1/11 D)1/13 E)2/9 SOLUTION:Number greater than 5 is 6, so only 1 number Total cases of dice = [1,2,3,4,5,6] So probability = 1/6 B) #### B QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number R of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=R Answer is C #### C QUESTION:What should come in place of the question mark (?) in the following equation? 45789+ 34567 = 610+ ? options: A)96543 B)13678 C)23456 D)56789 E)79746 SOLUTION:45789+ 34567 = 610+ ? 45789+ 34567 – 610 = 79746 Answer E #### E QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 109876 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 109876 / 5! = 109876 5! / (5!5!) = 10! / (5!5!) Answer: Option B #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:A contractor undertook to finish a job in 150 days and employed 200 men. After 50 days he found that only 1/4 of work was finished. How many extra days are needed if he employs 50 more men? options: A)20 B)25 C)30 D)35 E)45 SOLUTION:work part A=25% and work part B= 75% 25% work done by 200 people in 50 days if only one employee works then he takes 20050=10000 days and if work(B) is triple more ten he will take =100003 =30000 days if employees are 250 then days = 30000/250=120days then total days = 50+120 = 170 days how many extra days taken = 170-150 = 20 days ANSWER:A #### A QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)2 D)3 E)4 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a? options: A)10 B)B.13 C)18 D)26 E)50 SOLUTION:The prompt gives us a couple of facts to work with: 1) A and B are positive INTEGERS 2) A/B = 2.86 We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in). The simplest place to start is with... A = 286 B = 100 286/100 = 2.86 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 143 B = 50 143/50 = 2.86 There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A.... Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices. Final Answer: B #### B QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed? options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:Work done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the Printer were operating. Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm B #### B QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440 SOLUTION:Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 2640 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 1440. E is my answer. #### E QUESTION:The area of a triangle is with base 18m and height 6m? options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2 SOLUTION:1/2 18 * 6 = 54 m2 Answer: D #### D QUESTION:If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S? I. 1/10 II. 1/9 III. 1/11 options: A)None B)I only C)III only D)II and III only E)I, II, and III SOLUTION:Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10. On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91. We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer. #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight options: A)1/6 B)1/8 C)1/4 D)3/4 E)7/8 SOLUTION:Good question. So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved). we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2. We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ). So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or A. #### A QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)155 m B)150 m C)187 m D)177 m E)186 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:if a no. is divided by 342 then remainder is 47.then if that no. is divided by 18 then what will be the remainder? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:let quotient be k if that no. is divided by 342 and remainder 47. that no.= 342k+47 = (1819k)+(182)+11 =18(19k+2)+11 so remainder when divided by 18=11 answer A #### A QUESTION:If the area of a circle is 81pi square feet, find its circumference. options: A)48 B)38 C)51 D)92 E)18 SOLUTION:The area is given by pi pi × r × r = 81 pi r × r = 81 ; hence r = 81 feet The circumference is given by 2 × pi × r = 2 × pi × 9 = 18 pi feet correct answer is E) 18 #### E QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 321/4 = 8 mins. ANSWER:A #### A QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A? options: A)240 B)288 C)266 D)216 E)123 SOLUTION:(38 + 24):(48 + 54) 8:13 8/21 * 630 = 240 Answer: A #### A QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose? options: A)24 B)36 C)72 D)90 E)108 SOLUTION:Let the Breakfast set be {F , Y} Lunch be {I ,I , C,C , L1,L2} Dinner be {I,I,I , C,C,C, D1,D2,D3} There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner. So the set of Breakfast, Lunch and Dinner will {Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2 {Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6 {Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9 Adding all these gives 72. Answer is C #### C QUESTION:On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3. In this case: the x-intercept is the value(s) of x for s = 0. 0 = x^2 - x^3; 0 = x^2(1 - x); x = 0 or x = 1. Answer: C. #### C QUESTION:Mario and Nina each have a bag of marbles, each of which contains 10 blue marbles, 10 red marbles, an 10 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble? options: A)3/4 B)2/9 C)1/4 D)1/8 E)1/16 SOLUTION:Mario and Nina each select one marble from their respective bags. Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble Probability that either Mario or Nina select a red marble = (10/30)(10/30) + (10/30)(10/30) = 2(1/9) Probability that either Mario or Nina select a red marble = 2/9 Answer would be B. #### B QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? options: A)3/5 B)2/5 C)1/2 D)4/5 E)19/25 SOLUTION:There can be an odd product only if both integers are odd. P(odd product) = 1/22/5 = 1/5 P(even product) = 1 - 1/5 = 4/5 The answer is D. #### D QUESTION:The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160.The time after which it is due is : options: A)6 months B)8 months C)9 months D)10 months E)None SOLUTION:Solution P.W = Rs.(1760 - 160)= Rs.1600. ∴ S.I. on Rs.1600 at 12% is Rs.160. ∴ Time =(100x160/1600x12 ) = 5/6years = ( 5/6x12) months = 10 months Answer D #### D QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:When you draw 2 dices together, find the probability of getting numbers in pairs? options: A)1/5 B)1/6 C)1/7 D)1/11 E)1/12 SOLUTION:S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} N (S) = 36 Set of pairs, B = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}; N (B) = 6 P (getting numbers in pairs) = N(B)N(S)N(B)N(S) = 636636 = 1/6 B #### B QUESTION:In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr options: A)8.5 seconds B)2.86 seconds C)3.5 seconds D)2.5 seconds E)2.6 seconds SOLUTION:First convert speed into m/sec Speed = 126(5/18) = 35 m/sec Time = Distance/speed = 100/35 = 2.86 seconds Answer: B #### B QUESTION:What will be the product of (50-1)(50-2)(50-3)..............(50-79)(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true? I. c - a = 2 II. abc is an odd integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and III only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: C. #### C QUESTION:How many multiples of 5 are there between 70 and 358? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:5 * 14 = 70 5 * 71 = 355 Total no of multiples = (71 - 14) + 1 = 57 + 1 = 58 Answer is E. #### E QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 3232 !=476 #### C QUESTION:Two numbers are in the ratio of 1 : 2. If 8 be added to both, their ratio changes to 3 : 5. The greater number is options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let the ratio be X : Y, Given X/Y = 1/2 , (X + 8)/(Y + 8) = 3/5 => X = 16 And Y = 32 ANSWER:D #### D QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race? options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec SOLUTION:Time taken by B run 1000 meters = (1000 10)/16 = 625 sec. Time taken by A = 625 - 10 = 615 sec. Answer:E #### E QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2(44 + 124) = 2(16+48) = 128 Then, Finally Length (L) = 212 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2(22 + 242) = 2(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)100 /Initial Area i.e. % change in Area of four walls = (104-128)100 /128=- 18.75% (Decrease) Answer: Option D #### D QUESTION:In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)8.3% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100100=10,000. Now, the area obtained with wrong measurements would be 11495=10,830, which is 8.3% greater than the actual area. Answer: C. #### C QUESTION:In the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r = options: A)6 B)5 C)4 D)3 E)2 SOLUTION:An easy way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units (both points are on y=-1 line so the distance will simply be 1-(-2)=3) So the radius must be more than 3 units. The distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units (both points are on x=-2 line so the distance will simply be 4-(-1)=5) So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4. Answer: C. #### C QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z? options: A)1:8 B)1:4 C)2:1 D)4:1 E)10:1 SOLUTION:x= 5y, y= 2z X : Y , Y : Z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 So, X : Z = 10 : 1 (E) #### E QUESTION:Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm. options: A)25 B)45 C)35 D)15 E)40 SOLUTION:Required length = H.C.F. of 495 cm, 900 cm and 1665 cm. 495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37. Therefore, H.C.F. = 32 x 5 = 45. Hence, required length = 45 cm. Answer is B. #### B QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? options: A)600 B)2877 C)208 D)1882 E)191 SOLUTION:Explanation: Cost price = Rs.500 profit = 20% of 500 = Rs.100 Selling price = Cost price + Profit = 500 + 100 = 600 Answer:A #### A QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:a = 2n (n>=3), b = 2n - 2, c = 2n - 4 a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E ANSWER:E #### E QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)30/13 hours E)60/29 hours SOLUTION:Speed downstream = 20 + 9 = 29 kmph. Time required to cover 60 km downstream = d/s = 60/29 = 60/29 hours. Answer: E #### E QUESTION:What is the value of âˆš36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>âˆš16% =âˆš36/âˆš100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:rom the beginning; Initially milk to water is 12l : 8l remove half 6 - 4 add 10l milk 16 - 4 remove half 8 - 2 add 10l milk 18 - 2 18:2 = 9:1 ANSWER:B #### B QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:Which of the following equations has a root in common with x^2−4x+3=0 ? options: A)x^2-4x-4=0 B)x^2-2x+1=0 C)x^2-x-1=0 D)x^2-10x-1=0 E)x^2+1=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-3) = 0 so the two roots are 1 and 3. Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get -7; Putting 3 we get -7. Reject this option. (B) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. B is the answer. #### B QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(bx) B)Rs.{(bx)/a} C)Rs.{(ab)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b(x/a) = Rs. {(bx)/a} ANSWER B #### B QUESTION:Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,700 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip? options: A)14.0 B)13.0 C)12.0 D)11.0 E)10.0 SOLUTION:Solution:H stopped 700 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs. this means she reached there at 11:00. speed difference between them is 800-500=300 ft/hr so by the time H stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00 means 12:00 is the answer. C #### C QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11 inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing may help you with this one.) options: A)100 B)130 C)120 D)110 E)101 SOLUTION:3 x 11 = 33 V = 33 x missing measure V is 330 330 ÷ 33 = 10 which is the missing measure of the side of the box top 10 x 11 = 110 sq. ft. which is area of the top of the box. correct answer D #### D QUESTION:A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)22 days B)12 days C)67 days D)17 days E)18 days SOLUTION:C = 1/2 - 1/6 - 1/4 = 1/12 => 12 days Answer:B #### B QUESTION:I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price? options: A)$2000 B)$2500 C)$2400 D)$3120 E)$1540 SOLUTION:115% of cost - 110% of cost = $120 5% of cost = $120 cost = 120100/5 = $2400 Answer is C #### C QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen? options: A)119 B)1,200 C)3,240 D)3,600 E)14,400 SOLUTION:To meet the conditions we can have only 2 cases: 2 officers and 3 civilians: C25∗C39=840 3 officers and 2 civilians: C35∗C29=360 Total: 840+360=1,200. Answer: B. #### B QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball? options: A)10 cm B)12 cm C)14 cm D)16 cm E)18 cm SOLUTION:similar triangle properties.. 2/r+4 = 4/r-4 giving r = 14. Answer: C #### C QUESTION:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? options: A)15 B)18 C)11 D)12 E)19 SOLUTION:D 12 If there are n people, the first person will shake hand with n-1 persons, the second with n-2, the third with n-3, and the (n-1)th person with n-(n-1)=1 person means the last person. Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1 Which can be equated using n(n-1)/2=66 Hence, n=12 #### D QUESTION:J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r? options: A)93.5 B)90 C)6.75 D)6.25 E)2 SOLUTION:Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables. Let, P = 400 then J = (75/100)400 = 300 also J = (80/100)T i.e. T = 300100/80 = 375 and T = [1-(r/100)]P i.e. 100-r = 100T/P = 100375/400 = 93.75 i.e. r = 6.25 Answer: Option D #### D QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = prt/100 = 100000043/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? options: A)17603 B)17608 C)17628 D)17600 E)176023 SOLUTION:Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 * 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600 Answer: D #### D QUESTION:A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ? options: A)12 : 49 : 64 B)20 : 49 : 64 C)10 : 19 : 64 D)20 : 29 : 64 E)30 : 29 : 63 SOLUTION:Simply multiply profit sharing ratio with investment ratio to get investment amount ratio. Let X is the total investment â‡’14 x = 3 â‡’ 8 x = 7 â‡’ 7x = 8 â‡’ Final investment ratio = 12 : 49 : 64 A #### A QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 22=2^2=4. Total # of ways: 4C22^2=24. Answer: A #### A QUESTION:50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be: options: A)20 cm B)25 cm C)35 cm D)50 cm E)None of these SOLUTION:Explanation: Total volume of water displaced =(4 x 50) m3 = 200 m3 Rise in water level = 200/40×20= 0.25m = 25cm Answer: B #### B QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)6 B)12 C)20 D)24 E)27 SOLUTION:402/3 3/4= 20 Answer: C #### C QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest) options: A)27.5 years B)17 years C)17.5 years D)16.5 years E)15.5 years SOLUTION:Present total age of the members = 24(5) = 120 years. Present age of the youngest member = 10 years Present total age of the remaining four members = 120 -10 = 110 years Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years ANSWER:C #### C <<<Examples ends QUESTION:One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number? options: A)4 B)6 C)0 D)9 E)19 SOLUTION:Answer: Option D x/2 â€“ x/3 = 6 => x =6 3 + 6 = 9 #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (512/5)/100] P= 1500.Answer:A #### A QUESTION:The H.C.F. of two numbers is 12 and their difference is 12. The numbers are : options: A)66, 78 B)70, 82 C)94, 106 D)84, 96 E)None of these SOLUTION:Explanation: Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96. ANSWER IS D #### D QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up? options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball. Number of arrangements = 9!/(2!)2 3! Answer: E #### E QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test? options: A)768 B)243 C)246 D)280 E)224 SOLUTION:Let the maximum mark in each test be M. The candidate failed by 66 marks in the second test. pass mark in the second test = 249 + 66 = 315 45/100 M = 315 Pass mark in the first test = 40/100 M = 40/45 315 = 280. Answer:D #### D QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ? options: A)249 B)498 C)676 D)823 E)274 SOLUTION:slope of 2 and a y-intercept of 2 y-coordinate is 550 y = 2x + 2 548 = 2x x = 274 Answer: E. 274 #### E QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48. options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512 SOLUTION:P : 2/13 = 5/34 : 7/48 As the product of the means is equal to the product of the extremes. P7/48 = 2/13 5/34 P7/48 = 10/442 P = 480/3094 => P = 240/1547 Answer: C #### C QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is: options: A)90 cm B)6 dm C)1 m D)1.1 cm E)None of these SOLUTION:Explanation: Let the thickness of the bottom be x cm. Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000 => 320 × 250 × (160 - x) = 8000 × 1000 => (160 - x) = 8000×1000/320= 100 => x = 60 cm = 6 dm. Answer: B #### B QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these SOLUTION:Explanation: We know perimeter of square = 4(side) So Side of first square = 40/4 = 10 cm Side of second square = 32/4 = 8 cm Area of third Square = 1010 - 88 = 36 cm So side of third square = 6 [because area of square = sideside] Perimeter = 4Side = 46 = 24 cm Option B #### B QUESTION:In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order? options: A)360 B)720 C)620 D)180 E)36 SOLUTION:Two letters can be arranged in 2! ways. only one combination EIU is required. 6 letters can be arranged in 6! ways. thus 6!/ 2! * 1 = 360. A #### A QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 5002/25 =40sec ANSWER:A #### A QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 610 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3. We need to add 5 more to these 12 because of 9, 18, 27, and 36. The greatest integer of k is 17. The answer is C. #### C QUESTION:The digit in unit's place of the product 81 ×82×.....×89 is options: A)0 B)2 C)6 D)8 E)4 SOLUTION:Solution Required digit = Unit digit =(1×2×3×4×5×6×7×8×9) =0. Answer A #### A QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take? options: A)80 B)288 C)4^4 D)576 E)288^2 SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate.. Total five means 3 of one and 2 of other.. 1) choose 3 girls and arrange them... 4C33! = 4!= 24 2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C22!= 12 Total ways = 2412 = 288.. 2) same as above.. 2 girls and 3 boys.. 288 Total 2882=576 ANS:D #### D QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!10! 1211/21 =66 ANSWER:D #### D QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(90033)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)0.07 B)0.049 C)0.7 D)0.49 E)4.9 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi4910 = pih100100 (h is distance that the oil level dropped) h = 490/10,000 = 49/1000 = 0.049 ft The answer is B. #### B QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=2726^2 The answer is C. #### C QUESTION:At what rate of interest is an amount doubled in two years, when compounded annually? options: A)41.4% B)43.4% C)31.4% D)30% E)21.4% SOLUTION:Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4% ANSWER:A #### A QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years? options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none SOLUTION:Sol. A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28 Answer D #### D QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)Rs. 4980 B)Rs. 4991 C)Rs. 4996 D)Rs. 4997 E)Rs. 5000 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991. B) #### B QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels? options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28 SOLUTION:The number of ways to choose two letters is 8C2 = 28 The number of ways to choose two consonants is 5C2 = 10. P(no vowels) = 10/28 = 5/14 The answer is D. #### D QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (87654321)/(654321) = 87 =56 ANSWER:B #### B QUESTION:At what rate percent per annum will a sum of money double in 16years? options: A)10.6% B)3.65% C)6.25% D)8.32% E)11% SOLUTION:Let principle = P S.I. = P T = 16yrs Rate = 100P/P16 = 25/4% = 6.25% Answer is C #### C QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? options: A)25 B)30 C)45 D)20 E)50 SOLUTION:6p2 = 6 x 5 = 30 B) #### B QUESTION:if (p/q)-(q/p)=21/10 then what ia the value of(4p/q)+(4q/p) options: A)58/5 B)59/5 C)121/105 D)101/105 E)1/2 SOLUTION:p/q =a then q/p = 1/a a+1/a=21/10 by solving this we get a=5/2 then 45/2+42/5 = 58/5 ANSWER:A #### A QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3. options: A)27 B)26 C)28 D)25 E)24 SOLUTION:1/2(6+12)3=27 ANSWER:A #### A QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in? options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18 = 4/18 The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs. Answer:B #### B QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? options: A)250 B)300 C)350 D)400 E)500 SOLUTION:Nice problem. +1. First timetogetherthey run half of the circumference. Second timetogetherthey run full circumference. First time Brenda runs 100 meters, thus second time she runs 2100 = 200 meters. Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters. Answer: B. #### B QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:8/7 * 24 = 27.4 The answer is B. #### B QUESTION:1.5, 2.3, 3.1, 3.9, ..? options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15 SOLUTION:1.5+0.8=2.3 2.3+0.8=3.1 3.1+0.8=3.9 3.9+0.8=4.7 ANSWER:B #### B QUESTION:In the first 12 overs of a cricket game, the run rate was only 4.5. What should be the run rate in the remaining 38 overs to reach the target of 360 runs? options: A)9.55 B)6.25 C)6.75 D)8.05 E)7.25 SOLUTION:Required run rate = 360 - (4.5 x 12) /38 = 306/38 = 8.05 Option D #### D QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:The value of (34.310.4731.5)/(0.067323.257.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.310.4731.5)/(0.067323.257.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(1001000)/270-100]+100 = 2600 Answer is B #### B QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips? options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32 SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period? options: A)$1.18 B)$1.17 C)$1.16 D)$1.15 E)$1.14 SOLUTION:Let x be the number of loaves sold in May. Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June. The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) = (80 + 127 + 144) / (3) = 351/3 = $1.17 The answer is B. #### B QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)18 cm B)20 cm C)22 cm D)24 cm E)26 cm SOLUTION:2(l + b) = 5 b 1 2l + 2b = 5b 3b = 2l b = 2 l 3 Then, Area = 216 cm2 l x b = 216 l x 2 l = 216 3 l2 = 324 l = 18 cm. A) #### A QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $5760. What is the average monthly balance maintained by John in his account during the year? options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400 SOLUTION:bank balance is doubled with accumulation of interest tp 5760.. this means INTEREST is 5760/2=2880 for entire year.. although since interest is 10% of avg MONthly balance, it becomes 28800.. B #### B QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90? options: A)426 B)430 C)443 D)480 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:Which of the following is a prime number options: A)9 B)2 C)4 D)8 E)7 SOLUTION:Explanation: A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself. So from above options 2 is that number Option B #### B QUESTION:What inequality represents the condition 1<x<13? options: A)\|x\|<3 B)\|x+5\|<4 C)\|x-7\|<6 D)\|-5+x\|<4 E)\|3+x\|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any \|x-a\|<b a is a center and b is a half of length. So, \|x-7\|<12/2 represents our inequality (answer C) #### C QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? options: A)25% B)40% C)50% D)60% E)75% SOLUTION:34% is 9%-points above 25% and 6%-points below 40%. Thus the ratio of mixture Y to mixture X is 2:3. The percent of mixture X is 3/5 = 60%. The answer is D. #### D QUESTION:The odds against ram solving the problem are 6 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try? options: A)1/4 B)5/21 C)16/21 D)23/28 E)13/18 SOLUTION:Odds against Ram are 6:3 so probability that he will solve the problem is 1/3. Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12 It will be solved means that either Ram or Krishna or both will be able to solve it. P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 7/12 - (1/3)(7/12) = 13/18 E #### E QUESTION:A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 6%. What was its profit on the items sold in February? options: A)27.5% B)30% C)35% D)37.5% E)41% SOLUTION:Assume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25120x = 150x Price after the discount = 0.94150x = 141x Hence total profit = 41% Option E #### E QUESTION:Which of the following is closer to √0.8+√0.05? options: A)0.5 B)0.7 C)0.9 D)1.1 E)1.2 SOLUTION:√0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D. #### D QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average? options: A)69 B)70 C)71 D)72 E)75 SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D #### D QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:√7 percent of 7√7 = options: A)0.55 B)0.96 C)0.1 D)0.45 E)0.6 SOLUTION:The other solutions are great, but here's one more approach. First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION All test-takers must memorize the following approximations: √2 ≈ 1.4 √3 ≈ 1.7 √5 ≈ 2.2 √6 ≈ 2.4 √7 ≈ 2.6 So, √7 percent of 7√7 ≈ 2.6 percent of (7)(2.6) ≈ (2.6/100)(18.2) ≈ 47.32/100 ≈ 0.47 Check the answer choices to see that D is the only answer that's close. Answer: D #### D QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg? options: A)72 B)47 C)40 D)28 E)20 SOLUTION:940(30/100) = 282 ---- 6 ? ---- 1 => Rs.47 Answer:B #### B QUESTION:If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is: options: A)8 B)9 C)12 D)14 E)13 SOLUTION:Let the numbers be x and y Then x2-y2=39 And x-y=3 We get x+y=13 Solving x-y=3, x+y=13 X=8, y=5 Larger number 8 ANSWER A 8 #### A QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a? options: A)67 B)197 C)91 D)199 E)42 SOLUTION:1) A and B are positive INTEGERS 2) A/B = 3.98 A = 398 B = 100 398/100 = 3.98 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 199 B = 50 199/50 = 2.86 There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A.... Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices. Answer: D #### D QUESTION:By selling 66 bags, a shopkeeper gains the price of 33 bags. His gain per cent is options: A)91% B)100% C)95% D)98% E)93% SOLUTION:Suppose S.P of 66 bags = Rs 66 Therefore, Gain = Rs 33 => C.P = Rs 33 Gain % = 33/33 x 100 = 100% Gain = 100% ANSWER:B #### B QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm SOLUTION:Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 h = (4/3)π (12)3 => h = 9 cm Answer: Option E #### E QUESTION:A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is options: A)4 B)3 C)2 D)1 E)5 SOLUTION:Here we can assume that one subject is of 100 marks so total there are 5 subjects => 1005 = 500. Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total. The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio. Total ratio = 40 For 6 : (300/40)6 = 45 Similarly , we will get for others as 52.5 , 60 , 62.5 , 75. Hence , there are 3 subject where he secured more that 60 %. The answer is 3. B #### B QUESTION:Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years? options: A)6.9% B)2.9% C)9.9% D)5.9% E)4.9% SOLUTION:220.50 = (15003R)/100 R = 4.9% Answer: E #### E QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (1804R)/100 R = 5% Answer: A #### A QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π10 = 20 π cm Answer: A #### A QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)7/12 B)29/60 C)17/30 D)19/30 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/21/3=x/6 Platinum card unspent limit is= x-1/4x=3/4x So if gold card balance is transferred then the rest unspent will be 3/4x-x/6=7/12x So the ans is A #### A QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230m B)240m C)250m D)260m E)270m SOLUTION:speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s time= 9sec let the lenght of second train is x total distance covered= 260 + x therefore, D= speedtime thus 260 + x = 500/9 9 x= 500-260=240 m ANSWER:B #### B QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/84=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m. Answer: B. #### B QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”? options: A)5 B)7 C)49 D)20 E)25 SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). C #### C QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? options: A)7 B)7.5 C)8 D)8.5 E)9 SOLUTION:The sum of the numbers is 69 = 54 K+M = 54 - 13 - 8 - 8 - 7 = 18 Since K ≠ M, K and M do not equal 9. Thus one of the two numbers is 8 or less and one is 10 or more. Then middle two numbers in the set are 8 and 8. The median is 8. The answer is C. #### C QUESTION:The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is? options: A)$1500 B)$4000 C)$2000 D)$2500 E)$3200 SOLUTION:Let the income of A and B be $5x and $4x Let their expenditures be $3y and $2y 5x-3y = 1600-------1) 4x-2y = 1600-------2) From 1) and 2) x = 800 A's income = 5x = 5800 = $4000 Answer is B #### B QUESTION:The cube root of what integer power of 2 is closest to 50? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc. Let, Cube root of x is closest to 50 i.e. x is closest to cube of 50 = 505050 = 125000 But x must be equivalent to an Integer power of 2 2^10 = 1024 2^7 = 128 i.e. 2^17 = 1281024 = 128000 (approx.) i.e. 2^18 = 2561024 = 256000 (approx.) i.e. 2^16 = 641024 = 64000 (approx.) i.e. 2^17 which is closest to 125000 i.e. Integer power of 2 must be 7 Answer: option B #### B QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+10)=4/5 20x=4(3x+10) 8x=40 x=5 Quantity of alcohol = (4 x 5) litres = 20 litres. Answer is D. #### D QUESTION:A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done? options: A)572 B)672 C)472 D)372 E)None SOLUTION:Solution: 10C5: when both are not included. 10C4: when one of them is included. Number of ways = 10C5 +10C4+ 10C4 = 672 Answer: Option B #### B QUESTION:If f(x) = 3x^4 - 4x^3 - 2x^2 + 5x , then f(-1) = options: A)-4 B)-2 C)0 D)2 E)4 SOLUTION:f(-1) = 3(-1)^4 - 4(-1)^3 - 2(-1)^2 + 5(-1) = 3+4-2-5 = 0 The answer is C. #### C QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Minimuum should be 1 Maximum should be 4: 1 out of a or b to make the multiplication negative 3 out of c, d, e or f to make the multiplication negative. Negative+Negative<0 Answer:C maximum will be 5.. you dont require both the multiplicatin to be negative for entire equation to be negative... any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers... actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation.. ans D #### D QUESTION:The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)20 B)99 C)77 D)26 E)12 SOLUTION:10 * 2 = 20 years Answer: A #### A QUESTION:A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? options: A)48 B)99 C)266 D)28 E)17 SOLUTION:Explanation: If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48. Answer: A) 48 #### A QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:If x, y, and z are positive integers and x = 4y = 7z, then the least possible value of x + y + z is options: A)33 B)40 C)49 D)39 E)84 SOLUTION:x + y + z = x/4 + x + x/7 = (7 + 28 + 4 )x/28 =39x/28 39 is not divisible by 28, so for least value, x = 28 Answer - D #### D QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)1/2 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 4 = 4C2 Total possible outcomes - 2^4 (each child can be either a girl or a boy) Probability=2C14C2/2^4= 24/2222=8/16=1/2 Ans=D #### D QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:What is the area of a square with perimeter 8P ? options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16 SOLUTION:Each side is 2p A = (2p)^2 = 4(p^2) Answer B #### B QUESTION:Robert's salary was decreased by 60% and subsequently increased by 60%. how much percentage does he lose? options: A)10% B)20% C)25% D)36% E)50% SOLUTION:let original salary be $100 Salary after decreasing 60% = 100 - 100 x 60/100 = $40 Salary after increasing 60% on $40 = 40 + 40 x 60/100 = $64 Percentage of loss = 100 - 64 = 36% Answer : D #### D QUESTION:The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is: options: A)91 B)910 C)1001 D)1911 E)None of these SOLUTION:Explanation: Required number of students = H.C.F of 1001 and 910 = 91. Answer: A #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is? options: A)1/9 B)1/3 C)1/5 D)1/1 E)1/2 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 * 3200 = 400 Answer: D #### D QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------\|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (3540)/3 Hence Car2 will cover total distance in (3540)/(315) = 31.11 sec approx. Answer D #### D QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/10 B)3/11 C)4/13 D)5/14 E)6/17 SOLUTION:P(neither pen is defective) = 5/84/7 = 5/14 The answer is D. #### D QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen? options: A)1.34 B)2.84 C)3.84 D)4.34 E)5 SOLUTION:40(40/100) = 16 --- 50 ? --- 12 => Rs.3.84 Answer: C #### C QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate? options: A)69 B)70 C)71 D)72 E)73 SOLUTION:number of ways = 23!3! = 72 Answer is D #### D QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5) Answer - C #### C QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4âˆ’8C4âˆ’4C4=495âˆ’70âˆ’1=424 ANSWER:E #### E QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)100}=4% Answer is A. #### A QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/19 B)1/20 C)1/23 D)2/17 E)1/17 SOLUTION:(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 B) #### B QUESTION:Sum of 42 odd numbers is? options: A)1764 B)1774 C)1784 D)1794 E)1754 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 42 odd numbers = 42^2 = 1764 ANSWER:A #### A QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)12 B)45 C)77 D)88 E)51 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B <<<Examples ends QUESTION:What is the area of a square field whose diagonal of length 20 m? options: A)10 sq m B)200 sq m C)400 sq m D)500 sq m E)156 sq m SOLUTION:Explanation: d^2/2 = (20 20)/2 = 200 sq m Answer : B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)150 B)152 C)154 D)158 E)144 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:3889 + 13.952 - ? = 3854.002 options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79 SOLUTION:Let 3889 + 13.952 - x = 3854.002. Then x = (3889 + 13.952) - 3854.002 = 3902.952 - 3854.002 = 48.95. Answer is A #### A QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number options: A)400 B)256 C)120 D)490 E)None of these SOLUTION:Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 * x = 14 * 5040 x = (145040)/144 = 490 Option D #### D QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n? I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true. Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D QUESTION:What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21? options: A)2327 B)2757 C)3147 D)3587 E)3997 SOLUTION:When increased by 3, the number must include at least 23^25^27 = 3150 The answer is C. #### C QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5 SOLUTION:Note that we have 5positivetemperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits. Answer: B. #### B QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -225/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C? options: A)3√2 B)5 C)5√2 D)√(67) E)√(73) SOLUTION:height of cone=3 radius of base=4 so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle Hence the distance is sqrt(3^2+4^2)= 5 ANSWER:B #### B QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000 SOLUTION:Equation is correct, so math must be a problem. 0.1240,000+0.2(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000. Answer: B. #### B QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x) SOLUTION:Ans B Plug some numbers Let y = 40 houses and x = 20 then they painted 20 houses per week as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 20 = 65 houses per week total time they took = (40/20) + (40/65) = 2.6 weeks Putting the values of x and y in equation B (y +220)/(5x) = (40+220)/520 = 260/100 = 2.6 #### B QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? options: A)4 B)9 C)39 D)48 E)63 SOLUTION:Given: z=s^2+2s for 0≤s≤7 z(4) = 4^2 + 24 = 24 z(7) = 7^2 + 27 = 63 Therefore z(7) - z(3) = 63 - 24 = 39 km/hr Option C #### C QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit? options: A)10.5% B)12.5% C)15% D)25% E)30% SOLUTION:suppose there are X motorists. 10% of them exceeded the speed limit and received the ticket, i.e. X/10. Again, suppose total no. of motorists who exceeded the speed limit are Y. 60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5. it means 2Y/5 received the ticket. hence, 2Y/5 = X/10 or Y/X=1/4 or Y/X 100= 1/4 * 100= 25% D #### D QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 * 5/6 = 5 #### C QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)45 B)20 C)25 D)27 E)22 SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5 = 100/5 = 20. Answer:B #### B QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round? options: A)15 B)30 C)120 D)240 E)256 SOLUTION:Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!2! = 120. Hence C. #### C QUESTION:Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? options: A)20 B)24 C)27 D)30 E)40 SOLUTION:Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D. #### D QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 9 meters, width is 8 meters, and depth is 5 meters? options: A)152 m2 B)162 m2 C)180 m2 D)300 m2 E)314 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(98+85+95)=2(72+40+45)=2157=314 m2 Answer : E #### E QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800 100 = 75% ANSWER:B #### B QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days SOLUTION:B (x â€“ 5)/13 + x/20 = 1 x = 10 10/11 days #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ? options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these SOLUTION:Explanation: A:B:CA:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3) = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18. ANSWER IS C #### C QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream? options: A)15 B)17 C)19 D)18 E)16 SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 57/3 = 19 kmph. Answer:C #### C QUESTION:If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ? options: A)4 / 7 B)34 C)1 D)2 E)3 SOLUTION:Answer Given Exp. = 4 / 7 + {(2q - p) / (2q + p)} Dividing numerator as well as denominator by q, Exp = 1/7 + {2-p/q) / (2 + p/q)} = 1/7 + {(2 - 4/5) / (2 + 4/5)} = 1/7 + 6/14 = 1/7 + 3/7 =4/7 Correct Option: A #### A QUESTION:A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue? options: A)no change B)decreases by 6.5% C)increases by 6.5% D)increases by 5.6% E)None of these SOLUTION:Explanation : Reduction of price = (100 -15)% = 85% = 0.85 Increase of sale = (100+15)% = 115% = 1.15 Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5% Answer :B #### B QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? options: A)3002 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 100/247 7410 = 3000 Answer: B #### B QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond? options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525 SOLUTION:Solution Let S be the sample space. Then, n(S) = 52C3 = 22100 Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 26 =13C1 * 13C2= 1372 = 936 P(E) = n(E) / n(S) = 936 / 22100 = 234/5525 = 234/5525. Answer D #### D QUESTION:If n is a positive integer, then n(n+1)(n+2) is even without any condition options: A)divisible by 3 only when n is odd B)divisible by 4 whenever n is even C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n(n+1)(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8) B #### B QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase? options: A)3 B)4 C)6 D)9 E)10 SOLUTION:We have 5, 10, 10 and 20 to work with From least to greatest, we have... 5 (the least) 10 15 20 25 30 35 40 45 (the greatest) Total options = 9 Final Answer:D #### D QUESTION:A car covers a distance of 630 km in 6 ½ hours. Find its speed? options: A)105 kmph B)176 kmph C)298 kmph D)186 kmph E)268 kmph SOLUTION:630/6 = 105 kmph Answer:A #### A QUESTION:What percent of a day is 15 hours? options: A)37Ã—1/2% B)16Ã—1/2% C)18Ã—2/3% D)22Ã—1/2% E)None SOLUTION:Solution Required percentage = (15/24Ã—100)% = (75 / 2)%. = 37Ã—1/2%. Answer A #### A QUESTION:Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.? options: A)8 kmph B)11 kmph C)12 kmph D)14 kmph E)16 kmph SOLUTION:Explanation: Let the distance travelled by x km. Then, x/10-x/15=2 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr =60/10 hrs= 6 hrs. So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60/5kmph= 12 kmph ANSWER IS C #### C QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:Find the smallest number which when divided by 12 and 15 leaves respective remainders of 8 and 11. options: A)87 B)97 C)27 D)21 E)56 SOLUTION:Let 'N' is the smallest number which divided by 12 and 15 leaves respective remainders of 8 and 11. Required number = (LCM of 12 and 15) - (common difference of divisors and remainders) = (60) - (4) = 56. ANSWER:E #### E QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q? options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3 SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8 Answer:A #### A QUESTION:Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L options: A)1/3. B)1/2. C)3. D)2. E)6. SOLUTION:Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2 C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions. Hence, the number of all possible selections is 3 10 – 1. Answer C #### C QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? options: A)65 B)21 C)78 D)67 E)51 SOLUTION:Let the total number of workers be x. Then, 8000x = (12000 7) + 6000(x - 7) = 2000x = 42000 = x = 21. Answer: B #### B QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is: options: A)270 B)300 C)299 D)322 E)345 SOLUTION:the numbers are (18 x 11) and (18 x 15). Larger number = (18 x 15) = 270. ANSWER :A #### A QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:How many Books each of Volume 100 meter cube can be packed into a crate of volume 3000 meter cube? options: A)50 B)cannot be determined C)150 D)300 E)350 SOLUTION:Gud question with a simple concept. In geo if we want to insert one shape into another we need to know the dimensions of the two shapes. In above with volume given , we can come up with different shapes, so we cant know the answer For ex :3000 m3 can be 30010 or 30100 or just 30001 we don't know , so we cant calculate Answer : B #### B QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q\|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q\|Q) = 3/51 P(A\|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A\|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q\|Q) P(A\|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:Solve : 42 : 56 :: 110 : ? options: A)121 B)111 C)132 D)143 E)158 SOLUTION:67=42 78=56 1011=110 1112=132 ans 42:56::110:132 ANSWER:C #### C QUESTION:If x is an integer and 2.134 × 10^x is less than 21000, what is the greatest possible value for x? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:If x=4 2.134 × 10^4 = 21340 > 21000 So, x = 3 Answer : E #### E QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)14.9 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.8 - 19 x 15) kg = 11 kg. Correct Option: C #### C QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women? options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10 SOLUTION:w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: A #### A QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5729 B)5760 C)2889 D)3600 E)2799 SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 60 * 2.5 = 3600.Answer: D #### D QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)35 min B)30 min C)25 min D)20 min E)40 min SOLUTION:Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20 ANSWER IS D #### D QUESTION:Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum? options: A)20 B)22 C)25 D)27 E)29 SOLUTION:(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131 a + b + c = √625 = 25 C #### C QUESTION:Solve for x: 2x – y = (3/4)x + 6. options: A)(y + 6)/5 B)4(y + 6)/5 C)(y + 6) D)4(y - 6)/5 E)6(y-4)/5 SOLUTION:2x – y = (3/4)x + 6. or, 2x - (3/4)x = y + 6. or, (8x -3x)/4 = y + 6. or, 5x/4 = y + 6. or, 5x = 4(y + 6). or, 5x = 4y + 24. or, x = (4y + 24)/5. Therefore, x = 4(y + 6)/5 correct answer B #### B QUESTION:On a certain transatlantic crossing, 30 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets? options: A)33 1/3% B)75% C)50% D)60% E)66 2/3% SOLUTION:On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets? Solution: Let total number of passengers be 100 According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then 40% of X = 30 => X= 75. Answer B #### B QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common? options: A)2 B)1 C)3 D)0 E)12 SOLUTION:D is a set of multiples of 5. 999 is NOT a multiple of 5, hence none of its factors is a multiple of 5. Therefore, those two sets won't have any overlap. Answer: D #### D QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? options: A)20 % B)10 % C)15 % D)22 1/2% E)21% SOLUTION:Explanation: 9 = (140R)/100 R = 22 1/2 % ANSWER IS D #### D QUESTION:The area of a square is 625 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square. options: A)5 : 12 B)5 : 13 C)2:9 D)1:15 E)1:5 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 625 a = 25 L = 3a and b = a - 20 b : l = a - 20 : 3a = 5 : 75 = 1:15 Answer: D #### D QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? options: A)120 % B)140 % C)162/3 % D)20 % E)None SOLUTION:Sol. CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain. Answer D #### D QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/8001/600=1/4,800. Answer: B. #### B QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B QUESTION:In September, John sold 2323 more soap than in February. In November, he sold 5 percent more than in September. John's November sales were what percent greater than his February sales? options: A)10/3% B)65% C)214/3 % D)75% E)514/3% SOLUTION:Let february sale= x september sale= x+2/3x= 5x/3 November sale= 5x+3 + 55/1003x 21/12x= 1.75 x Hence November sale is 75% > February sale D is the answer #### D QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:The salary of a person was reduced by 20%. By what percent should his reduced salary be raised so as to bring it at par with his original salary? options: A)50% B)32% C)25% D)43% E)29% SOLUTION:Let the original salary be $100 New salary = $80 Increase on 80 = 20 increase on 100 = 20/80 100 = 25% Answer is C #### C QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together? options: A)6!/2! B)3!3! C)4!/2! D)4! (3!/2!) E)3!3!/2 SOLUTION:In the word ABROAD , there are 3 vowels - 2 A's and O Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together = (4! 3! )/2! We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! . The entire vowel group is considered as a single group . Answer D #### D QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 66 books, thus 76-68=7 books are NOT returned. {loaned out}0.30=7 --> {loaned out}=30. Answer: B. #### B QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:There are two taps, which are used to fill the tank and one tap to empty the tank. First tap fill the tank in 10 min., while the second takes quarter of an hour to fill the tank if both are operated independently.Third tap is capable of emptying the tank in seven and a half minutes. If all the taps are opened simultaneously how long (if ever) will it take for the tank to get filled completely? options: A)10 minutes B)20 minutes C)30 minutes D)40 minutes E)50 minutes SOLUTION:Pipe A fills the tank in 10 min Pipe B fills the tank in 15 min Pipe C empties the tank in 15/2 min If all the three opened simultaneously then in 1 min 1/10 + 1/15 - 2/15 of the tank will be filled that means 1/30 th of the tank will be filled in 1 min So it will take 30 minutes to fill the tank completely if all three pipes opened ANSWER:C #### C QUESTION:In 100 litres mixture milk and water are in the ratio 3:2. After adding how many liters of water its ratio will become 3:4 options: A)48 B)50 C)62 D)78 E)100 SOLUTION:Milk quantity = 3/5 * 60 = 36 water quantity = 100-36 = 64 new ratio of M:W = 36:64+x = 3:4 192+3x = 144 x = 48 Answer is A #### A QUESTION:If \|4x+6\| = 50, what is the sum of all the possible values of x? options: A)2 B)-2 C)4 D)-3 E)6 SOLUTION:There will be two cases 4x+6= 50 or 4x+6 = -50 => x =11 or x= -14 sum of both the values will be -14 +11 = -3 Answer is D #### D QUESTION:The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive? options: A)$434 B)$458 C)$438 D)$448 E)$478 SOLUTION:Explanatory Answer Let the sums of money received by A, B and C be x, y and z respectively. Then x - 1 : y - 2 : z -8 is 6a : 7a : 10a When $1, $2 and $8 are removed, we are removing a total of $11 from $1000. Therefore, 6a + 7a + 10a = 1000 - 11 = 989 i.e., 23a = 989 or a = 43 We know that z - 8 = 10a = 10 * 43 = 430 Therefore, z = 430 + 8 = $438 The correct choice is (c) #### C QUESTION:If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is options: A)48 km B)50 km C)40 km D)22 km E)70 km SOLUTION:B 50 km. Let the actual distance travelled be x km. Then x/10=(x+20)/14 --> 14x = 10x + 200 --> 4x = 200 --> x = 50 km. #### B QUESTION:If 280 people, constituting 5 percent of the population of a town, ride bicycles, and the others do not, then how many people in the town do not ride bicycles? options: A)5930 B)5600 C)5320 D)5110 E)4980 SOLUTION:5 % of X is 280 5/100 * X = 280 X = 280100/5 = 5600 So C. 5320 is the correct Answer No. of people Not Riding Bike = 5600 - 280 = 5320 answer is C #### C QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 12 * 5 = 30 m2 Answer: B #### B QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:The ages of Charlie and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is: options: A)15 years B)16 years C)135 years D)21 years E)18 years SOLUTION:A 15 years Charlie’s age = 3A and Vaibhav’s age = 5A { (3A + 9)/(5A + 9) }=3/4 => 4 (3A + 9) = 3 (5A + 9) => A = 3 Therefore, Vaibhav’s age = 15 years. #### A QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (527) - (425) = 135-100 = 35 Answer: Option A #### A QUESTION:A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is? options: A)6000 B)4000 C)2000 D)600 E)300 SOLUTION:412 : 236 : 436 2: 3: 6 2/11 3300 = 600 Answer: D #### D QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet) options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy) SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 6. The price per square yard is 27 / (xy/6) = 162/(xy). The answer is E. #### E QUESTION:A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set? I. 2 II. 5 III. 7 options: A)II only B)I only C)I,II only D)II,III only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+3 must be there. if -1 is the starting element the sequence is as follows. S ={-1,2,5,8,11....} if -1 is not the starting element the sequence is as follows S = {...-4,-1,2,5,8,11...} By observing the above two sequences we can say that 2,5 must be there in set S. Answer : C #### C QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes? options: A)36 B)54 C)108 D)270 E)324 SOLUTION:ONE Veggiematik machine can chop 36 carrots in 4 minutes So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ONE Veggiematik machine can chop 54 carrots in5minutes So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes In other words, SIX Veggiematik machines can chop 270 carrots in5minutes Answer D #### D QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? options: A)126 B)120 C)101 D)112 E)115 SOLUTION:8 shirts 9 pants we can combine 2 shirts with (12-3) pants 29=18 we can combine the other shirts (6) with any pants (9) 912=54 Thus total :108+18=126 ANS:A #### A QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:A man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)7.6 % B)7.7 % C)16.21 % D)13.6 % E)7.8 % SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 54 pens = Rs. 46 S.P. of 54 pens = 99% of Rs. 54= Rs. 53.46 Profit % = (Profit /C.P.) x 100 Profit% = (7.46/46) x 100 = 16.21 % ANSWER: C #### C QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase? options: A)21% B)42% C)80% D)96% E)120% SOLUTION:Let B be the base and H be the height of the original triangle. The original area is (1/2)BH. The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH The answer is A. #### A QUESTION:(3108 + 6160) / 28 options: A)380 B)350 C)331 D)310 E)None of these SOLUTION:Explanation: As per BODMAS rule, first we will solve the equation in bracket then we will go for division = (9268)/28 = 331 Option C #### C QUESTION:For any integer p, p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between 4 + 3 and 4 + 4, inclusive? options: A) None B) One C) Two D) Three E) Four SOLUTION:Generally p or p! will be divisible by ALL numbers from 1 to p. Therefore, 4 would be divisible by all numbers from 1 to 4. => 4+3 would give me a number which is a multiple of 3 and therefore divisible (since 4 is divisible by 3) In fact adding anyprimenumber between 1 to 4 to 4 will definitely be divisible. So the answer is none (A)! Supposing if the question had asked for prime numbers between 4 + 3 and 4 + 11 then the answer would be 1. For 4 +3 and 4 + 13, it is 2 and so on... A #### A QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|a\| = -a \|b - 4\| + \|ab + b\| = ? options: A)a) ab - 4 B)b) 2b - ab - 4 C)c) ab + 4 D)d) ab - 2b + 4 E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab + b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab + b =ab + 4 Answer: Option C #### C QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:What is the remainder of Q= 3^19 when divided by 10? options: A)0 B)1 C)5 D)7 E)9 SOLUTION:I looked for patterns: ^2 - units digit 9 ^3 - units digit 7 ^4 - units digit 1 ^5 - units digit 3 hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9 and we can then see: ^16 - units digit 1, or ^18 - units digit 9 and ^19 - units digit 7 therefore, Q=when divided by 10, the remainder must be 7.D #### D QUESTION:Company X provides bottled water to its employees in 5 liter bottles, $2 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $100 fixed monthly rate and $1 for 10L bottle each paid off? (Assume that no other costs apply) options: A) 121 B) 125 C) 132 D) 134 E) 138 SOLUTION:let the no. of 5 liter bottles be x, so the no. of 10l bottles will be x/2 (to equate the vol.) since the total cost will be equal , 2x= 100+x/2 so x= 133.33 or 134. Answer is (D). #### D QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85 Speed of the train is 85 kmph. Answer: Option C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 40007 = 28000. Answer : Option A #### A QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house? options: A)5 B)30 C)10 D)12 E)15 SOLUTION:Speed = 4.5 5/18 = 1.25 m/sec Time taken = 750/1.25 = 600 sec ie. 10 mins. Answer:C #### C QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:The area of a triangle is with base 4m and height 5m? options: A)15 B)19 C)56 D)10 E)36 SOLUTION:Explanation: Area=1/2bh 1/2 * 4 * 5 = 10 m^2 Answer : D #### D <<<Examples ends QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant. options: A)250 m B)560 m C)100 m D)320 m E)240 m SOLUTION:Explanation : Abhishek's speed = 100/5=20 m/s. Time taken by Abhishek to cover 500 m =500/20=25 seconds. Dishu's speed = 500/20 or 25 m/s Prashant's speed = 15 m/s Time taken by Dishu to meet Prashant in 500m race in opposite direction: Distance covered by Abhishek: =>500/(15+25). =>12.5 sec. =>12.5(20)= 250 m. Answer : A #### A QUESTION:What is the area of a square with perimeter 12P ? options: A) 16p^2 B) 4P C) 9P^2 D) P/16 E) P^2/16 SOLUTION:Each side is 3p A = (3p)^2 = 9p^2 Answer C #### C QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments? options: A)50% B)40% C)20% D)30% E)10% SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 10) * X percentage of apartments in the building are two-bedroom apartments ----> (1/10) * 100 ---> 10% Answer : E #### E QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is: options: A)28 B)30 C)40 D)50 E)72 SOLUTION:Let the numbers be 1x and 2x. Then, their L.C.M = 2x. So, 2x = 48 or x = 24. The numbers are 24 and 48. Hence, required sum = (24 + 48) = 72. ANSWER:E #### E QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and â€“4; #### B QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)70 B)80 C)90 D)50 E)60 SOLUTION:Solution Let x be the original price. x - 20 = 50 x - 20 + 20 = 50 + 20 x + 0 = 70 x = 70 Answer A #### A QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain? options: A)1.39% B)1.40% C)1.41% D)1.42% E)1.43% SOLUTION:Sol. Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%. Answer D #### D QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? options: A)42 B)70 C)140 D)196 E)315 SOLUTION:Ans: 196 7C1 * 8C2 Answer D) #### D QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18(K+(K+1)+...+(K+N-1)) = 18(N(2K+N-1)/2). So the average is 153=[18(N(2K+N-1)/2)]/N = 18(2K+N-1)/2 = 9 (2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---). By ), *) we have K=2, N=14. Since 153/18 = 8.5, 188<153<189. So the number of terms R which are smaller than the average is 182, 183, ..... ,188 ---> 7. The answer is C. #### C QUESTION:A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible? options: A)17 B)10 C)40 D)26 E)20 SOLUTION:Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20 Answer (E) #### E QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 520 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(104)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:In a suite there are men and cats. In all, there are 15 heads and 40 feet. How many men and how many cats are in the suite? options: A)8 men and 7 cats. B)7 men and 8 cats. C)6 men and 9 cats. D)10 men and 5 cats. E)11 men and 4 cats. SOLUTION:10 men and 5 cats. Let M = men and C = cats. We can come up with 2 equations. M + C = 15 2M + 4C= 40 Solving the 2 equations will give 10 men and 5 cats. Answer D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 9 = 150 meter Answer:A #### A QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”? options: A)5 B)7 C)49 D)20 E)25 SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). C #### C QUESTION:John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John? options: A)35 B)55 C)39 D)40 E)60 SOLUTION:Carla starts 30 minutes later and it takes 3 hr for carla to meet John So John total time travelled = 3hr + 30 minutes John distance = 30 * (3 1/2) = 105 so carla need to travle 105 to meet John in 3 hrs speed of carla = 105/3 = 35 miles per hour Answer is A #### A QUESTION:The monthly income of Suman in the year 2009 was approximately what percentage of the monthly income of Jyothi in the year 2010? options: A)22 B)27 C)26 D)29 E)21 SOLUTION:Answer:C #### C QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C? options: A)2250 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 75/247 7410 = 2250 Answer: A #### A QUESTION:62467 × 9998 = ? options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211 SOLUTION:D 624545066 62467 × 9998 = 62467 × (10000 - 2) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066 #### D QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final100 =21/121100=8/33100=17% approxiamately. option A is correct. #### A QUESTION:After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is? options: A)Rs.2989 B)Rs.5029 C)Rs.5000 D)Rs.5197 E)Rs.5029 SOLUTION:Given SP = Rs. 6800 Marked price = [SP(100)]/(100 - d%) = (6800 100)/(100 - 15) = Rs. 8000 If SP = Rs. 8000, profit 60% CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs.5000 Answer: C #### C QUESTION:If two sides of a triangle have lengths 3 and 7, which of the following could be the perimeter of the triangle? I. 9 II. 15 III. 19 options: A)None B)I only C)II only D)II and III only E)I, II, and III SOLUTION:Let x be the length of the third side. 7-3 < x < 7+3 4 < x < 10 14 < perimeter < 20 The answer is D. #### D QUESTION:On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters? options: A)15 B)27 C)39 D)270 E)480 SOLUTION:X=663/17= 39 Answer: C #### C QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (66) since each team has 6 players. So there are a total of 108 possibilities (363). I hope this method is easier for you to understand. #### C QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute? options: A)230/(30+10A) B)230/(30+60A) C)230/38A D)220/(30+10A) E)220/40A SOLUTION:Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution. Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes. 230 Kms in 60 minutes ==> 3.8km/hr. Substitute A with 3 in the answer options. Option A #### A QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3) options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69 SOLUTION:=> root 5/ root 3 = (root 5/ root 3)(root 3/ root 3) = root 15/ root 9 = 3.87/3 = 1.29 ANSWER:A #### A QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)650 SOLUTION:Explanation: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters =5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120 All the 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves =3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6 Hence, required number of ways =120Ã—6=720 ANSWER IS B #### B QUESTION:A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? options: A)5:4 B)1:4 C)3:1 D)3:5 E)3:4 SOLUTION:12:16 = 3:4 ANSWER:E #### E QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3% Answer B #### B QUESTION:In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number Q of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85? options: A)144 B)189 C)234 D)279 E)309 SOLUTION:Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2. Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant. If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279. (10x+18x) < 85. 28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3. (45x+48x) = 93x. Max (93x) Q= 279. Answer is D. #### D QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 3.57 = 214 km ANSWER:B #### B QUESTION:Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7? options: A)3/14 B)1/7 C)0 D)1/2 E)12/21 SOLUTION:METHOD-1 Probability that the number on first die is 7 = 0 Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7] Probability that Both Dice result in odd numbers = (0)(1/7) = 0 Answer: Option C #### C QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 321/4 = 8 mins. ANSWER:A #### A QUESTION:How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length? options: A)18.9 sec B)88.9 sec C)22.9 sec D)30.00 sec E)72.0 sec SOLUTION:D = 110 + 390 = 500 m S = 60 * 5/18 = 50/3 T = 500 * 3/50 = 30 sec Answer: D #### D QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5729 B)5760 C)2889 D)3600 E)2799 SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 2.5 = 3600.Answer: D #### D QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod? options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these SOLUTION:Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 7 :: 42.75 : x => 11.25 x x = 7 x 42.75 => x = (7 x 42.75) / 11.25 => x = 26.6 Answer : B #### B QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 800018 : (80004) + (400014) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass? options: A)6 B)9 C)8 D)7 E)5 SOLUTION:B = 9 2/3x= 20 x=30 for 80% approval we need 24 garments approved. already approved = 18 we need 6 more. Answer : A #### A QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A #### A QUESTION:The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840.At what rate of interest the same amount of interest can be received on the same sum after 5 years ? options: A)6% B)8% C)9% D)10% E)None SOLUTION:Solution S.I. = Rs. 840,R =5%,T= 8 Years. Principal = Rs.(800x840/5x8)= Rs. 2100. Now,P = Rs. 2100,S.I. = Rs. 840, T = 5 years. ∴ Rate =(100x840/2100x5) = 8%. Answer B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? options: A)600 B)640 C)680 D)720 E)760 SOLUTION:The number of seats in the theater is 15 + (15+2) + ...+ (15+38)= 20(15) + 2(1+2+...+19)= 20(15) + 2(19)(20)/2= 20(15+19) = 20(34) = 680 The answer is C. #### C QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 58820 = 44, 100, which is a square of 210 B #### B QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 9990 E)Rs. 10000 SOLUTION:Sol. Income in first year = x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:8 hens weigh equal to as many duck as are equal to 7 cats. All of them weigh 264kg only. Hen's weighs are? options: A)6 B)5 C)2 D)7 E)11 SOLUTION:8h = xd = 7c 8h + xd + 7c ----- 264kg. 8h+8h+8h ----- 264kg. 24h ------ 264kgs. => 1h = 11kg Answer: E #### E QUESTION:The average of first 11 prime numbers is? options: A)14.55 B)11.11 C)12.11 D)13.11 E)14.11 SOLUTION:Sum of 11 prime no. = 160 Average = 160/11 = 14.55 ANSWER: A #### A QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3p = (1.86^3)p. Similarly max value will be (2.1)^3p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 31.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill? options: A)1/5 B)1/3 C)2/7 D)3/5 E)3/11 SOLUTION:1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 B #### B QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:A 6000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)36 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (3,000 by that net inflow to get the minutes) - 36 min. Answer E. #### E QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:Fourthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? options: A) 60 B) 70 C) 100 D) 120 E) 140 SOLUTION:40% of the members have passed the test, thus 60% have not passed the test. We also know that 30+12=42 members have not passed the test, thus 0.6Total=42 --> Total=70. Answer: B. #### B QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)11 B)60 C)77 D)55 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 18/5 = 60 km/hr. Answer: C #### C QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number? options: A)17/24 B)3/8 C)1/2 D)5/8 E)5/3 SOLUTION:Explanation : Let a particular number (say) number 2 occupies position 1. Then all possible arrangement are given as: =>(2,1,3,4), (2,1,4,3), (2,3,4,1), (2,4,1,4), (2,4,1,3), (2,4,3,1). Out of these six, three (2,1,3,4), (2,3,1,4), (2,4,3,1) are not acceptable because numbers 3 and 4 occupy the correct positions. Hence, the required probability = 3/6 = 1/2. Answer : C #### C QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP? options: A)430 B)450 C)550 D)590 E)660 SOLUTION:Cost price = 540/90 x 100 = 600 To gain 10% = 600 x 10/100 = 60 SP = CP + gain = 600 + 60 = 660 Answer :E #### E QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet? options: A)267 B)2667 C)200 D)269 E)265 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai. Answer:C #### C QUESTION:Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ? options: A)CARFTINO B)CARFTION C)ARFCNOIT D)CARFNOIT E)SUIIQQWE SOLUTION:Explanation: The letter is the first half and the letter half of the word are separately reversed to obtain the code. Answer: D #### D QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x? I. 6/x II. -4/x III. 1/x options: A)I only B)II only C)I and II only D)I and III E)II and III SOLUTION:(x^2)(y^2) –2xy - 24 = 0 (xy – 6)(xy + 4) = 0 xy – 6 = 0 or xy + 4 = 0 xy = 6 or xy = -4 Since we need y in terms of x, we can isolate y in both of our equations. y = 6/x or y = -4/x Answer: C #### C QUESTION:Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is? options: A)8 days B)10 days C)20/3 days D)14 days E)16 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 Ã— 20/30 = 20/3 days C) #### C QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? options: A)4 min B)8 min C)9 min D)6 min E)1 min SOLUTION:S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min Answer:A #### A QUESTION:The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches? options: A)25 B)27 C)30 D)35 E)36 SOLUTION:Average in 5 matches = (230 + 340)/2+3 = 60+120 / 5 = 180/5 = 36 Answer is E #### E QUESTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? options: A)27 B)34 C)50 D)61 E)78 SOLUTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. Machine starts manufacturing Red and ended on Black. This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78 Only 78 is given in the options. So answer = 78 ANSWER:E #### E QUESTION:Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 21 have taken the preparatory course and 42 have not taken the course. How many members are there in the swim club? options: A) 40 B) 60 C) 80 D) 90 E) 140 SOLUTION:30% of the members have passed the test, thus 70% have not passed the test. We also know that 42+21=63 members have not passed the test, thus 0.7Total=63 --> Total=90. Answer: D. #### D QUESTION:A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? options: A)2ft. 7 inches B)4ft. 7 inches C)1ft. 7 inches D)3ft. 7 inches E)None of them SOLUTION:Length of board=7ft. 9 inches=(712+9)inches=93 inches. Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches Answer is A. #### A QUESTION:The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%? I will see what is the quickest way to solve it then I will provide the explanation options: A)6 B)7 C)9 D)10 E)11 SOLUTION:The following approach might be the easiest one and less error prone. We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time. Answer: A #### A QUESTION:A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)135 m B)786 m C)566 m D)546 m E)445 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec Length of the train = speed * time = 15 * 9 = 135 m Answer: A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A? options: A)15 km/hr B)16 km/hr C)17 km/hr D)18 km/hr E)None of these SOLUTION:Explanation : Total distance covered by B=206=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr Answer : A #### A QUESTION:A train 100 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is: options: A)16 km/hr. B)33 km/hr. C)21 km/hr. D)49 km/hr. E)76 km/hr. SOLUTION:Speed of the train relative to man =100/20m/sec=5 m/sec. =5 x 18/5 km/hr = 18 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr. x - 15 = 18 x = 33 km/hr. ANSWER:B #### B QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A's share in the profit? options: A)310 B)330 C)370 D)350 E)None of these SOLUTION:Explanation : Ratio of the initial capital of A and B = 4 : 5 Hence we can take the initial capitals of A and B as 4x and 5x respectively Ratio in which profit will be divided = (4x3) + (3/4)(4x)7 : (5x3)+ (4/5)(5x)7 = 12+21 : 15+28 = 33 : 43 A's share = 760 * 33/76 = 330.Answer : Option B #### B QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)299 B)277 C)266 D)992 E)188 SOLUTION:(80033)/100 = 72 920 + 72 = 992 Answer:D #### D QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C14C3)+(4C24C2)+(4C34C1)+4C4 = (44)+(66)+(44)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:What is the sum of all the prime numbers greater than 30 but less than 50? options: A)126 B)199 C)198 D)188 E)122 SOLUTION:Required sum = (31 + 37 + 41 + 43 + 47) = 199 Note: 1 is not a prime number Answer B #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:If x^2=3x+2, then x^3 = ? options: A)3x+2 B)6x+2 C)11x+6 D)8x-3 E)5x+4 SOLUTION:x^2 = 3x+2 x^3 = xx^2 = x(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6 The answer is C. #### C QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr? options: A)3.5 B)2.7 C)2.9 D)2.3 E)2.1 SOLUTION:Speed = 130 * 5/18 = 36 m/sec Time taken = 125/36 = 3.5 sec. Answer: A #### A QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is options: A)60 B)75 C)90 D)105 E)120 SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 9 = 135 sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75 Answer: B #### B QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ? options: A)11/24 B)11/25 C)13 D)13/15 E)None SOLUTION:Let the numbers be x x and y y Then x + y = 11 x y = 24 x+y=11xy=24 Hence, x + y x y = 11 24 x+yxy=1124 ⇒ 1 y + 1 x = 11 24 Answer is A #### A QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)10years B)12 years C)5 years D)3 years E)24 years SOLUTION:Explanation: 9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 years Answer:D #### D QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:3 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2candidates. In how many ways can one cast his vote? options: A)8 B)10 C)15 D)17 E)19 SOLUTION:There are 6 candidates and a voter has to vote for any two of them. So, the required number of ways is, = 6C2 = 6!/2!4! = 15. C #### C QUESTION:Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed? options: A)1050 B)25200 C)32400 D)5800 E)6800 SOLUTION:Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3) = 6C4 3C2 = 6C2 * 3C1 = 65 3 21 = 153= 45 Number of groups, each having 4 consonants and 2 vowels= 45. Each group consists of 6 letters. Number of ways of arranging 6 letters among themselves = 6! = (654321)= 720 Therefore, Required number of words= 45720= 32400 ANSWER:C #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 72/247 7410 = 2160 Answer: A #### A QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life? options: A)17% B)16% C)15% D)14% E)13% SOLUTION:Average = 7.6 SD = 2.6 7.6 - 2.6 < 72% of distribution < 7.6 + 2.6 5.0 < 72% of distribution < 10.2 28% is outside this range. Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2. Answer: D #### D QUESTION:If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is = options: A) 40320 B) 27720 C) 20160 D) 6720 E) 2520 SOLUTION:The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 32^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 7 * 5 * 3^2 * 2^3)/11 = 7598 = 2520. Answer: E. #### E QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be options: A)45 min B)60 min C)55 min D)70 min E)80 min SOLUTION:Time = 50/60 hr = 5/6hr Speed = 48mph distance = ST = 48 * 5/6 = 40km time = 40/60hr = 2/3hr New speed = 40* 3/2 kmph = 60kmph Answer : B. #### B QUESTION:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)7 D)12 E)32 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 36 + 40 + 10 - (12) - 2x x = 7 So, answer will be C #### C QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:If mn > 0, which of the following must be negative? options: A)mn B)mn^2 C)m/-n D)m/n E)m+n SOLUTION:Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive. Answer :C #### C QUESTION:The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all? options: A)10 B)19 C)04 D)12 E)07 SOLUTION:Add the numbers of watches. 2 + 1 + 1 =4. Answer is C. #### C QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 15 and 16. The larger of the two numbers is: options: A)338 B)278 C)322 D)368 E)121 SOLUTION:Clearly, the numbers are (23 * 15) and (23 * 16). Larger number = (23 * 16) = 368. Answer: D #### D QUESTION:A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different W arrangements of plays can be run, if the same play can’t be run more than once? options: A)24 B)125 C)243 D)504 E)729 SOLUTION:Number of W ways to choose the first play: 9 Second play: 8 Third:7 987= 504.D #### D QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2254/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)1110! B)98! C)87! D)76! E)65! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=1110! Ans:A #### A QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days Answer is C #### C <<<Examples ends QUESTION:9 - 3 ÷ 1/3 + 4 = ? options: A)4 B)3 C)6 D)9 E)12 SOLUTION:9 - 3 1/3 + 4 =9-3÷1/3+4 =9-(3X3) +4 =9-9+4 =4 CORRECT ANSWER : A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:0.[u]225[/u = 0.225225225..... Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5. Answer E #### E QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 600 = 80/100 * 600 = 480 Option A #### A QUESTION:A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost? options: A)3 2/3 B)5 2/3 C)6 2/3 D)4 2/3 E)7 2/3 SOLUTION:x/10 + 2/15 + 4/20 = 1 x = 40/6010 = 6 2/3 Answer: C #### C QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:Among the answers given below, which is nearly equal to √7? options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0 SOLUTION:2.6 is nearly equal to the square root of 7 2.62.6=6.76 2.52.5=6.25 difference 7 - 6.76=0.24 7 - 6.25=0.75 Since 0.24 is lesser of both, 2.6 is closer. Answer is C #### C QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? options: A)8 B)10 C)12 D)14 E)16 SOLUTION:Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump. Both pumps together can fill 1/6 of the pool each hour. 2.5x = 1/6 x = 1/15 1.5x = 1.5/15 = 1/10 The faster pump could fill the pool in 10 hours. The answer is B. #### B QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? options: A)23 years B)24 years C)25 years D)None of these E)18 years SOLUTION:Let the average age of the whole team by x years. 11x - (26 + 29) = 9(x -1) 11x - 9x = 46 2x = 46 x = 23. So, average age of the team is 23 years. Answer: Option A #### A QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction? options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these SOLUTION:Let the fraction be x/y. When the numerator decreased by 25% and the denominator decreased by 20%. (x 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5 ANSWER:E #### E QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^327 + 26^5. Answer: D. #### D QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:A worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $100? options: A)30 B)33 C)35 D)38 E)40 SOLUTION:Every two days, the net total is $5. After 32 days, the worker will have $80. On day 33, the worker will receive $20 for a net total of $100. The answer is B. #### B QUESTION:On a ferry, there are 27 cars and 13 trucks. The cars have an average mass of 1100 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1515.5 B)1616.5 C)1717.5 D)1818.5 E)1919.5 SOLUTION:The total mass of the vehicles is 271100+133000=68700 The average mass is 68700/40=1717.5 The answer is C. #### C QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph1/4hr=6.25 km total westward distance= 40kmph1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 40 =20 hours Answer is D #### D QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area? options: A)26% B)21% C)15% D)18% E)12% SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification) New h = 220a / 100 = 22a / 10 New b =(110a x 100) ==11a/10 New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100) increased area== (121a²/100) - a² Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21% answer :B #### B QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 512 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (410/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (1010/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (510)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (210/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (410/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B QUESTION:If x, 3, 5, 7 are there and the range and median of them are the same, what is the value of x? options: A)0 B)1 C)2 D)5 E)4 SOLUTION:Try taking the values of x as you suggested and then see if the median and the range are equal. Once you do that, you will get the answer yourself. Tried substituting values starting with 3, 5, 7... only x = 5 satisfies the condition. D #### D QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(248$ / 7children) = 35.42 Took the lowest number = 35 7 children = $245 $248 - $245 = staying $3 Correct option: C) 3$ #### C QUESTION:An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)18 B)24 C)30 D)45 E)60 SOLUTION:First let's consider the small notebooks. There are 5 ways to choose notebooks of the same color. The number of ways to choose four notebooks with different colors is 5C4=5. There are 10 different packages we can make with the small notebooks. We can use the same process to find 10 different packages with medium and large notebooks. The total number of different packages is 30. The answer is C. #### C QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!10! 1211/21 =66 ANSWER:D #### D QUESTION:If 75 percent of 600 is 50 percent of x, then x=? options: A)800 B)900 C)1000 D)1100 E)1200 SOLUTION:0.75 600 = 0.5 * x x = 7.5/5 * 600 = 900 #### B QUESTION:If x : y = 3 : 4, find (4x + 5y) : (5x - 2y). options: A)32/7 B)13/7 C)2/7 D)32/17 E)2/17 SOLUTION:. X/Y=3/4  (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2) =(3+5)/(7/4)=32/7 ANSWER A 32/7 #### A QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm. options: A)227 B)299 C)300 D)161 E)212 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (22 + 18) * (15) = 300 cm2 Answer: C #### C QUESTION:Tough and Tricky questions: Mixture Problems. A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture? options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5 SOLUTION:Answer = B) 5:15 ........................ Rum ..................... Coke ................. Total First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2) Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3) Total .................. 10 ............................. 28 .................... 38 Ratio = 10:30 = 5:15 B #### B QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is options: A)210 B)212 C)214 D)216 E)None of these SOLUTION:Solution P.W = Rs.(1080 - 180) = Rs. 900 S.I on Rs. 1080 =Rs.(180/900 x 1080) = Rs. 216. Answer D #### D QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps. if he step down 34 stairs he has only 18 sec. 30-18=12 12 secs for 8 steps.. 18 secs for 12 steps. 12+34=46 so ans is 46.. ANSWER:B #### B QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^102^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ? options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these SOLUTION:ExplanaƟon: Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)�(1/2) = 1/12 => B alone can complete the work in 12 hour Answer: B #### B QUESTION:There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection? options: A) 100 B) 103 C) 106 D) 108 E) 109 SOLUTION:Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x = 3p+1 x can take values 100 , 104 , 109 If the cards are counted 4 at a time , there is 1 left over x= 4q+4 x can take values 100 , 108 Therefore , x = 100 Answer A #### A QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:1.5, 2.3, 3.1, 3.9, ..? options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15 SOLUTION:1.5+0.8=2.3 2.3+0.8=3.1 3.1+0.8=3.9 3.9+0.8=4.7 ANSWER:B #### B QUESTION:The greatest ratio out of 2:1, 5:8, 3:2, 8:9 and 8:5 is? options: A)2:1 B)3:2 C)5:8 D)8:5 E)8:9 SOLUTION:2/1=2 5/8=0.625 3/2=1.5 8/9=0.888 8/5=1.6 ANSWER:A #### A QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi12/4 =12- pi3 ANSWER:B #### B QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N? options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N). Answer: B #### B QUESTION:Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m. options: A)25.8 B)26.8 C)27.8 D)20.5 E)21.8 SOLUTION:avg speed=2xy/(x+y) =21824/(18+24)=20.5 ANSWER:D #### D QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest? options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years SOLUTION:Explanation: Time = (100 x 60)/(400 x 12) years = 1.25 years. Answer: D #### D QUESTION:A is the average (arithmetic mean) of the first 7 positive multiples of 4 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:If A^2 - B^2 = 0, then let's assume that A = B. A must equal the 4th positive multiple of 4, thus A = 16, which also equals B. B is the second positive multiple of n, thus n = 16/2 = 8. The answer is D. #### D QUESTION:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible? options: A)20 B)40 C)C=50 D)C=80 E)C=120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10. But these 3 chosen couples can send two persons (either husband or wife): 222=2^3=8. Total # of ways: 5C32^3=80. Answer: D. #### D QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it? options: A)78 kg B)60 kg C)64 kg D)70 kg E)None SOLUTION:Sol. For 9 kg Zinc, mixture melted = (9+11) kg. For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg = 78 kg. Answer A #### A QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets? options: A)60 min B)50 min C)70 min D)65 min E)80 min SOLUTION:A 60 min Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. #### A QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:How many digits are in (12×10^14)(10×10^15)? options: A)24 B)25 C)26 D)27 E)32 SOLUTION:The question simplfies to (12×10^14)(10^16) => 1210^30 => Will contain 30 zeros +2 digit 12 =>32 Ans E #### E QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:A five digit number is to be formed using each of the digits 1, 2, 3, 4 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ? options: A)12 B) 36 C) 72 D) 60 E) 120 SOLUTION:Reqd ways = (Total No. of ways - cases when both 1 and 2 are together) 4 numbers can be arranged in 4 places in 4! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 3! ways. 1 and 2 can be arranged within themselves in 2!ways. Reqd. Answer = 4! - 3!2! = 24 - (62) = 12 Answer: A #### A QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)4 D)5 E)6 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)(1+1)=2^3 2^3+2^3=(2^3)(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school? options: A)5:2 B)2:3 C)10:3 D)3:7 E)2:5 SOLUTION:10% of B = 1/3 G 10B/100 = G/3 B = 10G/3 B/G = 10/3 B:G = 10:3 Answer is C #### C QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is options: A)A) 587 × 108 miles B)B) 587 × 1010 miles C)C) 587 × 10-10 miles D)D) 589 × 1012 miles E)E) 587 × 10-12 miles SOLUTION:The distance of the light travels in 100 years is: 5,890,000,000,000 × 100 miles. = 589,000,000,000,000 miles. = 589 × 1012 miles. The answer is (D) #### D QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles? options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26 SOLUTION:let the radius of circle is 'r' area of the circle which is at corner = (22/7r^2)/4 hence the area of all four circles are = 22/7r^2 areaof circle which is made on center of suare is = 22/7r^2 total area of all circles are = 222/7r^2...........................(1) if we construct the diagram we get the relation 4r = 2sqrt2 r = 1/sqrt2 put the value of r in eqn 1 and we get 222/71/2 = 22/7 = 3.14 area of suare = 2^2 = 4 area of remaining part = 4-3.14 = 0.86 ANSWER:B #### B QUESTION:8500 + (1600 ÷ ?) of 1/5 = 8501 options: A)310 B)312 C)320 D)325 E)345 SOLUTION:Explanation: => 8500 + (1600/?) × 1/5 = 8501 => 1600/? × 1/5 = 8501 - 8500 = 1 => ? = 1600/5 = 320 Answer: Option C #### C QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 6046 = 2760 runs Now excluding the two innings the runs scored = 5844 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:Two trains 150 meters and 180 meters long are running in the same direction with speeds of 102 km/hr, 66km/hr. In how much time will the first train cross the second options: A)37 sec B)22 sec C)27 sec D)35 sec E)33 sec SOLUTION:Explanation: Relative speed of the trains = (102 - 66) km/hr = 36 km/hr = (36Ã— 5/18) m/sec = 10 m/sec. Time taken by the trains to cross each other = Time taken to cover (150 + 180) m at 10 m /sec = (330/10) sec = 33 sec. Answer: Option E #### E QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? options: A)39 B)88 C)3 D)7 E)62 SOLUTION:Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Answer:A #### A QUESTION:Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in options: A)1 13/17 hours B)2 8/11 hours C)3 9/17 hours D)5 5/11 hours E)None SOLUTION:Solution Net part filled in 1 hour = (1/10 + 1/6 -1/12) = 11/60. Therefore, the tank will be full in 60/11 hrs. â€¹=â€º 5 5/11 hrs. Answer D #### D QUESTION:The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/18% B)18 2/11% C)18 2/91% D)18 9/11% E)12 2/11% SOLUTION:13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B #### B QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(Ã¢â‚¬â€œ4) 5 (Ã¢â‚¬â€œ4)1 #### A QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits? options: A)9/27 B)10/27 C)11/27 D)12/27 E)11/26 SOLUTION:(1/31/3)[guy1](1/31/3)[guy2] for 1 hit each: (4 ways) (2/31/3)(2/31/3), (2/31/3)(1/32/3), (1/32/3)(2/31/3), (1/32/3)(1/32/3) for 2 hits each:(1 way) (2/32/3)(2/32/3) Add all these cases, you will get answer as 11/27. ANSWER:C #### C QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:12,?,68,129,220,347,516 options: A)129 B)220 C)347 D)31 E)520 SOLUTION:222 + 4 = 12 444 + 4 = 68 555 + 4 = 129 666 + 4 = 220 7 7 7 + 4 = 347 8 8 8 + 4 = 516. 333 +4 = 31 ANSWER : D #### D QUESTION:Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and fiveteen copper coins, how many different sums from 1¢ to 160¢ can he make with a combination of his coins? options: A)80 B)85 C)81 D)160 E)157 SOLUTION:The total sum is 52 + 155 = 85¢. If you can make each sum from 1 to 85 (1¢, 2¢, 3¢, ..., 85¢), then the answer would be 85 (maximum possible). Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 84¢ and 82¢ (since total sum is 85¢ we cannot remove 1¢ or 3¢ to get 84¢ or 82¢). So, out of 85 sums 4 are for sure not possible, so the answer must be 85 - 4 = 81 sums or less. Only A fits. Answer: C. #### C QUESTION:50% of a number is added to 120, the result is the same number. Find the number? options: A)240 B)288 C)1687 D)997 E)121 SOLUTION:(50/100) * X + 120 = X X = 240 Answer:A #### A QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits? options: A)36 B)77 C)88 D)99 E)22 SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1) Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2) Multiplying equation (1) by 2 and subtracting it from equation (2), we get => 2r = 72 => r = 36. Answer: A #### A QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ? options: A)5 B)4 C)3 D)2 E)-2 SOLUTION:Since x is an integer, (-12x)^(4x) is always positive. So, 12x^4x = 12x^(15 - x) 4x = 15 - x 5x = 15 x = 3 Answer: C #### C QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2* 6! = 360 = B #### B QUESTION:How many numbers between 300 and 500 begin or end with 3? options: A)20 B)60 C)100 D)110 E)120 SOLUTION:How many numbers between 300 and 500 begin or end with 3? Just think that those numbers are: i) The ones ending in 3: 303, 313, 323, ... , 493 --> 20 numbers ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers BUT 10 out of the first 20 numbers are repeated in the second set. THEREFORE, the solution is 110 numbers. Answer: D #### D QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2 SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec.Answer: B #### B QUESTION:Evaluate:55- 1232 =? options: A)42 B)47 C)62 D)72 E)82 SOLUTION:According to order of operations, 12?3?2 (division and multiplication) is done first from left to right 12*2 = 4 2 = 8 Hence 55 - 1232 = 55- 8 = 47 correct answer B #### B QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)y(y+3) B)y^2(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)y(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:A and B started a business and invested in 4:5 ratio.after 3 month A takes back 1/4 part of his investment and B takes back 1/5 part of his investment.after 10 month there is profit of 76000 rs.calculate the profit share of A. options: A)35000 B)43000 C)33000 D)46000 E)38000 SOLUTION:let A invested 4x rs. and B invested 5x rs. ratio of A and B investment={(4x3)+[4x-1/44x]7}:{(5x3)+[5x-1/55x]7} =(12x+21x):(15x+28x)=33:43. total profit=76000 rs. share profit of A=[7600033/76]rs.=33000 rs. answer C #### C QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)30% E)Can't be calculated SOLUTION:The owner buys 100kg but actually gets 130kg; The owner sells 100kg but actually gives 90kg; Profit: (130-90)/90100=30% Answer: D. #### D QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5 6 = 30 Answer is B #### B QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 * 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000 SOLUTION:0.7(x-600)=0.6(x-400) 0.1x=420-240 x=1800 The answer is D. #### D QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 B)88 C)267 D)28 E)21 SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A? options: A)1 B)3 C)4 D)6 E)14 SOLUTION:6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 70 = 6K+4k =>k=7 Total Red's in bag A will be 2K = 14 E #### E QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price? options: A)40% B)8% C)25% D)16.66% E)9% SOLUTION:Original cost before weight adjustment: X Cost after 90% weight adjustment: 9/10 X 20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100 Mark up on original cost of X: (108X/100)/X-1 = 8/100 ANSWER:B #### B QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is? options: A)11 B)72 C)36 D)99 E)27 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240)/12 => x = 20 Speed of each train = 20 m/sec. = 20 * 18/5 =72 km/hr. Answer: B #### B QUESTION:The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? options: A)A)270 B)B)280 C)C)290 D)D)300 E)E)310 SOLUTION:Let the smaller number be x. Then larger number = (x + 1515). x + 1515 = 6x + 15 5x = 1500 x = 300 Smaller number = 300. D) #### D QUESTION:A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the cent tossed is also a head. options: A)4/5 B)3/5 C)2/5 D)3/4 E)1/2 SOLUTION:There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent) How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin) Therefore probability = 4/5 Option A #### A QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 14555 + 3555 = 2375 ANSWER:C #### C QUESTION:In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is? options: A)11 B)20 C)28 D)17 E)13 SOLUTION:Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20 Answer: B #### B QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:The average age of students in section A of 122 students is 28 years and the average age of students in section B of 180 students is 35 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)25years E)32years SOLUTION:The required average = (12228+18035)/122+180 = 32 years Answer is E #### E QUESTION:When sold at a 70% discount, a sweater nets the merchant a 40% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price? options: A)20% B)40% C)50% D)60% E)78.58% SOLUTION:we should be careful about what are we measuring % on/what is the base.. let the Marked up price =100.. Selling price= 100-70%of 100=30.. profit= 40%.. therefore the wholesale purchase cost= x.... 1.4x=30 or x=21.42... marked price was 100 so ... so answer is 78.58%.. E #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. options: A)180 B)181 C)182 D)178 E)168 SOLUTION:add the max weights 52+50+78=180 ANSWER:A #### A QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B * (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph SOLUTION:Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 C #### C QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 58820 = 44, 100, which is a square of 210 B #### B QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 24 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)188 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 24 : x => x = {\color{Blue} \frac{24\times 1}{0.128}} => x = 187.5 So time will be approx 188 seconds Answer: D #### D QUESTION:From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys? options: A)120 B)140 C)185 D)190 E)210 SOLUTION:The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are: (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a '''' (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185 C #### C QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^41+13^1., 4^13=4^26+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positivenegative = negative. Thus option C is always negative. #### C QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 370 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? options: A)237 B)287 C)197 D)740 E)720 SOLUTION:Explanation: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x. 2x/(x - 370) = 2 + 2(extra) => 2x - 740 = x => x = 740. Answer: D #### D QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost? options: A)32 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 80 : x 250 x = (100 * 80) x = (100 * 80) / 250 x = 32 ANSWER: A #### A QUESTION:If y exceeds x by 25%, then x is less than y by? options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3% SOLUTION:X=100 y=125 125------25 100-------? => 20% Answer:A #### A QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Let the number of men be m and so the number of women = 15-m Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start. Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days). Let the total work be 360 units (LCM of 180 and 120). 1 man does 360/120 = 3 units per day 1 woman does 360/180 = 2 units per day Based on above facts, Total work by men + women in these 17 days = 360 units m93 + (15-m)62 = 360, 27m + 180 -12m = 360, Solving m=12. Num of men = 12 and number of women = 15-12 = 3 ANSWER:C #### C <<<Examples ends QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Tough and Tricky questions: Coordinate Geometry. Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L? options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices (A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need (B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong (C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong (D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong (E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong A #### A QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 340 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 413 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually? options: A)1500 B)1750 C)2000 D)3500 E)2500 SOLUTION:An easy way too attempt this is by approximation: For the first quarter, he pays 8% of 10,000 which is $800. So for the four quarters in the year, he will approximately play 8004=3200 over the entire year. Because of compound interest it will be more than 3200. Approx. option D is correct. Answer :D #### D QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after? options: A)7 min B)9 min C)4 min D)9 min E)1 min SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1. x(2/75 + 1/45) + (30- x) 2/75 = 1 11x + 180 - 6x = 225 => x = 9 Answer:B #### B QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:What was the day of the week on, 18th July, 1776? options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days. 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days) Total number of odd days = (0 + 4) = 4. Required day was 'Thursday'. Answer:A #### A QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b? options: A)-512 B)-257 C)-256 D)-513 E)128 SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation. For the quadratic equation is in the form of ax^2+bx+c=0, The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b 512 can be expressed as product of two numbers in the following ways: 1 512 2 * 256 4 * 128 8 * 64 16 32 The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513. The least value possible for b is therefore -513. D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform? options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m SOLUTION:Speed = 300/24 = 25/2 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 25/2 => x = 187.5 m. Answer:C #### C QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m SOLUTION:D = 70 1 ½ = 105 km RS = 85 – 70 = 15 T = 105/15 = 7 h 3.30 + 7 h = 10.30 p.m. Answer:C #### C QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)20 D)21.1 E)23 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 920+7100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together? options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21) SOLUTION:A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 1/2 days. The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days. Answer:D #### D QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles? options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26 SOLUTION:let the radius of circle is 'r' area of the circle which is at corner = (22/7r^2)/4 hence the area of all four circles are = 22/7r^2 areaof circle which is made on center of suare is = 22/7r^2 total area of all circles are = 222/7r^2...........................(1) if we construct the diagram we get the relation 4r = 2sqrt2 r = 1/sqrt2 put the value of r in eqn 1 and we get 222/71/2 = 22/7 = 3.14 area of suare = 2^2 = 4 area of remaining part = 4-3.14 = 0.86 ANSWER:B #### B QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is options: A)250 B)276 C)280 D)285 E)None SOLUTION:Solution since the month begins with a sunday , so there will be five sundays in the month. Required Average = (510x5+240x25 / 30) = (8550 / 30) = 285 Answer D #### D QUESTION:What is the chance that a leap year selected at random contains 53 fridays? options: A)1/7 B)2/7 C)3/7 D)4/7 E)5/7 SOLUTION:normal year =365 days leap year = 366 days now there are 52 weeks i.e. 364 days+2 odd days the 2 odd may have Friday over a week has 7 days so probability = 2/7 ANSWER:B #### B QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is options: A)276 B)299 C)312 D)322 E)None SOLUTION:Solution Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. Answer D #### D QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27 SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30 We can write 30 as product of two numbers in following ways 130 215 310 56 4 cases = 42 i.e. 8 factors (including 1) Factors greater than 1 = 7 Answer: Option D #### D QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 5034 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 25 = 10. So, we need 10 to be in x! at least in power of 3. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ? options: A)x + 2000 = 1/3(x - 3000) B)1/3(x - 3000) = x C)x + 3000 = 1/3x D)x - 7000 = 1/3x E)x - 3000 = 1/5x SOLUTION:Plane's original altitude = x Plane's new altitude after ascending 2000 ft = x+2000 Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000 So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5 Answer (E) #### E QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers? options: A)121 B)133 C)145 D)150 E)165 SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by x + (x + 4) 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131 "The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131 Solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 As an exercise, check that the sum of the first and third is 131 less than three times B #### B QUESTION:A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72 SOLUTION:Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A #### A QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8) options: A)6/k B)8/k C)83k D)2/k E)1/k SOLUTION:Part of the book he can read in 1 minute = 1/k Part of the book he can read in 8 minutes =8/k. Answer: B #### B QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C24C1+4C14C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 14555 + 3555 = 2375 ANSWER:C #### C QUESTION:Jaclyn buys $60 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter options: A)1187.5 B)1234 C)1289 D)1425 E)None of these SOLUTION:Explanation: I=(p x r x t)/100 = 600009.5/100(18/12)^1/6 = 1425 Answer: D #### D QUESTION:40% of x is greater than 1/3rd of x by 110.what is x? options: A)1100 B)2100 C)1300 D)1650 E)1400 SOLUTION:4x/10-x/3=110 1x/15=110 x=1650 ANSWER:D #### D QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average? options: A)69 B)70 C)71 D)72 E)75 SOLUTION:Sum of the marks for the 11 students = 11 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D #### D QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? options: A)106.75 B)213.5 C)427 D)729 E)1,156 SOLUTION:Diagonal of a square =√2side of square => side =Diagonal/(√2) Area of square =ss =(diagonal^2)/2 Difference of both tv's =(34^2-27^2)/2 =427 ANSWER:C #### C QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? options: A)x B)(85/12)x C)(85/24)x D)(85/36)x E)(85/48)x SOLUTION:Let Q be the number of homework questions. Q = 4Q/5 + (5/17)(Q/5) + x Q = 68Q/85 + 5Q/85 + x 12Q/85 = x Q = (85/12)x The answer is B. #### B QUESTION:A positive integer x has 60 divisors and 7x has 80 divisors. What is the greatest integer y such that 7y7y divides n? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Total number of factors of x = 60 = (p+1)(q+1)(r+1)... = 2^2 3 * 5 Now note that 7x has only one 7 more than x. The number of all other prime factors stays the same. Total number of factors of 7x = 80 = (p+2)(q+1)(r+1)... = 2^4 * 5 Here, the 3 of previous expression has disappeared so it must have converted to 4. Does it make sense? Let's see: Total number of factors of x = 60 = 2^2 * 3 * 5 = (3+1)(2+1)(4+1) Total number of factors of 7x = 80 = 2^2 * 4 * 5 = (3+1)(3+1)(4+1) The powers of other factors stay the same. Only the power of 7 increases by 1. So initially, in x, the power of 7 must have been 2. Hence the maximum value of y must be 2. Answer (C) #### C QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number? options: A)228 B)103 C)286 D)122 E)102 SOLUTION:Explanation: Let the number be x x2 - 732 = 5280 x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2(100)(3) + 32 = (100 + 3)2 x = 100 + 3 = 103. Answer: B #### B QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60t=4 (since Maria had to run 4 laps before Nick would start) 10/60t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)18 sec B)70 sec C)21 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 120 + 280 = 400 m. The time required = d/s = 400/20 = 20 sec. Answer: D #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? options: A)15002 B)15001 C)15000 D)15007 E)15009 SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: options: A)1.8h B)3h C)4h D)5h E)None of these SOLUTION:Explanation: Upstream speed = B-S Downstream speed = B + s B - S = 15/5 = 3 km/h Again B = 4S Therefore B - S = 3 = 3S => S = 1 and B = 4 km/h Therefore B + S = 5km/h Therefore, Time during downstream = 15/5 = 3h Answer: B #### B QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000 SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? for first 5000 , 8% tax then we get 400$ as tax. Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount. A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount) 550+400 = 950$...hence this is the option. ANSWER :option A. #### A QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3110+31010 = 330 ANSWER:A #### A QUESTION:Tough and Tricky questions: Number Properties. If (z + 3)/6 is an integer, what is remainder when z is divided by 6? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:6/6=1 Ans B #### B QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue? options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17 SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/189/17 = 12/17. Answer: E. #### E QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is: options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in one years is: 5,870,000,000,000 = 587 10 ^10 The distance of the light travels in 1000 years is: = 587 * 10^10 x 10 ^3 = 587 x 10^13 miles Answer :A #### A QUESTION:Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring. options: A)2 B)4 C)6 D)8 E)None of them SOLUTION:Let the inner and outer radii be r and R meters. Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m. 2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m. Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m. Answer is B. #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)28% B)25% C)95% D)05% E)22% SOLUTION:800 --- 200 100 --- ? => 25% Answer:B #### B QUESTION:Which of the following CAN be the least common multiple of two positive integers 5 and 25? options: A)5 B)10 C)15 D)25 E)20 SOLUTION:LCM of 5, 25 is 25 Answer : D #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:If n is an integer, which of the following must be an even integer? options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10 SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 ) A: n^2-n-1 = -1 { If n = 1 } B: n^2-4n+6 = 3 { If n = 1 } C: n^2-5n+5 = 1 { If n = 1 } D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 } E: n^2+2n+10 = 13 { If n = 1 } Thus the only possible answer is (D) #### D QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 80 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)70 miles B)80 miles C)90 miles D)100 miles E)110 miles SOLUTION:Every hour, Nil gets ahead of Ethan 80 - 20 = 60 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 80 × 1 = 80 miles. correct answer B #### B QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: options: A)130 B)360 C)500 D)540 E)580 SOLUTION:L = 800 m S = 78kmph = 65/3 mps Time to pass tunnel = 1min = 60 sec t.f (800+X)/(60) = (65/3) =500 ANSWER:C #### C QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q\|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q\|Q) = 3/51 P(A\|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A\|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q\|Q) P(A\|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:26=12.Answer is B. #### B QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass? options: A)6 B)9 C)8 D)7 E)5 SOLUTION:B = 9 2/3x= 20 x=30 for 80% approval we need 24 garments approved. already approved = 18 we need 6 more. Answer : A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man’s rate in still water and rate of current? options: A)8.5 B)10.0 C)12.5 D)11.0 E)8.25 SOLUTION:Rate of still water = 1/2 (down stream + upstream) = 1/2 (45 + 23) = 34 Kmph rate of current = 1/2 (down stream - upstream) = 1/2 (45 - 23) = 1/2 (22) = 11 kmph Answer is D. #### D QUESTION:The simple interest at x% for x years will be Rs. x on a sum of: options: A)x B)x^2 C)100x D)100x^2 E)50x^2 SOLUTION:Explanation : P = ? R = x% Simple Interest,SI = x T = x years P=100× SI/RT=100 × x / x × x=100/x Answer : Option C #### C QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9 SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E âˆ© H) = (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2 D #### D QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is? options: A)$440 B)$450 C)$460 D)$470 E)$480 SOLUTION:avg = sum of observations/number of observations avg income=(250+400+750+400+500)/5 = 460 Answer is C #### C QUESTION:Which of the following is equal to 3.14 x 10^6) ? options: A)3.14 B)3140000 C)31400 D)314 E)314000 SOLUTION:= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is B. #### B QUESTION:For all positive integers n and m, the function A(n) equals the following product: (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8 SOLUTION:For all positive integers n and m, A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2) B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive. A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...} A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2) The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ... missing numbers are 1/8, 1/13, 1/16, .... B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25) here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values The largest reciprocal that present in B(25) but not in A(5) is 1/3 Answer A #### A QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/85/74/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5/18 = 10/3 m/s Hence time taken to cover 60 m = 603/10 = 18 seconds. Answer: D #### D QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x 104.76/100 * 104.76/100 = 8840 x1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow. options: A)32 B)36 C)40 D)44 E)50 SOLUTION:Explanation : Explation: Let length of bridge is X then middle of bridge is X/2. and Cow is standing at X/2-5 from the end so After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side. So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10 so remaining distance is 10m the cow is hit before 2m i.e cow covers 8m and train will cover 32 m. Answer : A #### A QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:40, 45, 50, 55, 60, 75, 75, 90, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69. 1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+99)=? options: A)7000 B)7250 C)7500 D)7750 E)6750 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 99=1+(n-1)2 => n=50 Use value of n in (1) then, Sn = (50/2)(1+99) = 2500 Ans:- 3(Sn) = 7500 Answer : C #### C QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found? options: A)14 B)18 C)15 D)10 E)20 SOLUTION:E 20 If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14. #### A QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? options: A)2 times B)2 1/5 times C)3 times D)4 times E)5 times SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24 = 2. A) #### A QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 15 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)28 C)50 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 15 are males, so remaining 90-15=75 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 75, 100%= 75100/60=125.. ans 40% of 125 =50 C #### C QUESTION:Find the missing in the series: 70, 56, 45, 41,___ options: A)22 B)287 C)2679 D)276 E)2771 SOLUTION:Answer:D #### D QUESTION:A baker filled with a measuring cup with 1/3 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? options: A)1/8 cup B)3/8 cup C)11/24 cup D)1/2 cup E)7/8 cup SOLUTION:1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24. so 50% more than what he started was = 1/3+1/2(1/3)=1/2 Amount of water needed to add = 1/2 - 1/24=11/24 C #### C QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram? options: A)769 1/7 grams B)769 3/13 grams C)769 8/3 grams D)769 1/3 grams E)769 1/13 grams SOLUTION:If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130. If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%. How many grams he has to give instead of one kilogram(1000 gm). 130 gm ------ 100 gm 1000 gm ------ ? (1000 100)/130 = 769 3/13 grams. Answer:B #### B QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)77/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-7 = 1/3 (B+7) ----> 3A-21 =B+7 Scenario 2 B-7 = 1/2 (A+7) -----> 2B-14 = A+7 From Scenario 1, B = 3A-28 Substitute B with this information in Stmt 2 2 (3A-28) -14 = A+7 ------> 6A -56-14 = A+7 ------> 6A- A = 70+7 ---> 5A= 77 A= 77/5, Answer choice A #### A QUESTION:Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 16 boys and 44 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic. Table method is shown above; here is how you will use logic: There are 6 happy boys. There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys. We have 6 happy boys and 6 sad boys. Total we have 16 boys. So 16 - 6 - 6 = 4 boys must be neither happy nor sad. Answer (B) #### B QUESTION:If n = 30! + 27, then n is divisible by which of the following? I. 25 II. 27 III. 29 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:27 divides 30! so 27 also divides 30! + 27. 25 and 29 divide 30! so they do not divide 30! + 27. The answer is C. #### C QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)(1000-9) = (1009)(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year? options: A)200 B)600 C)900 D)1600 E)2000 SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x. Let y be the number of female students this year. x/400 = 2(2x/y) y = 1600 The answer is D. #### D QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 9.33% D) 10.67% E) 11.7% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500100=~9.33% of the remaining solution of 7,500 gallons. Answer: C. #### C QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The product of 2 integers is negative Thus an odd number of integers need to be negative to have a negative product We are asked at most how many are required. So, the highest odd integer before 6,i.e. 1 Correct Option : A #### A QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is options: A)35.22 B)36.12 C)36.22 D)36.42 E)None SOLUTION:Solution Correct sum = (36x50+44-23) = 1821. âˆ´ Correct mean = 1821 / 50 = 36.42. Answer D #### D QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:The residents of the town A participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town A, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)- 30 B)- 20 C)- 6 D)- 12 E)- 16 SOLUTION:(21-62)<number of hours that Pat watched television last week <(21-61) =9<W<15 12=C. #### C QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:A can give B 70 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)139.78 B)139.13 C)139.22 D)111.0 E)111.12 SOLUTION:A runs 1000 m while B runs 930 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/930 = 860.21 m. B can give C = 1000 - 860.21 =139.78m. Answer:A #### A QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? options: A)30days B)35days C)40days D)44days E)45days SOLUTION:Explanation: (A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5 A complete remaining work in 2/550 = 20 Total work = 10+20= 30days Answer: Option A #### A QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 6 = 720 Answer:C #### C QUESTION:Some of the 50% solution of acid was removed and this was replaced with an equal amount of 14% solution of acid. As a result, a 23% solution of acid was obtained. What fraction of the original solution was replaced? options: A)1/2 B)1/3 C)2/3 D)3/4 E)4/5 SOLUTION:Let x be the fraction of the original solution that was replaced. 0.5(1-x)+0.14(x)=0.23 0.36x=0.27 x=3/4 The answer is D. #### D QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? options: A)525 B)665 C)412 D)235 E)856 SOLUTION:Answer: Option B 8 84 = 672 â€“ 7 = 665 #### B QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination? options: A)50 B)100 C)120 D)140 E)180 SOLUTION:60%x+80%(400-x)=65%400 Ans=100 ANSWER:B #### B QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 412=48 6 dozens of bananas cost is rs8 then 68=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 * (2/25) = 44 seconds Answer: E #### E QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(8400047/2)/100 = i i = 11760 Answer: D #### D QUESTION:40 is subtracted from 60% of a number, the result is 50. Find the number? options: A)150 B)140 C)130 D)120 E)110 SOLUTION:(60/100) * X – 40 = 50 6X = 900 X = 150 ANSWER:A #### A QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)21 C)25 D)26 E)24 SOLUTION:Solution Given Data 3 positive integers Average of a, b, and c = 20. So, a+b+c3a+b+c3 = 20 or a + b + c = 60 a ≤ b ≤ c Median = (a + 11) Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c Therefore, b = a + 11 Objective To find the least value of 'c' Theoretically, the least value of c is when c = b. Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11) Or 3a = 38 or a = 12.66 So, b = c = 12.66 + 11 = 23.66 However, we know that these numbers are all integers. Therefore, a, b, and c cannot take these values. So, the least value for c with this constraint is NOT likely to be when c = b Let us increment c by 1. Let c = (b + 1) In this scenario, a + (a + 11) + (a + 12) = 60 Or 3a = 37. The value of the numbers is not an integer in this scenario as well. Let us increment c again by 1. i.e., c = b + 2 Now, a + (a + 11) + (a + 13) = 60 Or 3a = 36 or a = 12. If a = 12, b = 23 and c = 25. The least value for c that satisfies all these conditions is 25. Correct answer is choice C. #### C QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)7297 B)2977 C)2871 D)6925 E)2981 SOLUTION:Explanation: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: D #### D QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)265 m B)755 m C)245 m D)127 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer:C #### C <<<Examples ends QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:12,?,68,129,220,347,516 options: A)129 B)220 C)347 D)31 E)520 SOLUTION:222 + 4 = 12 444 + 4 = 68 555 + 4 = 129 666 + 4 = 220 7 7 7 + 4 = 347 8 8 8 + 4 = 516. 333 +4 = 31 ANSWER : D #### D QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white SOLUTION:In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated Answer: A #### A QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 Ã— (1/10) = 1/5 Remaining work = 1 â€“ 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is options: A)u B)v C)w D)y E)z SOLUTION:a is one time, b,2 times so on... so 323=n(n+1)/2.. 0r n(n+1)= 646... now 2526=650...2425<646 so n= 25. and 25th alphabet is Y. ans D #### D QUESTION:The wages earned by Robin is 50% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)18.75% B)23% C)30% D)50% E)7% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.510 = 15 Wage of Charles = 1.6 10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-15)/15 * 100% = 1/15 * 100% =7% Answer E #### E QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race? options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec SOLUTION:Time taken by B run 1000 meters = (1000 * 10)/16 = 625 sec. Time taken by A = 625 - 10 = 615 sec. Answer:E #### E QUESTION:How many integers between 4000 and 5000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 445_ --> 4 446_ --> 3 447_ --> 2 448_ --> 1 456_ --> 3 457_ --> 2 458_ --> 1 467_ --> 2 468_ --> 1 478_ --> 1 Number of integers =20 D #### D QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5 options: A)40 B)20 C)25 D)30 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40 Answer: Option A #### A QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)109% B)160% C)100% D)600% E)108% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)299 meters B)278 meters C)500 meters D)276 meters E)299 meters SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: C #### C QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:What is the least integer that is a sum of four different prime numbers each greater than 50? options: A)232 B)234 C)236 D)238 E)240 SOLUTION:The sum of the four smallest primes greater than 53+59+61+67=240. The answer is E. #### E QUESTION:In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is? options: A)35yrs B)40yrs C)50yrs D)60yrs E)70yrs SOLUTION:Let B's present age = x years Then A's present age = x+10 years x+10+20 = 2(x-20) x + 30 = 2x - 40 x = 70years Answer is E #### E QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person? options: A)18 B)56 C)16 D)17 E)14 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 46 + Q => Q = 16 Answer:C #### C QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after? options: A)7 min B)9 min C)4 min D)9 min E)1 min SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1. x(2/75 + 1/45) + (30- x) 2/75 = 1 11x + 180 - 6x = 225 => x = 9 Answer:B #### B QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9 SOLUTION:Speed of Peter = x/9 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x Option D The values 100m and 200m have no role to play here and are just given to confuse you. #### D QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9 SOLUTION:Original share of 1 person =1/6 New share of 1 person =1/5 Increase =1/5 - 1/6 =1/30 Required fraction = (1/30)/(1/6)=1/5 Answer is D. #### D QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100 P1’s income = Rs 51100 = Rs.5500 ANSWER:D #### D QUESTION:A 2-year certificate of deposit is purchased for R dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years? options: A)k(1.06)^2 B)k(1.06)^8 C)k(1.015)^2 D)R(1.015)^8 E)k(1.03)^4 SOLUTION:Annual Rate of interest= 6% Quaterly rate of interest= 6/4% = 1.5% Now, periods of compounding in 2 years= 8 (8 quarters) Thus R(1.015)^8 Answer: D #### D QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122 SOLUTION:Explanation: Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 Answer: B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:The product of all the prime numbers less than 30 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^9 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19 ,23, 29 = 110^7 2.32.910^9 =6.6710^9 E #### E QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 => v2 = 20 => v1 = 5 => p1 = 20 Answer - D #### D QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W? options: A) 60 B) 61 C) 62 D) 63 E) 64 SOLUTION:60 = 2235 factor count =3 61= prime number 62 = 231 factor count=2 63=337 factor count=2 64=222222 factor count=1=W answer is A. #### A QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:If log10 2 = 0.3010, the value of log10 80 is: options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252 SOLUTION:= log10 8 + log10 10 = log10 (23 ) + 1 = 3 log10 2 + 1 = (3 x 0.3010) + 1 = 1.9030. ANSWER B #### B QUESTION:A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it? options: A)110 B)120 C)128 D)143 E)145 SOLUTION:First Purchased = 250 Wes= 128 C #### C QUESTION:if log 5 = 0.69897, the number of digits in 5128 is options: A)90 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46 ie, its characteristic = 89 Hence, number of digits in 2128 = 89+1 = 90 Answer: Option A #### A QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers total time taken = time taken by 1 worker 3. Time taken by 1 worker = 168 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7 total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)11 B)408 C)2881 D)287 E)221 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 13 + 21 = 34 T = 12 D = 34 * 12 = 408 Answer:B #### B QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:Positive Integer A gives the remainder of 9 when divided by another positive Integer B. If A/B = 47.45, what is the value of B? options: A)96 B)75 C)48 D)20 E)12 SOLUTION:I think the answer should be 25. This is how i solved. .45 of B = Remainder .45 of B = 9 B = (9 100) / 45 = 20. D #### D QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)100 / Initial Value % Reduction= (Reduction in Price)100 / Initial Value i.e. % Reduction= (350)100 / 500 = 70% Answer: Option A #### A QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:P makes x sprockets per hour. Then Q makes 1.1x sprockets per hour. 880/x = 880/1.1x + 10 1.1(880) = 880 + 11x 11x = 88 x = 8 The answer is D. #### D QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? options: A)$8 B)$14 C)$5 D)$15 E)$0 SOLUTION:1/5 x $60 = $12 for sandwich 1/6 x $60 = $10 for museum 1/2 x $60 = $30 for book $12 + $10 + $30 = $52 spent $60 - $52 = $8 left over correct answer A #### A QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24 SOLUTION:Explanation: 10 * 16 + 36 – 26=170 => 170/10 = 17 A) #### A QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was: options: A)2500 B)2520 C)3000 D)3100 E)None of these SOLUTION:Explanation : Number of valid votes = 70% of 9000 = 6300. Valid votes polled by other candidates = 40% of 6300 (40/1006300) = 2520. Harsh Mishra a year ago 0 upvotes Answer : B #### B QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight? options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb SOLUTION:Sol. 66÷6 = 11. Answer : B #### B QUESTION:WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF: options: A)no loss no gain B)20 % profit C)4% loss D)2% profit E)2% loss. SOLUTION:The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20% So the original rates of the items are 1380 and 2070 respectively So the total he spend for those 2 items is 3450 but he ended up in selling them with (16562) 3312 So the loss is 3450 - 3312 = 138 The loss percentage is (138/3450) 100 = 4% loss - Answer C #### C QUESTION:At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? options: A)62.5 B)62.8 C)62.1 D)62.9 E)32.5 SOLUTION:Explanation: CP = 47.50 SP = 47.50(125/100) = 59.375 MP(95/100) = 59.375 MP = 62.5 Answer: A #### A QUESTION:A certain sum amounts to Rs.1525 in 3 years and Rs.1875 in 5 years. Find the rate % per annum? options: A)6.76% B)3.76% C)5.26% D)5.76% E)4.76% SOLUTION:3 --- 1525 5 --- 1875 -------------- 2 --- 350 N = 1 I = 75 R = ? P = 1525 - 225 = 1300 75 = (13001R)/100 R = 5.76% ANSWER:D #### D QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? options: A)45 B)65 C)75 D)78 E)90 SOLUTION:A + B + C = 3 84 = 252 A + B + C + D = 4 * 80 = 320 ---- (i) So, D = 68& E = 68 + 6 = 74 B + C + D +E = 79 * 4 = 316 --- (ii) From Eq. (i) & (ii) A-E = 320 – 316 = 4 A = E +4 = 74 + 4 = 78 D #### D QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts? options: A)2 B)4 C)6 D)8 E)9 SOLUTION:- 4 hours: 1,000 -2 hours: 2,000 Now: 4,000 + 2 hours: 8,000 + 4 hours: 16,000 + 6 hours: 32,000 Answer : C #### C QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12.5N E)20 SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 + 1.5x$500 = $500 + $750 =$1250 This is 12.5 times the 1992 number, so the correct answer is 12.5N. D #### D QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11 SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways. The required probability = (9 * 4) = 36/78 = 6/13 Answer: B #### B QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)787 C)178 D)179 E)172 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!2! or 43/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? options: A)3. B)7. C)10. D)16. E)15. SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins Distance traveled by the bird traveling from West-Town = 4 4= 16 Answer: D #### D QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:The equation of line q is y = 4/3x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.510075=0.5125* x => x=60; SO answer is 60=C #### C QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd? options: A)5/18 B)13/36 C)3/8 D)5/8 E)23/36 SOLUTION:player begins with containing tiles 1 to 10 and have equal probability of selecting means Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there. Next , player draws one title , if number is even player stops or otherwise title is odd without replacement player draws second title. If second title is even , player stops or title is odd without replacement player draws third title. in third title , without replacement of first and second title, player draws and stops it. the sum of tilte probability is odd. here two conditions are possible. 1st condition is 1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/105c1. Here are we are not selecting 1st condition as even stops because sum of tile is odd. Here 5 odd numbers are there we can select 1out of 5 odd numbers. without replacement of fist we select second tilte is even. is 5/105c1/9c1. here we are selecting one number out of remaining 9 numbers. so probability is 5/18. we are selecting 1 even number out of 5. 2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title. Then probability is 5/104/93/8=1/12. Finally sum of probability of two conditions is 5/18+1/12 =5/18. so option A is correct. #### A QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed? options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr SOLUTION:Average speed = (24555)/(45+55) = 49.5km/hr Answer is B #### B QUESTION:In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ? options: A)3 hours B)2.4 hours C)1.4 hours D)1 hour E)None of these SOLUTION:Explanation: Let the duration of the flight be x hours. Then 600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0 Neglecting the negative value for x we get x = 1 Answer: D #### D QUESTION:X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join? options: A)6 months B)8 months C)4 months D)2 months E)5 months SOLUTION:Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000 Let investment period of Z be x months. Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x) = 240 : 300 : 30x = 8 : 10 : x The share of Z in the annual profit of Rs. 50000 is Rs. 14000. => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7 => 25x = 7x + (18 * 7) => x = 7 months. Z joined the business after (12 - 7) months. i.e., 5 months. Answer:E #### E QUESTION:The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is? options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9 SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:What is the tens digit of 36^5? options: A)1 B)7 C)5 D)3 E)9 SOLUTION:36^5 = 6^7 (6^2)=66 = 36 (6^3)= 366 = .16 (6^4)= .166 = ..96 (6^5) = ..966 = ..76 (6^6) = ..766 = ...56 (6^7) = ....566 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^7 ( dont actually calculate full values) and answer is D: 3 #### D QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph1/4hr=6.25 km total westward distance= 40kmph1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 3 specific shirts with 2 specific pants? options: A)66 B)51 C)36 D)70 E)56 SOLUTION:Total no of combinations available is= 8 shirts X 9 pants = 72 Eliminate the 3shirts X 2 pants combo = 6 which gives.......>> 72-6=66 ANSWER: A #### A QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 76 = 42 litres of 2% solution and 36 = 18 litres of 12% solution. Answer (E) #### E QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 25001.5/1.4= 2478 Answer:- D #### D QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:The sum of first nine prime numbers is? options: A)12 B)100 C)24 D)28 E)30 SOLUTION:Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. B #### B QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3x ANSWER:D #### D QUESTION:The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is? options: A)11 B)12 C)77 D)85 E)65 SOLUTION:5000 = 72(100/R)2 5 R2 = 720 => R = 12.Answer:B #### B QUESTION:The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N. options: A)797 B)254 C)597 D)997 E)297 SOLUTION:According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient divisor + remainder = 18* 14 + 2 = 254 correc answer B #### B QUESTION:If eight machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job? options: A)45 B)60 C)75 D)96 E)100 SOLUTION:using the std formula m1d1h1/w1=m2d2h2/w2 substituting the values we have 81/24/3=25/3x (converted 30 min into hours =1/2) 16/3=10/3x x=8/5 hour so 96 minutes ANSWER:D #### D QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)6 E)5 SOLUTION:2x x = 128 => x= 8 Answer: A #### A QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is? options: A)Rs. 850 B)Rs. 900 C)Rs. 980 D)Rs. 990 E)Rs. 1000 SOLUTION:Sol We have, A : Rs.1U2D Let the pr xnpal be R5 x Then mterest u — 12 : wzo — x Therefore, by u xglurmula. _umxx ’ Rx’: ( , _ma>< 1nzn—xv \4Ve\|\a\e,Jc— 5“ :> ~(:51DD—S(or6x:51UU or, J: : w 350 . The sum of money burrowed : Rs. 850 A) #### A QUESTION:7+2=56 6+3=48 5+5=45 2+1=4 4+9=?? Solve it? options: A)92 B)48 C)42 D)38 E)72 SOLUTION:x+y=x[y+(x-1)]=x^2+xy-x 7+2=7[2+(7-1)]=49+14-7=56 6+3=6[3+(6-1)]=36+18-6=48 5+5=5[5+(5-1)]=25+25-5=45 2+1=2[1+(2-1)]=4+2-2=4 4+9=4[9+(4-1)]=16+36-4=48 Answer :B #### B QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is? options: A)30 B)45 C)50 D)60 E)75 SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2 1^3+2^3+3^3+-----+5^3 = (56/2)^2 = 225 Required average is = 225/5 = 45 Answer is B #### B QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 1860 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? options: A)60 B)90 C)70 D)80 E)40 SOLUTION:Answer is B. Six majors are as follows: a + b + c + d + e + f Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20 4 of the majors have 300 seniors: a + b + c +d = 300 There are a total of 410 seniors. So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90. B #### B QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:If log1087.5 = 5.9421, then the number of digits in (875)10 is? options: A)30 B)70 C)27 D)26 E)25 SOLUTION:X = (875)10 = (87.5 x 10)10 Therefore, log10X = 10(log1087.5 + 1) = 10(5.9421 + 1) = 10(6.9421) = 69.421 X = antilog(69.421) Therefore, number of digits in X = 70. ANSWER:B #### B QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3110+31010 = 330 ANSWER:A #### A QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? options: A)1/5 B)2/7 C)2/9 D)3/10 E)4/11 SOLUTION:The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9. The answer is C. #### C QUESTION:The percentage increase in the area of rectangle , if each of its side is increased by 20% is? options: A)30% B)44% C)50% D)55% E)60% SOLUTION:Let original length = x meters original breadth = y meters original area = xy m^2 New length = 120x/100 New breadth = 120y/100 = 6y/5 New area = 6x/5 6y/5 = 36xy/25 m^2 Increase percent = 11xy/25 * 1/xy 100 = 44% Answer is B #### B QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. options: A)121km B)242km C)224km D)112km E)115km SOLUTION:Explanation: Average Speed =2Ã—21Ã—24/21+24=22.4 km/hr Total distance =22.4Ã—10=224 km ANSWER IS C #### C QUESTION:If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? options: A)s.575 B)s.595 C)s.590 D)s.580 E)s.585 SOLUTION:80 = (4504R)/100 R = 5% I = (45065)/100 = 135 450 + 135 = 585 ANSWER:E #### E QUESTION:How many words can be formed by using all letters of the word ‘DESK’ ? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The word contains 4 different letters. The number of permutations is 4! = 24 The answer is C. #### C QUESTION:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 4518 -45x + 36x =3100 or 9x = -3100 +4518 x= 510/9 = 56.6% B #### B QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? options: A)6 B)9 C)12 D)15 E)18 SOLUTION:2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 3024 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 3024 / 80 oxen = 9 days The answer is B. #### B QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting? options: A)1355 B)1350 C)1450 D)1600 E)2000 SOLUTION:science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 and 5x art books = 2000 E #### E QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50 9/10 x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:Operation#is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Any multiple of 10 is even. Any two-digit prime number is odd. (even+odd)/2 is not an integer. Thus # does not yield an integer at all. Therefore P=0. Answer: A. #### A QUESTION:In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? options: A)36 B)2^43 C)24 D)38 E)47 SOLUTION:Working backward from the day it's covered: day 39: fully covered day 38: half covered So 38 days ANSWER:D #### D QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it? options: A)30 days B)35 days C)40 days D)45 days E)50 days SOLUTION:Explanation: Let ‘x’ be the number of days taken by B alone to finish the whole work Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days. Then, working together, 3x/2 × x/3x/2 + x = 18 days 3x × x/5x = 18 3x/5 = 18 Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days. Answer: Option A #### A QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:If x=-2, which of the following is(are) true? I. x^2=-\|x\| II \|x\|=-x III x/-3 = -2/3 options: A)II only B)I only C)III only D)I,II only E)II, III only SOLUTION:I. x^2=-\|x\| -2^2 = - \|-2\| Not true II \|x\|=-x \|-2\| =-( -2 ) true III x/-3 = -2/3 Not true Answer : A #### A <<<Examples ends QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector? options: A)1/72 B)1/36 C)1/18 D)1/12 E)1/9 SOLUTION:Its an AP question .... it is given clearly in the question . Let the smallest angle be a and the circle has 8 sectors and hence 8 angle with a common difference d hence all the angles can be written in AP form with Cd as d , a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d, given that a+7d = 80 --------1 also a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360) which is 8a + 28d = 360 --------2 solving 1 and 2 we get a=10 We are almost done , now the question ask what fraction of the wheel’s area is represented by the smallest sector ? (30/360)( pie rr)/ (pie rr) = 30/360= 1/12 D ans .... #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3? options: A)3/10 B)3/20 C)2/5 D)1/2 E)1/3 SOLUTION:S={1,2,3,….20} E={3, 6,9,12,15,18} P(E)=6/20 =3/10 Option A #### A QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24 SOLUTION:Explanation: 10 * 16 + 36 – 26=170 => 170/10 = 17 A) #### A QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:From 2005 to 2015 the world's population grew by 11.27%, and from 2005 to 2010 the world's population grew by 6.20%. What was the percentage growth in the world's population from 2010 to 2015? options: A) 5% B) 6% C) 2% D) 2.5% E) 5.5% SOLUTION:Let the world's population in 2005 = x; then, for 2005-2010, the population equation is x + 0.0620x = 1.0620x, for 2005-2015, the population equation is x + 0.1127x = 1.1127x; so, the growth from 2010 to 2015 = (1.1127x - 1.060x)/(1.062x) = 0.05 (rounded). Thus, the answer is 5%. Answer is A #### A QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000. 36/7 has a remainder of 1. Jan. 8th is: Friday + 1 day = Saturday The answer is D. #### D QUESTION:How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 options: A)3 B)4 C)5 D)6 E)7 SOLUTION:B 4 By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. #### B QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q? options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3 SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8 Answer:A #### A QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? options: A)20 B)60 C)100 D)120 E)150 SOLUTION:y = 0.50.5x = x/4 y%x = 9 (y/100)x = 9 (x/400)x = 9 x^2 = 9400 x = 60 The answer is B. #### B QUESTION:Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 Â½ sec ANSWER A #### A QUESTION:Q=(429)^2 * 237 * (1243)^3 is thrice of ? options: A)33605 * 31960 * (1243)^2 B)33654 * 538219 * (1243)^2 C)33891 * 533247 * (1243)^2 D)34122 * 532004 * (1243)^2 E)34606 * 534572 * (1243)^2 SOLUTION:Q=(429)^2237(1243)^3 is an odd number. Among answer choices only C is an odd number, (so thrice C also will be an odd number). Answer: C. #### C QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score? options: A)662 B)672 C)654 D)642 E)721 SOLUTION:8 * 83 = 664 – 10 = 654 ANSWER:C #### C QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14Ã—30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—14) Ratio of the capacity of a man and woman =1/(15Ã—14) : 1/(14Ã—30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 21,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 147% D) 150% E) 225% SOLUTION:The percent increase is (21947-8902)/8902=13045/8902=1.47 So the approximate answer is C #### C QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head?? options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these SOLUTION:1Rs coin head=1/2 2Rs coin Tail=1/2 5Rs coin head=1/2 =(1/2)(1/2)(1/2) =1/8 ANSWER:B #### B QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x 5) = (0.75 9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house? options: A)12 B)20 C)30 D)15 E)24 SOLUTION:His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24 He can buy a new house in 24 years ANSWER:E #### E QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is? options: A)299 m B)777 m C)200 m D)167 m E)128 m SOLUTION:2(l + 100) = 600 => l = 200 m Answer:C #### C QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet? options: A)2 : 30 PM B)11 : 30 AM C)1 : 30 PM D)12 : 30 PM E)None of these SOLUTION:Let after t hours they meet then, 3t + 4t = 17.5 ⇒ t = 25 ∴ Time = 10 am + 2.5 h = 12 : 30 am Answer D #### D QUESTION:If n is a natural number, then(6n^2+6n) is always divisible by? options: A)6 only B)6 and 12 C)12 only D)by 18 only E)None of these SOLUTION:(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Correct Option: B #### B QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it? options: A)22 B)38 C)60 D)88 E)90 SOLUTION:Explanation: Let the required no of hours be x. Then Less men , More hours (Indirect Proportion) \inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90 Hence, 10 men can do it in 90 hours. Answer: E) 90 #### E QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is options: A)112 B)22 C)56 D)27 E)35 SOLUTION:Explanation: Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 28. L.C.M. of 16 and 28 = 112. Answer: Option A #### A QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell? options: A) 140 B) 103 C) 105 D) 115 E) 120 SOLUTION:First 100 machines = 3% commission = 0.0310010000 = 30000 Commission from sale of next machines = 46000 - 30000 = 16000 So 40 more machines.. Total = 140 machines IMO A.. #### A QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 105 ⇒ 1.75x = 105 ⇒ x = 60 coins Answer D #### D QUESTION:Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together. options: A)10x11/10 B)10x10/11 C)11x10/11 D)12x10/11 E)None SOLUTION:Solution At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart. So, the minute hand gain = (30 - 20)minute 55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min. The hands will be in the same straight line but not together at 10x10/11 min.past 8. Answer B #### B QUESTION:How many numbers from 29 to 79 are exactly divisible by 11 options: A)5 B)7 C)8 D)9 E)11 SOLUTION:29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers Option 'A' #### A QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390(85/100)(75/100) = 248 Answer: C #### C QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000 options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000 SOLUTION:A==30,000 B==10,000 C==40,000 so, ration are3:1:4 profit 14000 so,, 14000/8==1750 so,, A==5250, B==1750,, C==7000 ANSWER:D #### D QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")(Number of ways the vocalist can sing "new songs")= 1510=150 Answer: C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)34 B)97 C)37 D)80 E)22 SOLUTION:1/2 d (10 + 6) = 640 d = 80 Answer: D #### D QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in? options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec ANSWER: D #### D QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:14 times a number gives 210. The number is options: A)11 B)12 C)15 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 14×N=210⇒N=15 Correct Option: C #### C QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x))) 2=5%(13+x)-------->x=27 Ans B #### B QUESTION:The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of options: A)20% B)19% C)18% D)11% E)10% SOLUTION:Say the original price of the TV was $p, then the final price would be (0.9p)∗0.9=0.81p. Therefore the original price was discounted by 19%. Answer: B. #### B QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 140.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 57400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 65006 : 84005 : 100003 = 656 : 845 : 1003 = 136 : 84 : 203 = 132 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 19014 = 2660 Answer is C #### C QUESTION:In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had? options: A)10.7% B)20% C)25% D)33 1/3 E)58 1/3 SOLUTION:No of bank customers in 1985 = 60 x .45 = 27 No of bank customers in 1987 = 144 x .25 = 36 increase in % = 100 X 9/27 = 100/3 or 33 1/3 D is the correct answer #### D QUESTION:A person borrows Rs. 6000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year. options: A)120 rs B)150 rs C)160 rs D)180 rs E)200 rs SOLUTION:Gain in 2 years = [(600062)/100]-[(600042)/100] 720-480=240 Gain in 1 year =(240/2)=120 rs ANSWER:A #### A QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)84 = 36. The answer is E. #### E QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is? options: A)126 B)156 C)190 D)300 E)260 SOLUTION:Sol. Let width = x, Length = (10+x) Perimeter = 2(x+(10+x)) = 2(2x=10) & 2(2x+10)6.5 = 1950 X = 70 Required perimeter = 2(70+80) = 300 D #### D QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears? options: A)300 B)250 C)130 D)303 E)111 SOLUTION:830-527=303. Answer is D. #### D QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y? options: A)2 B)1 C)0 D)5 E)6 SOLUTION:Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x can not equal 0 D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer. Answer A #### A QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 24)/2 = 288 Answer: D #### D QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None SOLUTION:Formula = S1S2/S2-S1 T1+T2/60 = 46/2 17/6 = 24/2 * 17/60 = 17/5 = 3 2/5 Km A #### A QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts? options: A)3/4 B)5/8 C)7/8 D)11/16 E)15/16 SOLUTION:P(missing all 4)=(1/2)^4=1/16 P(success on at least one attempt)=1-1/16=15/16 The answer is E. #### E QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 205 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) options: A)200π B)240π C)300π D)480π E)1,200π SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280 Revolutions in one second= 1320 Revolutions in 60 seconds (one minute)= 132060 Total distance traveled= total revolutions distance traveled in one revolution 132060 2π10/5280= 300π C is the answer #### C QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)28% B)25% C)95% D)05% E)22% SOLUTION:800 --- 200 100 --- ? => 25% Answer:B #### B QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 85, what is the value of c âˆ’ a? options: A)25 B)80 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=170 --2 subtracting 1 from 2 we have c-a=80; ANSWER:B #### B QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? options: A)66 B)83.5 C)84 D)95 E)76 SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4 = 84 ANSWER:C #### C QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2(0.1)^3(0.9)^2 1 Tail and 4 Heads, Probability = 5C1(0.1)^4(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:In a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal? options: A)41 B)30 C)35 D)33 E)36 SOLUTION:D 33 There is a meal for 200 children. 140 children have taken the meal. Remaining meal is to be catered to 60 children. Now, 200 children 110 men. 60 children = (110/200)x 60= 33 men. #### D QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km. Speed = Distance/Time Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours] Required speed = 3000 x 3/5 km/hr = 1800 km/hr. Answer: Option B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/2 of the absentee ballets were thrown out and 1/2 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/2 1/2 (total absentee votes) = 1/4 (total votes)=1/412000=3000 Answer is B #### B QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered: 2 skeins at $2.50 per skein (not discountable) 8 skeins at $8.40 per skein (discountable) 7 skeins at $5.99 per skein (discountable) Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn? options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64 SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.) 7 x $5.99 = $41.93 $67.20 + $41.93 = $109.13 discountable $109.13 x .10 = $10.91 (rounded) $109.13 - $10.91 = $98.22 for discounted yarn 2 x $2.50 = $5.00 for un-discounted $98.22 + $5.00 = $103.22 cost of yarn $103.22 x 1.13 = $116.64 with tax and shipping (5% + 8% = 13%) correct answer A #### A QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now? options: A)76 days B)98 days C)32 days D)45 days E)24 days SOLUTION:1600 ---- 28 days 1600 ---- 24 1200 ---- ? 160024 = 1200x x = 32 days Answer: C #### C QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is: options: A)22 B)24 C)77 D)26 E)81 SOLUTION:Explanation: Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. Answer: B #### B QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)33 B)277 C)40 D)88 E)11 SOLUTION:The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150 Profit(%) = (31150 - 22250)/22250 * 100 = 40% Answer: C #### C QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is S? options: A)50+A/200 B)50+3S/100 C)50+S/40 D)100+S/50 E)100+3S/100 SOLUTION:50+S/40=C #### C QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row? options: A)15 years B)31 years C)27 years D)82 years E)12 years SOLUTION:Total age seven persons = (28 7)years Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively. Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years. Answer: B #### B QUESTION:If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y? options: A)1/7 B)14 C)15 D)52/7 E)60/7 SOLUTION:3x-y=6 ...equation 1 x+2y=8 ...equation 2 adding both the equations 4x+y=14 correct answer option B #### B QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:How many seconds will a 300 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)11 sec B)18 sec C)77 sec D)14 sec E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 300 * 3/50 = 18 sec. Answer: B #### B QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)None of these SOLUTION:Explanation : Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer : Option C #### C QUESTION:I am an odd number; take away an alphabet and I become even. What number am I? options: A)6 B)8 C)9 D)3 E)7 SOLUTION:E 7 (SEVEN-S=EVEN) #### E QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is options: A)250 B)276 C)280 D)285 E)None SOLUTION:Solution since the month begins with a sunday , so there will be five sundays in the month. Required Average = (510x5+240x25 / 30) = (8550 / 30) = 285 Answer D #### D QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3p = (1.86^3)p. Similarly max value will be (2.1)^3p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 31.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order? options: A)AOTDSP B)AOTPDS C)AOTDPS D)AOSTPD E)None of these SOLUTION:Explanation : In alphabetical order : A D O P S T A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A. A D _ _ _ _ : empty places can be filled in 4!=24 A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24 this total crosses 42. So We should not consider all the words starting with AO. A O D _ _ _ : 3!= 6 A O P _ _ _ : 3!=6 Till this 36 words are obtained, we need the 42nd word. AOS _ _ _ : 3!= 6 Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD. So given word is AOSTPD Answer : D #### D QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-? options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these SOLUTION:Explanation: 112% of CP = Rs.42750 :. CP = Rs.42750x100/112 = Rs.38169. Answer: Option B #### B QUESTION:Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age. options: A)60 years B)80 years C)70 years D)76 years E)86 years SOLUTION:Let Kumar’s present age be x years and Sailesh’s present age be y years. Then, according to the first condition, x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1) Now. Kumar’s age after 10 years = (x + 10) years Sailesh’s age after 10 years = (y + 10) (x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2) Solving (1) and (2), we get x = 70 and y = 30 Kumar’s age = 70 years and Sailesh’s age = 30 years. ANSWER:C #### C QUESTION:If a - b =4 and a2+b2=52 , find the value of ab. options: A)8 B)26 C)18 D)42 E)36 SOLUTION:Explanation: We know 2ab=(a2+b2)âˆ’(aâˆ’b)2 2ab=52âˆ’16=36 =>ab=18 Option C #### C QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =âˆšb : âˆša = âˆš400 : âˆš625 = 20 : 25 Answer D #### D QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase? options: A)3 B)4 C)6 D)9 E)10 SOLUTION:We have 5, 10, 10 and 20 to work with From least to greatest, we have... 5 (the least) 10 15 20 25 30 35 40 45 (the greatest) Total options = 9 Final Answer:D #### D QUESTION:If the selling price of 50 articles is equal to the cost price of 20 articles, then the loss or gain percent is: options: A)45% B)23% C)20% D)60% E)56% SOLUTION:C.P. of each article be Re. 1. Then, C.P. of 50 articles = Rs. 50; S.P. of 50 articles = Rs. 20. Loss % = 30/50 * 100 = 60% ANSWER D #### D QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2879 C)2700 D)2797 E)2761 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer:A #### A QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? options: A)3 B)4 C)2 D)9 E)12 SOLUTION:Rate of machine R =1/8 Rate of machine S =1/4 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/8 +x/4 =1/2 3x/8=1/2 x=8/6=1.3=2 So no of machine R is 2 Answer C #### C QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) a^2 Area of Frame + Painting = a^2 + (1/2)a^2 = (3/2)a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to bsqrt2 so, b sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)a^2 so, a^2 = (2/3)b^2 = (2/3)18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 463/4 = 34.5L Alcohol in Sol2: 102/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)100 = 68.75% ANSWER:C #### C QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:The number 0.8 is how much greater than 1/2 ? options: A)½ B)3/10 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .8-1/2=x 8/10-1/2=x x= 3/10 ans B #### B QUESTION:The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 50% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 75 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:No of people from 10 - 11 is x No of people from 11 - 12 is 3x/4 No of people from 12 to 1 is (3/2)(3x/4) Given that 3x/4 + (3/2)(3x/4) = (3x/4)(5/2) = 75 Then x = 40 D #### D QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:8 hens weigh equal to as many duck as are equal to 7 cats. All of them weigh 264kg only. Hen's weighs are? options: A)6 B)5 C)2 D)7 E)11 SOLUTION:8h = xd = 7c 8h + xd + 7c ----- 264kg. 8h+8h+8h ----- 264kg. 24h ------ 264kgs. => 1h = 11kg Answer: E #### E QUESTION:A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was? options: A)10 years B)12 years C)14 years D)16 years E)17 years SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. E #### E QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : options: A)8 B)9 C)4 D)18 E)None SOLUTION:Ratio of rates of working of A and B = 2 : 1 So, ratio of times taken = 1 : 2 B's 1 day's work = 1/12 Therefore A's 1 day's work = 1/6 (A + B)'s 1 day's work = (1/6 + 1/12)= 1/4 So, A and B together can finish the work in 4 days. Answer: C #### C QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)187 B)180 C)289 D)216 E)279 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B #### B QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed? options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph SOLUTION:424/(13/2) = 4242/13 =65.2 kmph ANSWER:C #### C QUESTION:Which of the following points falls outside of the region defined by 2y≤6x−10? options: A)(5, 1) B)(3, -8) C)(2, 0) D)(0, -2) E)(0, -14) SOLUTION:Equation given is 2y<=6x-10 Simplifying this; y<=3x-5 Plug in the values provided in the options, A. 1<=10 B. -8<=4 C. 0<=1 D.-2<=-5 E. -14<=-12 Option C is the answer. #### C QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:D) 6 #### D QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 115=55 Answer : B #### B QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D <<<Examples ends QUESTION:In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70. options: A)27 B)88 C)26 D)29 E)71 SOLUTION:Explanation: Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x) 3x + (70 – x)(-1) = 38 4x = 38 + 70 = 108 x = 27 ANSWER:A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/896=36 people in the room under the age of 21. Answer: B. #### B QUESTION:If x:y=9:4 then (7x-3y) : (7x+3y)=? options: A)51:76 B)6:13 C)51:75 D)51:76 E)None of these SOLUTION:Explanation: x/y = 9/4 (Given) (7x − 3y)/(7x + 3y) 7(x/y) − 3/7(x/y)+3 ( on dividing Nr and Dr by y) (7(9/4) − 3)/(7(9/4) + 3) (63/4 − 3/1)/(63/4 + 3/1) [(63 − 12)/4]/[(63 + 12)/4] = 51/75 (7x-3y) : (7x+3y) = 51:75 Answer: Option C #### C QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 34/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:Let the original side of the square be x. (x-12)(x-10) = 120 = 1012 x = 22 The answer is B. #### B QUESTION:Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __? options: A)276 B)277 C)278 D)279 E)None of these SOLUTION:Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B #### B QUESTION:1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$125 C)$145 D)$135 E)$155 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145. ANSWER : OPTION C =$145 #### C QUESTION:Two whole numbers whose sum is 72 cannot be in the ratio options: A)3 : 4 B)3 : 5 C)4 : 5 D)5 : 7 E)None SOLUTION:Sol. The sum of the ratio terms must divide 72. So, the ratio cannot be 3 : 4. Answer A #### A QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: Q=2550+(10050)=7550.B #### B QUESTION:If xy > 0, which of the following must be negative? options: A)-x/y B)xy C)x/y D)2xy E)2x/y SOLUTION:- / + = - Answer : A #### A QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was. options: A)Rs 14000 B)Rs 25000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=Pâˆ—Râˆ—T/100 =>P=S.I.âˆ—100/Râˆ—T =>P=9000âˆ—100/12âˆ—3=Rs25000 Option B #### B QUESTION:By investing in 1623% stock at 64, one earns Rs. 1600. The investment made is options: A)s. 9600 B)s. 7500 C)s. 5640 D)s. 6144 E)s. 6760 SOLUTION:Explanation : Market Value = Rs.64 Face Value is not given and hence take it as Rs.100 16 2/3% of the face value = 50/3 ie, to earn 50/3, investment = Rs.64 Hence, to earn Rs.1600, investment needed = 64×3×1600/50=6144 Answer : Option D #### D QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last? options: A)8 B)10 C)12 D)18 E)20 SOLUTION:Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 . for-^—=18 days. D #### D QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:A team consists of 4 boys and 3 girls. If you pick two persons at the same time, what's the probability that one person is boy and other one is girl ? options: A)2/7 B)5/7 C)4/7 D)3/7 E)1/2 SOLUTION:P(1st b, 2nd g) = 4/73/6 = 4/14; P(1st g, 2nd b) = 3/74/6 = 4/14. P = 4/14 + 4/14 = 4/7. Answer: C. #### C QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed? options: A)1180 B)1320 C)1540 D)1760 E)1920 SOLUTION:22C3 = 222120 / 6 = 1540 The answer is C. #### C QUESTION:A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes? options: A)40 B)400 C)500 D)5,000 E)40,000,000 SOLUTION:if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144. The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682 The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways) we thus have, 4 10101010 1010= 4000000.E #### E QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result? options: A)600 B)480 C)538 D)650 E)560 SOLUTION:23th result = sum of 45results - sum of 44 results 1045-1622+2022 = 450-352+440 = 538 Answer is C #### C QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)3000 - (1/10)%3000 = 300 - (1/1000)3000 = 300 - 3 = 297 The answer is B. #### B QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long? options: A)1/6 B)1/4 C)2/3 D)3/4 E)11/12 SOLUTION:So please: Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/31/4=11/12. Answer: E. #### E QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:The fourth proportional to 14, 22 and 28 is? options: A)21 B)66 C)88 D)99 E)44 SOLUTION:(2228)/14 = 44 Answer: E #### E QUESTION:a, b, c, and d are positive consecutive even integers and a < b < c < d. If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers? options: A)2 B)4 C)8 D)12 E)20 SOLUTION:We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on. The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will. However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8. The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C). #### C QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A. options: A)240 B)388 C)288 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 756 = 288 Answer: C #### C QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is? options: A)126 B)156 C)190 D)300 E)260 SOLUTION:Sol. Let width = x, Length = (10+x) Perimeter = 2(x+(10+x)) = 2(2x=10) & 2(2x+10)6.5 = 1950 X = 70 Required perimeter = 2(70+80) = 300 D #### D QUESTION:In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8. Answer C #### C QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? options: A)5520 B)2789 C)5550 D)2889 E)2788 SOLUTION:Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600. Average monthly production of salt for that year = 66600/12 = 5550. Answer: C #### C QUESTION:If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)3/50 E)1/20 SOLUTION:Perhaps it is also easy to just translate the % into fractions: 6%: 6/100 = 3/50 7%: 7/100 8%: 8/100 = 4/50 =2/25 9%: 9/100 Only 3/50 exists in the answer choices, so ANS D #### D QUESTION:If four coins are tossed, the probability of getting two heads and two tails is ? options: A)3/8 B)3/6 C)3/1 D)3/2 E)3/4 SOLUTION:Since four coins are tossed, sample space = 24 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = 6/24 = 3/8 Answer: A #### A QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)12 B)15 C)16 D)18 E)19 SOLUTION:one day work done by A=1/20 work done by A in 2 days=1/10 work done by A,B,C on 3rd day=1/10+1/10=1/5 1/5th of the work will be completed at the end of 3 days the remaining work =1-1/5=4/5 1/5 of work is completed in 3 days total work wiil be done in 35=15 days ANSWER:B #### B QUESTION:How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R? options: A)59 B)11!/(2!2!2!) C)56 D)76 E)11!/(3!2!2!2!) SOLUTION:E- -R We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}. We should consider two cases: 1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR. 2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56. Total = 56 + 3 = 76. Answer: D. #### D QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000 options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000 SOLUTION:A==30,000 B==10,000 C==40,000 so, ration are3:1:4 profit 14000 so,, 14000/8==1750 so,, A==5250, B==1750,, C==7000 ANSWER:D #### D QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10? options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18 SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once. There are 66=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12. D #### D QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent? options: A)25% B)5% C)10% D)15% E)20% SOLUTION:3000 --- 600 100 --- ? => 20% Answer: E #### E QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ? options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550 SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040 Which is 100 - 20 = 80% of his monthly salary ∴ His salary = 10040x100/80 = 12550 Answer : E #### E QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? options: A)100 B)72 C)110 D)135 E)145 SOLUTION:Explanation : Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x. .'. 60% of x = 36 +5/6 36 =>60/100 x = 66 =>x = 110 Answer : C #### C QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4100))^4 Amount = 15000 (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:Mary works in a restaurant a maximum of 60 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? options: A)300 B)420 C)560 D)320 E)400 SOLUTION:Mary receives $8(20)=$160 for the first 20 hours. For the 40 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(40)=$400. The total amount is $160+$400 = $560 Answer C 560. #### C QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:In Bangalore there is a well known Science Institute. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from the other's equal 30.' Then the other man spoke . 'Our ages multiplied together equal 1624.' What were their ages? options: A)60 and 23 B)66 and 25 C)29 and 56 D)71 and 43 E)58 and 28 SOLUTION:E Their ages were respectively 58 and 28 #### E QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). (140/100 * 5x), (150/100 * 7x) and (175/100* 8x) 7x, 21x/2 and 14x The required ratio = 7x : 21x/2 : 14x 14x : 21x : 28x 2 : 3 : 4 Answer = A #### A QUESTION:There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 1716/2 = 136 The total number of games in the season is 10136 = 1360. The answer is C. #### C QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1 SOLUTION:From the wording in the prompt, we're essentially mixing two liquids: Liquid X is 40% concentrate Liquid Y is 25% concentrate We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra: X = # of ounces of liquid X Y = # of ounces of liquid Y (.4X + .25Y) / (X + Y) = .35 .4X + .25Y = .35X + .35Y .05X = .1Y 5X = 10Y From here, you have to be CAREFUL to answer the question that is ASKED. 5X = 10Y Y/X = 5/10 = 1/2 ANSWER:B #### B QUESTION:The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin? options: A)23% B)18.75% C)30% D)30.55% E)100% SOLUTION:Explanatory Answer Let the wages earned by Erica be $100 Then, wages earned by Robin and Charles will be $144 and $160 respectively. Charles earns $44 more than Robin who earns $144. Therefore, Charles' wage is 44/144100 = 30.55%. The correct choice is (D) #### D QUESTION:A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent? options: A)18 1/9 % B)18 9/3 % C)18 1/3 % D)14 2/7 % E)18 7/3 % SOLUTION:C.P. of 1 kg = 595/85 = Rs. 7 S.P. of 1 kg = Rs. 8 Gain % = 1/7 100 = 100/7 = 14 2/7 % Answer: D #### D QUESTION:3,8,18,38,78,__ options: A)158 B)156 C)154 D)150 E)148 SOLUTION:8=32+2 18=82+2 38=182+2 78=382+2 158=782+2 ANSWER:A #### A QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:1/6 = 0.1666666... (a repeating pattern one digit long) A #### A QUESTION:9 - 3 ÷ 1/3 + 4 = ? options: A)4 B)3 C)6 D)9 E)12 SOLUTION:9 - 3 1/3 + 4 =9-3÷1/3+4 =9-(3X3) +4 =9-9+4 =4 CORRECT ANSWER : A #### A QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 25 = 10. So, we need 10 to be in x! at least in power of 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels? options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28 SOLUTION:The number of ways to choose two letters is 8C2 = 28 The number of ways to choose two consonants is 5C2 = 10. P(no vowels) = 10/28 = 5/14 The answer is D. #### D QUESTION:At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)2 B)7 C)C)120 D)D)144 E)E)720 SOLUTION:The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E #### C QUESTION:(1/5)^q * (1/4)^18 = 1/(2(10)^35). What is q? options: A)17 B)18 C)34 D)35 E)36 SOLUTION:We need to arrive at a common base. --> (5)^(-q) * 2^(-36) = 2^(-36)5^(-35) 5^(-q)=5^(-35) -q=-35 q=35=D #### D QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){18, 20} B){8, 10} C){28, 38} D){6, 10} E){5, 10} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others. Hence Answer : B #### B QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (7506+ 770 20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge? options: A)$40,000 B)$45,000 C)$50,000 D)$55,000 E)$60,000 SOLUTION:The customer receives $75 for the first $5000. The customer receives $125 for the next $5000. Let x be the total amount of the customer's annual charge. $200 + 0.03(x-10,000)=0.028x 0.002x=100 x=50,000 The answer is C. #### C QUESTION:At a recent small town election for mayor a total of 971 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place? options: A)134 B)178 C)197 D)166 E)194 SOLUTION:The number of votes the winning candidate received was 971 + 53 + 79 + 105 /4= 302. The second received 302 – 53 = 249, The fourth place received 302 – 105 = 197. C #### C QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 12.. so total who won N = 11+12 = 23.. B #### B QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 76 = 42 litres of 2% solution and 36 = 18 litres of 12% solution. Answer (E) #### E QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (512/5)/100] P= 1000 Answer: A #### A QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform? options: A)240 B)188 C)177 D)260 E)320 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Length of the train = 20 * 20 = 400 m. Let the length of the platform be x m . Then, (x + 400)/36 = 20 => x = 320. Answer: E #### E QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 5 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)153602 D)60000 E)153604 SOLUTION:Perimeter = Distance covered in 5 min. =(12000/60) x 5m = 1000 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1000 or x = 100. Length = 300 m and Breadth = 200 m. Area = (300 x 200) m2 = 60000 m2. Answer: D #### D QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten? options: A)30 B)25 C)20 D)15 E)10 SOLUTION:There are two conditions: 1. Roslin got at least one score of each of 1, 2, 3, 4, and 5. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30. Answer: A. #### A QUESTION:If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. options: A)35 7/8 B)36 C)21 3/7 D)34 5/7 E)34 6/7 SOLUTION:Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts. If we use 8 tons of cement, then we'll get 5/730 = 21 3/7 tons of mixture. Answer: C. #### C QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C QUESTION:Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to decrease 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be: options: A)100% less than N B)200% less than N C)Equal to N D)100% greater than N E)200% greater than N SOLUTION:Correct answer is (D). This year, the price of a tree is price1=P/N. If this price decreases by 50% it becomes Price2=P/N0.5 Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N0.5) i.e. N/0.5 i.e. 2N Which is 100% greater than N. #### D QUESTION:If a is a positive integer, which of the following could NOT be the square of a? options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752 SOLUTION:A number ending with 2 can never be a perfect square. Units digit of a perfect square must be: 1,4,9,6,5 Answer E) #### E QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form. options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11 SOLUTION:Solution We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions 3 2/3 = 33 / 3 + 2 / 3 = 11 / 3 7 1/3 = 73 / 3 + 1 / 3 = 22 / 3 The ratio 3 2/3 : 7 1/3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 Simplify = 11 / 22 = 1 / 2 The ratio is 1 / 2 or 1:2 ANSWER IS D #### D QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. options: A)5113 B)5117 C)5120 D)8119 E)10115 SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year. If x = initial number of trees = 5120 Year 1 = 5/4x Year 2 = (5/4)(5/4)x Year 3 = (5/4)(5/4)(5/4)x Year 4 = (5/4)(5/4)(5/4)(5/4)x Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500 Hence, correct answer = C #### C QUESTION:A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square? options: A)148/29 B)168/29 C)168/26 D)158/29 E)198/29 SOLUTION:By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle. Then s = ½(10 + 17 + 21) = 24, and A = 84. A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21. Now drop a perpendicular of length h onto the side of length 21. We also have A = ½ × base × perpendicular height. Hence A = 21h/2 = 84, from which h = 8. Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.) Let the square have side of length d. Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1. Therefore the length of the side of the square is 168/29. ANSWER:B #### B QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:In how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct. options: A)144 B)24 C)576 D)48 E)16 SOLUTION:4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways. W_W_W_W Number of ways = 4!4! = 24 24 = 576 Answer C #### C QUESTION:A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 24 on Wednesday, what would be the value of D calculated on the following Saturday? options: A)3450 B)3860 C)4220 D)4670 E)5040 SOLUTION:On Saturday, the value would be 76524 = 5040 The answer is E. #### E QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.90.8x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill 1/5 + 1/8 = 13 / 40 of a tank Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item? options: A)18 B)21.6 C)22 D)25.7 E)27 SOLUTION:Producer price = $15; The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $151.2 = $18 after the store takes a commission of 30% of the final price --> (final price)0.7 = $18 --> (final price) = $25.7. Answer: D. #### D QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (22) + (11) + (1/31/3) = 46/9 Proportion of work done by B = (11) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment? options: A)$503 B)$504 C)$505 D)$506 E)$507 SOLUTION:Explanation: Cash price = $21 000 Deposit = 10% × $21 000 = $2100 Loan amount = $21000 − $2100 = $18900 I=prt/100 I=11340 Total amount = 18900 + 11340 = $30240 Regular payment = total amount /number of payments Answer: B #### B QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? options: A)2% B)17% C)25% D)65% E)83% SOLUTION:New Value – Old Value)/Old Value x 100 We are given: February sales this year = 400 million February sales last year = 320 million We need to determine the percent increase between sales from last year to sales this year. Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula. (New Value – Old Value)/Old Value x 100 [(400 – 320)/320] x 100 = 25%. The answer is C. #### C QUESTION:What is x if x + 3y = 33 and y = 10? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Substitute y by 10 in x + 3y = 33 x + 3(10) = 33 x + 30 = 33 If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence x = 3 correct answer C #### C QUESTION:Two numbers are in the ratio 5:8 and thier H.C.F is 4. Find the numbers. options: A)25 and 40 B)20 and 32 C)30 and 48 D)15 and 24 E)16 and 25 SOLUTION:Explanation: Let two numbers 5x, 8x their H.C.F = 4 Therefore H.C.F is 4 i.e, x in this case. Therefore The numbers are 5 x 4 = 20 8 x 4 = 32 Answer: Option B #### B QUESTION:A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls? options: A)59 B)33 C)52 D)68 E)80 SOLUTION:A 59 The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red. #### A QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph SOLUTION:Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'x' km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 => x = 49 km/hr. ANSWER IS A #### A QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 * 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E QUESTION:A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)8.7 days B)2.0 days C)6.6 days D)7.7 days E)4.8 days SOLUTION:C = 1/2 - 1/8 - 1/8 = 5/24 => 4.8 days Answer: E #### E QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------\|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (3540)/3 Hence Car2 will cover total distance in (3540)/(315) = 31.11 sec approx. Answer D #### D QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data? options: A) 6 B) 2.5 C) 9 D) 11 E) 13 SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 45=20 seconds it can upload 5100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds. Answer: B. #### B QUESTION:How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length? options: A)12.9 sec B)12.1 sec C)24.2 sec D)16.8 sec E)14.9 sec SOLUTION:Speed = 36 5/18 = 10 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/10 = 24.2 sec. Answer: C #### C QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be. options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=ST=485/6=40km time=45/60hr=3/4hr New speed = 40* 4/3 kmph= 53kmph Answer : B #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)102400 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 1x metres and breadth = 4x metres. Then, 2(1x + 4x) = 1600 or x =160. Length = 160 m and Breadth = 640 m. Area = (160 x 640) m2 = 102400 m E #### E QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:A football matches has been organized in such a fashion, every participating team plays a match against every other team once and only once. If 36 matches are totally played, how many teams participated? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:For a match u need 2 teams. Suppose there are totally 'n'teams. Now we have to choose 2 teams out of 'n' teams. nC2 = 36; Solve to get n=9. n(n-1)/2 = 36 9(9-1)/2 = 36 9(8)/2 = 36 72/2 = 36 So, answer is 9 If 36 matches are totally played. ANSWER:C #### C QUESTION:After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article? options: A)1400 B)1300 C)1200 D)1100 E)None of these SOLUTION:Explanation: CP (76/100) = 912 CP= 12 * 100 => CP = 1200 Answer is C #### C QUESTION:What is the value of: -9^7 + 9^9 ? options: A) 9^2 B) -18^16 C) 63(9^7) D) -80(9^7) E) 80(9^7) SOLUTION:-9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E. #### E QUESTION:If the denominator of a fraction is increased by 4, then the fraction becomes 5/8. If the numerator is 11 less than the denominator, find the numerator. options: A)25 B)20 C)30 D)15 E)35 SOLUTION:iniatial fraction=x/y; after increasing deno..by 4=> x/(y+4)=5/8; given x = y - 11; then (y-11)/(y+4)=5/8=>y=36; x = 36-11 = 25 ANSWER:A #### A QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each. options: A)360000;180000;270000 B)270000;180000;360000 C)180000;360000;270000 D)270000;360000;270000 E)None of them SOLUTION:Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then, (3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5 1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5 108x /(72x+6480000)=3/4  432x = 216x + 19440000 =216x = 19440000 =x=90000 Hence, A’s initial investment = 3x = Rs. 2,70,000; B's initial investment = 2x = Rs. 1,80,000; C's initial investment = 4x = Rs. 3,60,000. Answer is B. #### B QUESTION:If A(k)=(k+1)^-k, and k=0, what is the value of A(A(A(k)))? options: A)0 B)(2/3)^(1/2) C)1 D)(3/2)^(1/2) E)(2/3)^-2 SOLUTION:A(A(A(0)))=A(A(1))=A(1/2)=(1/2+1)^-1/2=(2/3)^(1/2) Thus, the answer is B. #### B QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:If a - b = 3 and a^2 + b^2 = 28, find the value of ab. options: A)19 B)15 C)10 D)8 E)13 SOLUTION:2ab = (a^2 + b^2) - (a - b)^2 = 25 - 9 = 16 ab = 8. Answer is D. #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 70 ⇒ 1.75x = 70 ⇒ x = 40 coins Answer C #### C QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. options: A)15 B)25 C)30 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 * 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:C #### C QUESTION:In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: options: A)2 B)4 C)7 D)12 E)15 SOLUTION:Sol. Speed in still water = 1/2 (9+5) kmph = 7 kmph. Answer C #### C <<<Examples ends QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months. options: A)7500 B)6500 C)8125 D)9125 E)None of them SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years. Simple Interest = (PRT)/100 = Rs.(73,000(50/3)(3/4)*(1/100))= Rs.9125 Answer is D. #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together? options: A)89! B)88! C)79! D)98! E)None SOLUTION:Solution: No. of ways in which 10 paper can arranged is 10! Ways. When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers. These 9 papers can be arranged in 9! Ways. And two papers can be arranged themselves in 2! Ways. No. of arrangement when best and worst paper do not come together, = 10!- 9!.2! = 9!(10-2) = 8.9!. Answer A #### A QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white? options: A)3/4 B)4/5 C)7/8 D)1 E)None of these SOLUTION:Explanation: Total cases = 6 + 24 = 30 Favourable cases = 24 So probability = 24/30 = 4/5 Answer: A #### A QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION:How many words can be formed by using all letters of the word “BIHAR” options: A)452 B)320 C)365 D)456 E)120 SOLUTION:The word BIHAR contains 5 different letters. Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120 Ans: E #### E QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9124= 6D28 D2 = 9124/68 = 9 ANSWER:B #### B QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 3016=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 65% increase on the price he bought it. What percent of profit did he make on the original price? options: A)A)2% B)B)12% C)C)14% D)D)20% E)E)32% SOLUTION:Original price = 100 CP = 80 S = 80(165/100) = 132 100 - 132= 32% E) #### E QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:Which of the following equations has a root in common with x^2−4x+3=0 ? options: A)x^2-4x-4=0 B)x^2-2x+1=0 C)x^2-x-1=0 D)x^2-10x-1=0 E)x^2+1=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-3) = 0 so the two roots are 1 and 3. Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get -7; Putting 3 we get -7. Reject this option. (B) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. B is the answer. #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: . options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720 SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:The current of a stream runs at the rate of 3 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)A)7.24 B)B)2 C)C)8.5 D)D)6.67 E)E)3 SOLUTION:S = 3 M = x DS = x + 3 US = x - 3 6/(x + 3) + 6/(x - 3) = 2 x = 7.24 Answer:A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago? options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4 SOLUTION:3x-25/2x-25 = 4/3 Therefore x=-25 Age cannot be negative. Answer: D #### D QUESTION:How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together? options: A)56 B)72 C)48 D)60 E)59 SOLUTION:The given word contains 5 different letters. Taking the vowels EA together, we treat them as one letter. Then, the letters to be arranged are XTR (EA). These letters can be arranged in 4! = 24 ways. The vowels EA may be arranged amongst themselves in 2! = 2 ways. Number of words, each having vowels together = (24x2) = 48 ways. Total number of words formed by using all the letters of the given words = 5! = (5x4x3x2x1) = 120. Number of words, each having vowels never together = (120-48) = 72. Ans: B #### B QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 17=7.Also 172 gives 1 Hence unit's digit in the product =71=7. Option A #### A QUESTION:What is the probability of drawing a queen from a deck of 52 cards? options: A)4/13 B)1/13 C)4 D)1 E)2/13 SOLUTION:Total number of cards,n(s)=52 Total number of queen cards,n(e)=4 p(e)=n(e)/n(s)=4/52=1/13 Option B is answer #### B QUESTION:If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)? options: A) 1 B) 13 C) 26 D)25 E) 1014 SOLUTION:x = 14 + 16 + ... + 62 = (largest + smallest)/2 (# of terms) = (14 + 62)/225 = 3825. GCD of 25 and 3925 is 25. Answer: D. #### D QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4100))^4 Amount = 15000 (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16 SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800 The number of females older than 70 years old is 0.6850 = 510 The number of people who are either female or younger than 70 is 1800+510 = 2310. P(a person is younger than 70 or male) = 2310/2600 = 231/260 The answer is A. #### A QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A QUESTION:What is the HCF of 2/3, 4/15 and 6/5 options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15 Answer: Option E #### E QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N? options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N). Answer: B #### B QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)6 B)(P-7)5 C)(P-7)2 D)(P-7)3 E)(P-7)4 SOLUTION:M/84 =(P-7)/21 M = (P-7)84/21 =(P-7)4 E #### E QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n(n+1)/2 with n being 23, so equal to 23 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years? options: A)35 years B)77 years C)55 years D)44 years E)33 years SOLUTION:Let the present ages of X and Y be 5x and 6x years respectively. Then, (5x + 7)/(6x + 7) = 6/7 7(5x + 7) = 6(6x + 7) => x = 7 X's present age = 5x = 35 years.Answer: A #### A QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y? options: A)6 B)3 C)4 D)5 E)7 SOLUTION:lets start from z, as per the question stem z + 5 + 7 = 16 -->> z= 4 similarly, y + 4 + 5 = 7 --> y = -2 similarly,, x + -2 + 4 = 5 --> x = 3 hence , x-y = 3+2 = 5 ANSWER:D #### D QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 168 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7 total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 80 km downstream? options: A)2 hours B)3 hours C)4 hours D)5 hours E)None SOLUTION:Solution Speed Downstream = (13 + 4) km/hr = 17 km/hr. Time taken to travel 80 km downstream =(80 / 17)hrs = 4 hrs 42 minutes. Answer E #### E QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ? options: A)18 B)12 C)25 D)13 E)7 SOLUTION:Teacher's age= 10x+y so student's age= 10y+x.. after 5 years , 10x+y+5=2(10y+x+5).... so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18 #### A QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =âˆšb : âˆša = âˆš400 : âˆš625 = 20 : 25 Answer D #### D QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is options: A)37 B)36 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2(b-10) => 2b-a = 30 ......(i) a = b+6 =>2b-b-6 = 30 b=36 so the present age of b is 36 years ANSWER:B #### B QUESTION:A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)240 B)250 C)260 D)230 E)220 SOLUTION:Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 36 => 300+L = 15×36 = 540 => L = 540-300 = 240 meter Answer is A. #### A QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 71 min C)6 hrs 32 min D)6 hrs 27 min E)6 hrs 23 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 Â½ = 75 km RS = 75 â€“ 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other? options: A)384 B)396 C)576 D)24 E)696 SOLUTION:Number of total arrangements = 5! Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 22 Total number of arrangements - Number out of restrictions = Result 5! - (4!22) = 120 - (2422) = 24 Answer D #### D QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform? options: A)45 B)47 C)49 D)51 E)53 SOLUTION:Let the length of the train be x meters. When a train crosses an electric pole, the distance covered is its own length x. speed = 36 km/h = 36000 m / 3600 s = 10 m/s x = 14 10 = 140 m. The time taken to pass the platform = (140 +370)/ 10 = 51 seconds The answer is D. #### D QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10987) ==> 5040 ANSWER A #### A QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) options: A)200π B)240π C)300π D)480π E)1,200π SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280 Revolutions in one second= 1320 Revolutions in 60 seconds (one minute)= 132060 Total distance traveled= total revolutions distance traveled in one revolution 132060 2π10/5280= 300π C is the answer #### C QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c11c11c1)/5c3 =3/10 ANSWER:A #### A QUESTION:The largest 4 digit number exactly divisible by 88 is? options: A)9930 B)9936 C)9944 D)9952 E)9960 SOLUTION:Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944. C) #### C QUESTION:A certain sum of money at simple interest amounted Rs.640 in 10 years at 3% per annum, find the sum? options: A)442.3 B)492.3 C)592.3 D)402.3 E)472.3 SOLUTION:640 = P [1 + (103)/100] P = 492.30 ANSWER:B #### B QUESTION:A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows? options: A)24 B)72 C)720 D)336 E)420 SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is permutations = 5! = (5)(4)(3)(2)(1) = 120 The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is permutations = 3! = (3)(2)(1) = 6 Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 1206 = 720 Answer: C. #### C QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ? options: A)-280 B)300 C)-350 D)-380 E)None SOLUTION:In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -. Let x = the sum required. Then according to the statement x + 680 - 80 = 250 And x = -350. Answer C #### C QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 3 5 b Therefore (3 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 b Therefore, b = 3^3 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 57 = 35 Correct answer A. #### A QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C? options: A)2250 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 75/247 * 7410 = 2250 Answer: A #### A QUESTION:If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = n 5a2 + 7b2 = n 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:An old priest fell on a bottom of the well of a church. The well is 16 inches deep. At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches. In how many days priest will come out of the well ? options: A)12-days B)14-days C)11-days D)19-days E)10-days SOLUTION:A 12-days In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6666 = 2^43^4 Total factors = (4+1)(4+1) = 64 = 24 Answer C. #### C QUESTION:At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 10'o clock. options: A)60sec B)62sec C)66sec D)64sec E)54sec SOLUTION:At 6'0 clock, clock ticks 6 times. So, there must be 5 intervals between clock ticks. Time Between first and last ticks = 30sec So, 1 interval = 30/5 = 6sec So 6'o clock 5 6=30sec 7'o clock 6 6=36sec . . 9'o clock 8 6=48sec 10'o clock 9 6=54sec So, 54sec at 10'o clock. ANSWER:E #### E QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in? options: A)6 B)12 C)28 D)42 E)21 SOLUTION:The part of the tank filled by three pipes in one hour = 1/14 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/14= 1/21. The tank can be filled in 21 hours. Answer:E #### E QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:What approximate value should come in place of the question mark (?) in the following equation? 1.542 × 2408.69 + 5134.632 = ? options: A)4600 B)4800 C)5200 D)6400 E)8800 SOLUTION:Explanation 3700 + 5100 = 8800 Answer E #### E QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(28-10) kmph = 4 kmph. Answer B #### B QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ? options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms SOLUTION:Solution Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B QUESTION:The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is options: A)11 B)13 C)15 D)17 E)18 SOLUTION:Sequence is contain prime numbers. Final sequence : 2,3,5,7,11,13,17,19 ANSWER:B #### B QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour? options: A)6 metre B)12 metre C)120 metre D)1200 metre E)2200 metre SOLUTION:Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600 :. Distance moves = (600 20) cms = 12000 cms In metres = 120 metre Answer: C #### C QUESTION:If P (A) = 0.18, P (B) = 0.5 and P (B\|A) = 0.2, find P(A n B)? options: A)0.28 B)0.36 C)0.45 D)0.56 E)0.7 SOLUTION:P(B\|A) = P(A n B)/P(A) P(A n B) = P(B\|A) × P(A) P(A n B) = 0.2 × 0.18 P(A n B) = 0.36 B) #### B QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream? options: A)19 B)88 C)14 D)12 E)17 SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 57/3 = 19 kmph. Answer:A #### A QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) â€“ 24009 ] = Rs. (27000 â€“ 24009) = Rs. 2991. Answer B #### B QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies options: A)250 B)150 C)100 D)50 E)200 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 ANSWER E #### E QUESTION:The length Q of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length Q of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive? options: A)None B)One C)Two D)Three E)Four SOLUTION:$ is basically a factorial of a number. So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive. From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range. For example: 7!+2=2(34567+1) --> a multiple of 2, thus not a prime; 7!+3=3(24567+1) --> a multiple of 3, thus not a prime; ... 7!+10=10(3467+1) --> a multiple of 10, thus not a prime. Answer: A. #### A QUESTION:Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 36/49, what is the probability that the next one she draws will be pink? options: A)1/7 B)4/7 C)3/7 D)16/49 E)40/49 SOLUTION:The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 36/49 = (6/7) (6/7) Therefore probability that the next one she draws is pink = 1/7 Option (A) #### A QUESTION:A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$3,000 C)$3,700 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,300 So, the HUNDREDS DIGITS of the 15th investment must be 7 Answer: C #### C QUESTION:In a mixed college 160 students are there in one class. Out of this 160 students 1/4 students are girls. How many boys are there ? options: A)A)40 B)B)60 C)C)80 D)D)120 E)E)140 SOLUTION:Total Number of Students :160 Total Girls : 1601/4 =40 Total Boys : 160-40 = 120 Answer is D #### D QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:There are two taps, which are used to fill the tank and one tap to empty the tank. First tap fill the tank in 10 min., while the second takes quarter of an hour to fill the tank if both are operated independently.Third tap is capable of emptying the tank in seven and a half minutes. If all the taps are opened simultaneously how long (if ever) will it take for the tank to get filled completely? options: A)10 minutes B)20 minutes C)30 minutes D)40 minutes E)50 minutes SOLUTION:Pipe A fills the tank in 10 min Pipe B fills the tank in 15 min Pipe C empties the tank in 15/2 min If all the three opened simultaneously then in 1 min 1/10 + 1/15 - 2/15 of the tank will be filled that means 1/30 th of the tank will be filled in 1 min So it will take 30 minutes to fill the tank completely if all three pipes opened ANSWER:C #### C QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)8 B)6 C)4 D)5 E)9/2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1 When B starts: No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1 Solving the above two equations for xy x = 1/9 y = 1/9 → Total work done by AB in a day = 1/9 + 1/9 = 2/9 → No. of days to complete the work when both work together = 9/2; Answer: E #### E QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who speak both the languages? options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32 SOLUTION:let the student who speaks tamil-x let the student who speaks telugu-y as (xuy)-(xny)=total 30+30-(xny)=50 =10 B) #### B QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and â€“4; #### B QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+1112) = 12!11!(133) = 12!11!(719) The greatest prime factor is 19. The answer is C. #### C QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .250+.6x=.5(50+x) x=150 Answer E #### E QUESTION:Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill? options: A)A)1/8 B)B)1/3 C)C)1/9 D)D)1/2 E)E)1/4 SOLUTION:1/10 + 1/15 = 1/6 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 Answer:B #### B QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)35 kmph D)23 kmph E)14 kmph SOLUTION:S = (10 + 60)/2 = 35 kmph Answer:C #### C QUESTION:If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. options: A)35 7/8 B)36 C)21 3/7 D)34 5/7 E)34 6/7 SOLUTION:Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts. If we use 8 tons of cement, then we'll get 5/730 = 21 3/7 tons of mixture. Answer: C. #### C QUESTION:What least number must be subtracted from 427398 so that remaining number is divisible by 15 options: A)3 B)5 C)7 D)9 E)None of these SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option A #### A QUESTION:If (5^15)(9^8)=3(15^x), what is the value of x? options: A) 7 B) 9 C) 11 D) 13 E) 15 SOLUTION:(5^15)(9^8)=3(15^x) => 5^15 3^16 = 3 * 3^x * 5^x => 5^15 * 3^16 = 3^(x+1) * 5^x Value of x = 15 Answer E #### E QUESTION:Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business? options: A)6 : 13 : 90 B)5 : 12 : 90 C)5 : 11 : 80 D)6 : 11 : 90 E)12 : 6 : 90 SOLUTION:Ratio of their investments = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90 Answer D #### D QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 16.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)20.4 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 141. Total age of five men added later = 414 - 312 = 202. Hence, the total average of five men = 102/5 = 20.4 ANSWER:D #### D QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400 SOLUTION:6600:4400:11000 3:2:5 3/10 * 11000 = Rs.3300 AnswerA #### A QUESTION:The cost price of 20 articles is equal to the selling price of 25 articles. The loss percent in the transaction is options: A)5 B)20 C)25 D)30 E)None of these SOLUTION:Let C.P. of 1 article = 1 then C.P. of 25 articles = 25 and S.P. of 25 articles = 20 ∴ loss % = 25−20/20×100=25% Answer C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!2=48. Answer: D #### D QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40x+52x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)100 = 25% ANSWER:A #### A QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)8.7 days B)2.0 days C)6.6 days D)7.7 days E)4.8 days SOLUTION:C = 1/2 - 1/8 - 1/8 = 5/24 => 4.8 days Answer: E #### E QUESTION:number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9 options: A)1290 B)1296 C)1380 D)1480 E)1580 SOLUTION:we have to make 4 digit number in which the format is d> c > b > a __ __ __ __ 1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4) 2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3) 3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2) 4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1) hence every place can be filled by 6 digits, 6* 6* 6* 6 = 1296 ANSWER:B #### B QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)ab D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him. Options: options: A)1 apple B)2 apple C)3 apple D)4 apple E)5 apple SOLUTION:This is equivalent to finding the first number that is divisible by 7 that occurs before 4267. In order to divide the sum in 7 parts, the amount must be divisible by 7 Divisibility rule of 7: The sum of the digits must be divisible by 7 Sum of digits of 4267 = 19 and 7 is divisible by 7. Hence, we need to remove 5 to this number for it to be divisible by 7 Correct Option:E #### E QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)22 days B)77 days C)24 days D)17 days E)18 days SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days Answer: C #### C QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married? options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70 SOLUTION:--------------------M------W--------Total Marrried----------20-----20---------40 Not married-----10-----50---------60 Total-------------30-----70--------100 need married woman/total woman, so 20/70=2/7 C #### C QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files? options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr SOLUTION:Server J processes 480/4 files per hour = 120 per hour Server Y processes 180/8 files per hour = 60 per hour Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour 480/180 = 2 2/3 hours=C #### C QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 68.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)787 C)178 D)179 E)172 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 20505=10250 10250-10000=250 Answer E #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 19.7%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)26% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 19.70 Let marked price be Rs. x. Then, 95/100 x = 119.70 x = 11970/95 = Rs. 126 Now, S.P. = Rs. 126, C.P. = Rs. 100 Profit % = 26%. Answer: B #### B QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed. options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec SOLUTION:If length of train is l and speed of train is s, then l/s = 10 (l+180)/s = 20 (l+180)/l = 20/10 =2 l+180 =2l l= 180 l=180 mtrs s= l/10 = 180/8 = 10 m/sec ANSWER:A #### A QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:There are 100 boys in a hostel. Each plays either cricket or softball or both. If 60% play cricket and 50% play softball, how many play both? options: A)20 B)50 C)10 D)100 E)60 SOLUTION:n(A) = 50100/100 = 50 n(B) = 60100/100 = 60 n(AUB) = 100 n(AnB) = 50+60-100 = 10 Answer is C #### C QUESTION:In what time will a train 140 m long cross an electric pole, it its speed be 144 km/hr? options: A)3.5 sec B)4.25 sec C)5 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 5/18 = 40 m/sec Time taken = 140/40 = 3.5 sec. ANSWER:A #### A QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)6925 B)6887 C)6728 D)6725 E)2871 SOLUTION:: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: A #### A QUESTION:Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog? options: A)16.5 kmph B)16.6 kmph C)16.4 kmph D)16.9 kmph E)16.2 kmph SOLUTION:In an average speed of 22 kmph horse got dog in 6 hours So distance=speedtime distance=226=132km Dog takes 8 hours to travel 132 km. So the speed if dog is speed=distance/time speed=132/8=16.5 kmph Answer: 16.5 kmph Answer A #### A <<<Examples ends QUESTION:If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)? options: A)35 B)45 C)55 D)65 E)75 SOLUTION:(a^2-b^2)(b^2-c^2) = (a+b)(a-b)(b+c)(b-c) = (a+b)(-1)(b+c)(-1) = (a+b)(b+c) Therefore, the product should have factors with a difference of 2. 35 = 57, so this is a possible value for the original expression. The answer is A. #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n(n+1)/2 with n being 23, so equal to 23 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour. options: A)2 B)1.5 C)2.25 D)3 E)1.75 SOLUTION:The distance between the man's home and the store is 500 meters. 3 times means that the man made the 500 meter trip 6 times in total. 6 * 500 = 3000 meters or 3 km. Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075. Correct answer is 2.25 km per hour #### C QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)299 B)277 C)266 D)992 E)188 SOLUTION:(80033)/100 = 72 920 + 72 = 992 Answer:D #### D QUESTION:A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase? options: A)$18 B)$20 C)$22 D)$24 E)$25 SOLUTION:Let x be the daily wage before the increase. 1.4x = $28 x = $20 The answer is B. #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? options: A)65 B)44 C)86 D)29 E)26 SOLUTION:Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Answer: B #### B QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet? options: A)33 B)37 C)27 D)28 E)23 SOLUTION:Explanation: Other side = = = = 6 ft Area of closet = (6 x 4.5) sq. ft = 27 sq. ft. Answer: C) 27 #### C QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in options: A)2 days B)1 day C)3 days D)5 days E)7 days SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. B) #### B QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The distance between the nest and the ditch is 250 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 250 = 7500. D = ST 7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km) D) #### D QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103? options: A)2500 m^2 B)2510 m^2 C)2520 m^2 D)2540 m^2 E)2590 m^2 SOLUTION:Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C #### C QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7? options: A)397 B)401 C)403 D)405 E)364 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=364. Answer: E. #### E QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)14 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m. Answer C #### C QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 * Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 420=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways SOLUTION:The boy can select one trouser in thirteen ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 13 15 = 195 ways. Answer:D #### D QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W? I. 9 II. 15 III. 27 options: A)I only B)II only C)I and II only D)I and III only E)I, II, and III SOLUTION:Ans: C W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)3 means x must contain 3^2 and 5^2 so with these conditions we know that 9=3^2 and 15=35 both have required factors for the divisibility of lowest int for x which is 925 but 27 is not a divisor because it can't divide 925 fully. so Ans : C #### C QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 1334 = 156 Answer: E #### E QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is even C)AB is even options: A)I only B)II only C)III only D)II,III only E)None of the above SOLUTION:If AB is Odd then C will not even. O+E = O If B is even AB is even always. But If C is Odd E+O = O None of the above are true #### E QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 41(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is? options: A)22 B)28 C)27 D)36 E)88 SOLUTION:(912)/3 = 36 Answer:D #### D QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? options: A)229 B)108 C)278 D)72 E)112 SOLUTION:S = 120/6 18/5 = 72 kmph Answer: D #### D QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)4 D)5 E)6 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? options: A)4 min B)8 min C)9 min D)6 min E)1 min SOLUTION:S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min Answer:A #### A QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500 SOLUTION:OFFICIAL SOLUTION: The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve: 550 + (0.08)(x – 4,000) = 0.10x Distribute the 0.08: 550 + 0.08x – 320 = 0.10x Combine terms and subtract 0.08x from both sides: 230 = 0.02x Divide both sides by 0.02: 11,500 = x Your answer is A. #### A QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 1110^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)231 B)150 C)200 D)450 E)451 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 5C2) = 200 Ans: C #### C QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1x X=11.81% Answer D) #### D QUESTION:A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? options: A)16 km B)87 km C)89 km D)67 km E)20 km SOLUTION:Let the distance between A and B be x km. Total time = x/(9 + 1) + x/(9 - 1) = 3.5 => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x = 16 km. Answer:A #### A QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(490+x)/5=92 x=(592)-(490) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:Let x be the amount of liquid Q to be added. (3/8)40 + x = (6/11)(40+x) 1320 + 88x = 1920 + 48x 40x = 600 x = 15 The answer is E. #### E QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is: options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons SOLUTION:Explanation: Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying] Volume of {\color{Black} \frac{1}{40}} part = 3 gallons Volume of whole = (3 x 40) gallons = 120 gallons. Answer: C #### C QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers? options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9 SOLUTION:Let two numbers be x and y. Equation (i): x + y = 18 Equation (ii): x - y = 4 Solve system of equations: 2x=22 x=11 y=7 Answer C is correct. #### C QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps. if he step down 34 stairs he has only 18 sec. 30-18=12 12 secs for 8 steps.. 18 secs for 12 steps. 12+34=46 so ans is 46.. ANSWER:B #### B QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (1213.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:a man spends $2.6 for parking and $34.4 for petrol to travel in car from monday to friday.if he travel by public transport it costs $1.06,find the percentage of savings? options: A)75.6 B)85.6 C)85.7 D)95.7 E)105.7 SOLUTION:2.6+34.4=37 for 5 days 1.065=5.3 37-5.3=31.7 now the required saving percentage is (31.7/37)100=85.6 ANSWER:B #### B QUESTION:A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:ALTERNATE APPROACH Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations. Given Perimeter is 150 So, 2 ( L + B ) = 150 Or, L + B = 75 Now use the answer options ( Given Length ; Breath will be half the length) (A) 40 L = 40 ; B = 20 L + b = 60 (B) 50 L = 50 ; B = 25 L + b = 75 (C) 60 L = 60; B = 30 L + b = 90 (D) 70 L = 70; B = 35 L + b = 105 (E) 80 L = 80; B = 40 L + b = 120 Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B) #### B QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5 options: A)15 B)20 C)25 D)32.5 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5 Answer: Option D #### D QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay? options: A)m/(5d) B)20d C)5d D)5dm E)20d/m SOLUTION:Total income of Sara in a month = d5m dollars. = d5m = 5dm Answer is D #### D QUESTION:In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 93% of the products of M3 III are not defective. What is the percentage of defective in the stockpile? options: A)3% B)5% C)2.5% D)4% E)3.6% SOLUTION:Explanation : Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3. Products from M1 = 40, from M2 = 30 and from M3 = 30. Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.07 x 30 = 2.1 Therefore, total number of defective products = 3.6 Answer : E #### E QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 243 =72 ratio of their ages = 1:2:3 Age of the youngest = 721/6 = 12 years Answer is C #### C QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? options: A)8 B)9 C)8.5 D)9.5 E)10.5 SOLUTION:In such questions, you need to start from the end. Last 4 days John works alone and completes 4 (1/10) = 2/5 of the work. So 3/5 of the work should have been completed by the two of them together before Jane left. Their combined rate of work is 1/20 + 1/12 = 8/60 Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days. So total number of days taken to complete the work =9/2 + 4 = 8.5 days. C #### C QUESTION:There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green? options: A)40 B)8 C)15 D)25 E)50 SOLUTION:98−x/100−x=96100 Or, 9800−100x=9600−96x Or, 200=4x Or, x=50 ANSWER:E #### E QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:A number is missing from the number series below. Can you find it ? 84, 155, ?, 399 , 584, 819. options: A)275 B)350 C)399 D)258 E)449 SOLUTION:D The missing number is 258. 84 = 4^3 + 3^2 + 4 155 = 5^3 + 5^2 + 5 399 = 7^3 + 7^2 + 7 584 = 8^3 + 8^2 + 8 819 = 9^3 + 9^2 + 9 Thus, 258 = 6^3 + 6^2 + 6 #### D QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 66 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x â€“ 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (10080)/(8001) = 10% Answer: E #### E QUESTION:A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? options: A)20 B)24 C)25 D)26 E)30 SOLUTION:Ans.(A) Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways #### A QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 8? options: A)2/13 B)3/45 C)5/36 D)6/73 E)4/15 SOLUTION:n(S) = 66 = 36 E = {(2,6),(3,5),(4,4),(5,3),(6,2)} Probability = 5/36 Answer is C #### C QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? options: A)2015 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2014) = 2015 Ans: A #### A QUESTION:Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount. options: A)680 B)700 C)720 D)730 E)750 SOLUTION:From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal. As the annual Interest is to be calculated, the time period T =1. Plugging these values in the simple Interest formula, I = P x T x R = 8,000 x 1 x 0.09 = 720.00 Annual Interest to be paid = $720 answer :C #### C QUESTION:From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected? options: A)1/10 B)4/9 C)1/2 D)9/15 E)2/3 SOLUTION:The total number of ways to choose 2 children from 6 is 6C2 = 15 The number of ways to choose 1 boy and 1 girl is 33 = 9 P(1 boy and 1 girl) = 9/15 The answer is D. #### D QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage? options: A)33 B)50 C)99 D)87 E)71 SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 4) SP of 60 articles = Rs. 150 (30 * 5) Profit percentage = (150 - 100)/100 * 100 = 50% Answer: B #### B QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these SOLUTION:Explanation: Error = (25.5 - 25.461) = 0.039 Required percentage = 0.039/ 25.461Ã—100=0.153 Option B #### B QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2 SOLUTION:John's speed - 12 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles. Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr. Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours Answer B #### B QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c? options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3 SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}). But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms. Answer: C. #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? options: A)5 A B)10 A C)15 A D)18 A E)25 A SOLUTION:Movies: 75 % comedies. 25 % remaining genre. Now in this 25 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 2x/3. Total 5x/3. 5x/3 = 25; x = 15 Action movies: 15 % Drama movies: 10 % we can say that out of 100 z,: comedies: 75 z action: 15 z drama: 10 z Now action movies were A This means: A = 15 z. z = A/ 15 Comedies: 75 z = 75 * (A/15) 5 A A is the answer. #### A QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:What percent of 120 are 90? options: A)33 B)66 C)75 D)44 E)31 SOLUTION:(?% /100) * 120 = 90 ? = 75% Answer: C #### C QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)376 C)1267 D)198 E)621 SOLUTION:624/6 = 104 kmph Answer: A #### A QUESTION:The area of a triangle is with base 3m and height 4m? options: A)4 m2 B)6 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 3 * 4 = 6 m2 Answer: B #### B QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100100=10,000. Now, the area obtained with wrong measurements would be 11695=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 320000/5=12000 ANSWER:E #### E QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.49 C)Rs.4082.48 D)Rs.4082.40 E)Rs.4082.13 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer: D #### D QUESTION:Which of the following MUST yield an integer when divided by 11? options: A)The sum of eleven consecutive positive integers. B)The square of a prime number. C)The sum of two odd integers. D)The product of three consecutive odd numbers. E)The difference between a multiple of 8 and a multiple of 3. SOLUTION:For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, Ans(A). #### A QUESTION:The sum of first nine prime numbers is? options: A)12 B)100 C)24 D)28 E)30 SOLUTION:Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. B #### B QUESTION:Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be options: A)9,000 B)12,000 C)11,000 D)10,000 E)None of these SOLUTION:Sum invested by A, B and C is 5 × 12 : 7 × 12 : 6 × 6 + 3 × 6 or, 60 : 84 : 54 or, 10 : 14 : 9 \Share of C = 9⁄33 × 33,000 = 9,000 Answer A #### A QUESTION:A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total? options: A)220 B)250 C)280 D)300 E)340 SOLUTION:Let the total number of ounces in the drink be x. % of orange = 25% % of watermelon = 40% % of grape = 100% - 65% = 35% 0.35x = 105 x = 300 Therefore there are a total of 300 ounces in the drink. The answer is D. #### D QUESTION:In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at M/2 with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining? options: A)33.33% B)50% C)60% D)66.66% E)None of these SOLUTION:Solution: MP = M SP = M/2 % Discount = [(M/2) /M] 100 = 50%. Answer: Option B #### B QUESTION:Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:Let x be the amount of soup at the beginning. After lunch, the remaining soup was (4/5)x. After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x. The answer is B. #### B QUESTION:Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel. options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160 SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180; Vessel B = 500 gallons --> milk = 375, water = 125; Vessel A + B = 800 gallons --> milk = 495, water 305. The ratio = 495/305 --> reduce by 5 = 99/61. Answer: A. #### A QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 162 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B QUESTION:In a certain code language, '3a, 2b, 7c' means 'Truth is Eternal'; '7c, 9a, 8b, 3a' means 'Enmity is not Eternal' and '9a, 4d, 2b, 8b' means 'Truth does not perish'. Which of the following means 'enmity' in that language ? options: A)3 B)9 C)8 D)6 E)2 SOLUTION:Explanation: Justification: In the second and third statements, the common code is '9a' and the common word is 'not'. So, '9a' means 'not'. In the first and second statements, the common codes are '7c' and '3a' and the common words are 'is' and 'Eternal'. So, in the second statement, '8b' means 'enmity'. Answer: C) 8b #### C QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 6 km/h. The man's rate is? options: A)5 kmph B)6 kmph C)7 kmph D)4 kmph E)9 kmph SOLUTION:Explanation: DS = 16 US = 6 S = ? S = (16 - 6)/2 =5 kmph Answer: A #### A QUESTION:Find the sum of all odd numbers upto 100. options: A)200 B)1000 C)2500 D)3140 E)3200 SOLUTION:Sol. The given numbers are 1, 3, 5, 7, ..., 99. This is an A.P. with a = 1 and d = 2. Let it contain n terms. Then, 1 + (n - 1) x 2 = 99 or n = 50. Required sum = (n/2) (first term + last term) = 50(1 + 99)/2 = 2500. ANSWER C 2500 #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 185x+152x=180 x=180/215 x=0.837209 time taken for type A problem=1520.837209=25.11628min ANSWER:B #### B QUESTION:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have? options: A)7 B)5 C)6 D)8 E)9 SOLUTION:take the example of 4... it has 3 positive divisors (1,2,4) Now, take the example of 64... it has only 7 divisors.. so A is the ans #### A QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected. What is the probability that a smartphone bundle that will be rejected by quality control? options: A) 0.25 B) .05^10 C) 1-0.94^10 D) 1-0.05^10 E) 0.95^10 SOLUTION:Find the probability of the opposite event and subtract from 1. The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10. P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10. Answer: C. #### C QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100100 = 132 10% discount Then price = 132 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this? options: A)264 B)328 C)460 D)588 E)642 SOLUTION:(8c6)(7c5) [8!/(6!2!)][7!/(5!2!)] 2821 588 D #### D QUESTION:The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N. options: A)797 B)254 C)597 D)997 E)297 SOLUTION:According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient divisor + remainder = 18* 14 + 2 = 254 correc answer B #### B QUESTION:A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)24 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x2+y4=140 heads: x1+y1=48 implies, 2x+4y=140 and x+y=48 solving these two equations, we get x=26 and y=22 Therefore, hens are 26. ANSWER:D #### D QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions. Hence, the number of all possible selections is 3 10 – 1. Answer C #### C QUESTION:the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with? options: A)21 B)31 C)41 D)51 E)61 SOLUTION:He start out with 31eggs. In the end, he have 3eggs left. So, 32 +1= 7 72 +1= 15 152 +1= 31 31eggs he had initially. ANSWER:B #### B QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2PD or m - 2PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:The area of playground is 6000 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter. options: A)a) $144 B)b) $150.50 C)c) $168 D)d) $158.60 E)e) $160.70 SOLUTION:total volume unit cost = total cost or, 6000 * 0.01 * 2.8 = total cost = 168=C #### C QUESTION:A student is ranked 13th from right and 8th from left.how many are there? options: A)18 B)19 C)20 D)21 E)22 SOLUTION:13th from right means = x + 12 8th from left means = 7 + x Total = 12+7+1 = 20 ANSWER:C #### C QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 3016=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 4C2 = 66 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)(3/7)(4/6)(3/5) [4!/(2!2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:David is able to sell a hand-carved statue for $1150 which was a 15% profit over his cost. How much did the statue originally cost him? options: A)$496.30 B)$512.40 C)$1000 D)$574.90 E)$588.20 SOLUTION:Cost price = 1150/115100 = 1000 Answer : C #### C QUESTION:1398 x 1398 = ? options: A)1624404 B)1851404 C)1951404 D)1954404 E)None of these SOLUTION:Explanation : 1398 x 1398 = (1398)2 = (1400 - 2)2 = 14002 - (2 × 1400 × 2) + 22 = 1960000 - 5600 + 4 = 1954404. Answer : Option D #### D QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:The area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is? options: A)48 B)40 C)52 D)54 E)58 SOLUTION:Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 16 will be divided into 3 parts= 10, 3 and 3 (Making one square and two right triangles) For the right triangle, height will be= (5^2-3^2)^1/2= 4 And the area of trapezoid = 1/2 (B1+B2)H= 1/2264= 52 C is the answer #### C QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[24+(50-1)2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)7 D)12 E)32 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 36 + 40 + 10 - (12) - 2x x = 7 So, answer will be C #### C QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B <<<Examples ends QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 * Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 71+1 (71+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 1/2 hours B)20 1/7 hours C)20 1/3 hours D)20 3/2 hours E)20 1/4 hours SOLUTION:1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours Answer: A #### A QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? options: A)42 B)70 C)140 D)135 E)315 SOLUTION:1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 3 candidates for the math dep., which gives as 3 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!8!= (910) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 345 = 135 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans D #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (54 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? options: A)7cdx/100 B)d + 7cx/100 C)7d + xc/100 D)7d + 7xc/100 E)7cdx SOLUTION:Answer is D. #### D QUESTION:A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)8:8 B)9:8 C)9:6 D)9:5 E)9:13 SOLUTION:(36 + 66): (6.512) 54:78 => 9:13 Answer: E #### E QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales? options: A)8% B)15% C)35% D)42% E)56% SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%. Answer D #### D QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:If an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)7168 SOLUTION:0.72^10=0.71024=716.8 The answer is E. #### E QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)60% B)80% C)65% D)75% E)None of these SOLUTION:A's marks = 80 ; B's marks = 60. Let x% of A = B => x/100 * 80 = 60 => x = (60 * 100)/80 = 75 B's marks is 75% of A's marks. ANSWER:D #### D QUESTION:Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues? One digit is divisible by 1. Two digits are divisible by 2. Three digits are divisible by 3. Four digits are divisible by 4. Five digits are divisible by 5. Six digits are divisible by 6. Seven digits are divisible by 7. Eight digits are divisible by 8. Nine digits are divisible by 9. Ten digits are divisible by 10. options: A)3816547290 B)3816557290 C)3816547280 D)3813547290 E)3816147290 SOLUTION:A 3816547290 #### A QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2254/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)x = 240 => x = (240 100)/60 = 400 Answer B #### B QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/85/74/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){11,26} B){18,19} C){16,18} D){16,16} E){14,16} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others. Hence Answer : E #### E QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)7/12 B)29/60 C)17/30 D)19/30 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/21/3=x/6 Platinum card unspent limit is= x-1/4x=3/4x So if gold card balance is transferred then the rest unspent will be 3/4x-x/6=7/12x So the ans is A #### A QUESTION:Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ? options: A)5.5 Hours B)7.5 Hours C)8.5 Hours D)9.5 Hours E)6.5 Hours SOLUTION:In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19 So fill tank fill up in 19/2= 9.5 Hours ANSWER:D #### D QUESTION:The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is options: A)1008 B)1015 C)1022 D)1032 E)1043 SOLUTION:Required Number = (L.C.M of 12, 16, 18,21,28)+7 = 1008 + 7 = 1015 Answer: B #### B QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x? options: A)-4 B)-2 C)5 D)13 E)22 SOLUTION:The equation that can be formed is: 3x-4=16-x or, 4x=20 or, x=5. Answer : C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)16 B)18 C)24 D)22 E)26 SOLUTION:C 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose? options: A)5 B)8 C)11 D)15 E)17 SOLUTION:Explanation : Let a, b, c be the Englishmen and d, e, f be the Frenchmen. Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls. Answer : B #### B QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M): m------M---------------W w In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 315/60 =15/20 miles and the man walks the distance mM, which is 39/60 = 9/20 mile. The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes. Answer B. #### B QUESTION:The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between Bunuel, can you please explain this one? options: A)0 and 0.5 B)0.5 and 1 C)1 and 1.5 D)1.5 and 2 E)2 and 2.5 SOLUTION:Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase). Try x=1 --> LHS=3^5=813=243 and RHS=4^4=644=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1. Answer: E. #### E QUESTION:According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI? options: A)30m B)40m C)35m D)38m E)50m SOLUTION:30% of total FDI given to Gujarat is $90m. so,100% is $300m. 20%of 300m=60m. 50%of 60m=30m. ANSWER:A #### A QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : options: A)8 B)9 C)4 D)18 E)None SOLUTION:Ratio of rates of working of A and B = 2 : 1 So, ratio of times taken = 1 : 2 B's 1 day's work = 1/12 Therefore A's 1 day's work = 1/6 (A + B)'s 1 day's work = (1/6 + 1/12)= 1/4 So, A and B together can finish the work in 4 days. Answer: C #### C QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than SOLUTION:Correct answer is (A). This year, the price of a tree is price1=P/N. If this price increases by 50% it becomes price2=P/N1.50 Then with P dollars, you can grow P/price2 tress i.e. P/(P/N1.50) i.e. N/1.5 i.e. .67% less A #### A QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:if log 7 = 0.845098, the number of digits in 7128 is options: A)100 B)120 C)109 D)280 E)110 SOLUTION:Explanation: log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17 ie, its characteristic = 108 Hence, number of digits in 2128 = 108+1 = 109 Answer: Option D #### D QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)30000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 5400 ( 18 × 300 = 5400) 100% -------> 30000 votes (100 × 300 = 30000) C #### C QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.9281.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? options: A)72 B)83 C)45 D)53 E)64 SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Answer:A #### A QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = t 5a2 + 7b2 = t 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-? options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these SOLUTION:Explanation: 112% of CP = Rs.42750 :. CP = Rs.42750x100/112 = Rs.38169. Answer: Option B #### B QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z? options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)% SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1 z is m% of y MEANS z= (m/100 )* y------------------------eq2 Find equation of xz substitute value of y from 2nd equation into Ist equation so x= (n/100)(100z/m) so x= (n/m)z or x= (100n/m)z/100 so answer E is 100n/m %.E #### E QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 -13 = -26 Answer: A #### A QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction? options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these SOLUTION:Let the fraction be x/y. When the numerator decreased by 25% and the denominator decreased by 20%. (x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5 ANSWER:E #### E QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell? options: A) 140 B) 103 C) 105 D) 115 E) 120 SOLUTION:First 100 machines = 3% commission = 0.0310010000 = 30000 Commission from sale of next machines = 46000 - 30000 = 16000 So 40 more machines.. Total = 140 machines IMO A.. #### A QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)P +(1/4)Q = (3/8)P+(3/4)Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 750 = 80/100 * 750 = 600 Option C #### C QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!2=48. Answer: D #### D QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:A work can be finished in 30 days by 30 women. The same work can be finished in fifteen days by 15 men. The ratio between the capacity of a man and a woman is options: A)1:3 B)4:3 C)2:3 D)4:1 E)2:4 SOLUTION:Work done by 30 women in 1 day = 1/30 Work done by 1 woman in 1 day = 1/(30×30) Work done by 15 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×15) Ratio of the capacity of a man and woman =1/(15×15) : 1/(30×30)) = 1/225 : 1/900 = 1/1 :1/4 = 4:1 Option D #### D QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area? options: A)26% B)21% C)15% D)18% E)12% SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification) New h = 220a / 100 = 22a / 10 New b =(110a x 100) ==11a/10 New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100) increased area== (121a²/100) - a² Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21% answer :B #### B QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out? options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None SOLUTION:Solution Volume = πr2h ‹=› (22 /7 ×3×3×24)m3 ‹=›678.6 m3. Answer A #### A QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2(3)^2 = 1009 = 900 Vehicles inspected within 3 hours = 603/9 = 19 P = 19/900 Ans:D #### D QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length? options: A)87 B)69 C)40 D)72 E)24 SOLUTION:Speed = 75 Km/hr = 75(5/18) m/sec = 125/6 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (6/125) = 24 seconds Answer: E #### E QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 828 / (28-20) = 28 Answer is B #### B QUESTION:If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p? options: A)(p+1)/p B)(p - 1)/p C)p/(p + 1) D)p/(1-p) E)(1 - p)/p SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: D #### D QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 125 cm 64 cm. What is the perimeter of the square? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B QUESTION:A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads? options: A)400 B)1550 C)1575 D)1600 E)1625 SOLUTION:Area Covered by Road Along the Length = 5200 = 1000 Square Meter Area Covered by Road Along the Width = 5120 = 600 Square Meter Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 55 = 25 Total Area of the Roads T= 1000+600-25 = 1575 Answer: option C #### C QUESTION:What number has a 3:4 ratio to the number 400? options: A)130 B)100 C)200 D)300 E)120 SOLUTION:3:4 = x: 200 4x = 3400 x=300 ANSWER:D #### D QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 5050 = 2500m = 2.5km Speed = 602.5=150km/hr Answer is D #### D QUESTION:How many different ways can you select a pilot and a co pilot if you have 30 people to choose from? options: A) 870 B) 920 C) 1398 D) 4950 E) 9900 SOLUTION:You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot. So the answer is in a sense (30C2) x 2 = 870. Ans A #### A QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:There are 11 cans in the refrigerator. 6 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)445 SOLUTION:Answer: E #### E QUESTION:A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? options: A)77 days B)21 days C)88 days D)55 days E)44 days SOLUTION:WC = 1:2 2x + x = 1/14 => x = 1/42 2x = 1/21 => 21 days Answer: B #### B QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:A motorcyclist made 3 roundtrips to the park until he ran out of gas back at home. Te park is 1500 meters away from his home. His speedometer was broke and he wanted to calculate his speed. It took him two and half hours to complete the journey. How fast was the motorcyclist traveling? options: A)25 B)60 C)36 D)45 E)32 SOLUTION:The distance from the park to the motorcyclist home was 15000 meters. He made the trip 3 times in total with each trip being 30000 meters. multiply 3 by 30000 to get 90000 meters or 90km in total. D= ST 90000/2.5 = T which comes to 36000 meters or 36 km per hour Correct answer = 36 #### C QUESTION:If an average hard drive had a capacity of 0.1 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)1536 SOLUTION:0.12^10=0.11024=102.4 The answer is D. #### D QUESTION:Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length? options: A)6 B)8 C)10 D)14 E)16 SOLUTION:In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT. So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10. Answer: C. #### C QUESTION:How many possible integer values are there for x if \|4x - 3\| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: \|4x-3\| < 6 let 4x=a therefore we have \|a-3\| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? options: A)$1.08 B)$1.41 C)$1.74 D)$1.98 E)$2.16 SOLUTION:2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E. #### E QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 23 x = 6 Answer is E #### E QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe? options: A)15 B)60 C)75 D)90 E)105 SOLUTION:This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one. Teena covers 55 miles in 60 mins. Yoe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +15 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 15 miles in 60 mins So answer 30+60= 90 mins.D #### D QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 Ã— 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X. options: A)16.8% B)17.4% C)17.9% D)18.5% E)19.1% SOLUTION:Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20 Selling price of an orange = 10 --> Cost price = 10/1.25 = 8 A > O 23(A) + 10(O) = 653 653 - 23(A) has to be divisible by 10 --> Units digit has to be 0 Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value Between 11 and 21, If A = 11, O = 30 --> Not possible If A = 21, O = 17 --> Possible Cost price = 2021 + 817 = 420 + 136 = 556 Profit = 653 - 556 = 97 Profit% X= (97/556)100 = 17.4% Answer: B #### B QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 72 = 48 Answer: B #### B QUESTION:A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)1 B)4 C)9 D)11 E)13 SOLUTION:221 + 43 = 264/17 = 9 (Remainder) C #### C QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? options: A)12 years B)13 years C)15 years D)14 years E)18 years SOLUTION:Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) => 2x = 28 => x = 14 years. D #### D QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother. options: A)24 years B)25 years C)26 years D)27 years E)28 years SOLUTION:At the present, Sara's age is x. Sara's mother's age is y=6x. Next year, Sara's age will be x+1. Sara's mother's age will be y+1=5(x+1). From the two equations, we can calculate Sara's age: y=6x y+1=5 (x+1) 6x+1=5x+5 6x-5x=5-1 x=4 If Sara is currently 4 years old, and her mother is 6 times older, then her age is 6x=6×4=24. ANSWER: A #### A QUESTION:23,8,34,81,33,... options: A)24 B)25 C)26 D)27 E)28 SOLUTION:23 : 2^3=8 34 : 3^4=81 33 : 3^3=27 ANSWER:D #### D QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. options: A)19 B)20 C)21 D)22 E)23 SOLUTION:in case of cycle no of handshakes = no of persons hence ans = 20 ANSWER:B #### B QUESTION:On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is? options: A)22 B)99 C)27 D)11 E)37 SOLUTION:Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30. S.I for one year = Rs. 330. S.I. on Rs. 330 for 1 year = Rs. 36.30 Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D #### D QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x? I. 6/x II. -4/x III. 1/x options: A)I only B)II only C)I and II only D)I and III E)II and III SOLUTION:(x^2)(y^2) –2xy - 24 = 0 (xy – 6)(xy + 4) = 0 xy – 6 = 0 or xy + 4 = 0 xy = 6 or xy = -4 Since we need y in terms of x, we can isolate y in both of our equations. y = 6/x or y = -4/x Answer: C #### C QUESTION:If the cost price of 12 pens is equal to the selling price of 11 pens, the gain percent is: options: A)80% B)90% C)9% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 11 pens = Rs. 11; S.P. of 11 pens = Rs. 12. Gain % = 1/11 * 100 = 9% Answer:C #### C QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4? options: A)2:8 B)2:1 C)2:2 D)2:3` E)2:7 SOLUTION:Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5  Milk in 1 lit mixture in A = 8/13 lit  C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2  milk in 1 litre mixture in B – 5/7 lit  C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4  milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13  Required ratio = 2/91 : 1/13 = 2:7 Answer:E #### E QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D #### D QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)16 sec B)13 sec C)17 sec D)21 sec E)23 sec SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/20 = 6 m/sec. Relative speed = 12 + 6 = 18 m/sec. Required time = (120 + 120)/18 = 13 sec. Answer: B #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg? options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None SOLUTION:Required ratio = 750 : 250 = 3 : 1 Answer A #### A QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/99 B)33/91 C)36/91 D)33/97 E)33/33 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 33/91 Answer: B #### B QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.2 per box per month for the record storage, what is the total amount that the company pays each month for record storage? options: A)a. 150 B)b. 300 C)c. 600 D)d. 120 E)e. 200 SOLUTION:Volume Per Box: 15x12x10 = 1,800 Total Volume: 1,080,000 Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600 Price Per Month: Number of Boxes * Price Per Box = 600 * 0.2 = 120 Answer: D #### D QUESTION:Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three times. The probability that the colours, yellow, red and blue appear in the first, second and third tosses respectively is options: A)1/36 B)1/18 C)1/32 D)1/37 E)None of these SOLUTION:Probability of getting yellow color = P(Y) = 3/6 = 1/2 Probability of getting red color = P(R) = 2/6 = 1/3 Probability of getting blue color = P(B) = 2/6=1/3 So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 = 1/18 ANSWER:B #### B QUESTION:What is the minimum value of z for which z^2 + z - 3/14 > 0 is not true? options: A) -5/7 B) -3/7 C) -1/7 D) 1/7 E) 4/7 SOLUTION:I think B -3/7 is the best ans... #### B QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed? options: A)36 B)64 C)72 D)80 E)100 SOLUTION:you count up combinations twice. 498... and let me name 6 with students A,B,C,..,F after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same. I don't think that's the only mistake. 64 is a factor of = 2^24^2 144 is a factor of = 2^43^2. These are very different numbers and you cannot divide 144 with something to get to 64. #### B QUESTION:If x and y are non-zero integers, and 36x^4 – 4y^4 = 6x^2 + 2y^2, which of the following could be the value of x2 in terms of y? options: A)2y^2+1/6 B)2y^2+1/8 C)2y^2+1 D)2y^2 E)2y SOLUTION:36x^4 – 4y^4 = 6x^2 + 2y^2 (6x^2 + 2y^2) (6x^2 - 2y^2) = 6x^2 + 2y^2 6x^2 - 2y^2 = 1 6x^2 = 2y^2+1 x^2 = 2y^2+1/6 Answer : A #### A QUESTION:If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? options: A)20 % B)10 % C)15 % D)22 1/2% E)21% SOLUTION:Explanation: 9 = (140R)/100 R = 22 1/2 % ANSWER IS D #### D QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:Average of five numbers is 26. If one number is excluded the average becomes 28. The excluded number is options: A)10 B)12 C)16 D)20 E)18 SOLUTION:Explanation: Number is (526) - (428) = 130-112 = 18 Answer: Option E #### E QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1800 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 9x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700. Hence, (R - p) = (2700 - 900) = 1800 Answer : A #### A QUESTION:In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together? options: A)None of these B)48 C)32 D)64 E)57 SOLUTION:Explanation : The word 'JUDGE' has 5 letters. It has 2 vowels (UE) in it and these 2 vowels should always come together. Hence these 2 vowels can be grouped and considered as a single letter. That is, JDG(UE). Hence we can assume total letters as 4 and all these letters are different. Number of ways to arrange these letters = 4!= 4 x 3 x 2 x 1 = 24 In the 2 vowels (UE), all the vowels are different. Number of ways to arrange these vowels among themselves = 2! = 2 x 1 = 2 Total number of ways = 24 x 2 = 48. Answer : Option B #### B QUESTION:A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? options: A)4:7 B)4:0 C)4:3 D)4:1 E)4:2 SOLUTION:12:9 = 4:3 Answer: C #### C QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it? options: A)110 B)120 C)128 D)143 E)145 SOLUTION:First Purchased = 250 Wes= 128 C #### C QUESTION:A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? options: A)16 B)24 C)26 D)30 E)160 SOLUTION:One of the approaches: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20. But each of these 3 couples can send two persons (husband or wife): 222=2^3=8. Total # of ways: 6C32^3=160. Answer: E. #### E QUESTION:A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent? options: A)8 B)10 C)15 D)17 E)19 SOLUTION:30 25 = 750 425 ----------- 325 25 + 7.50 = 32.5 325/32.5 = 10 B #### B QUESTION:Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)14 E)16 SOLUTION:The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: D. #### D QUESTION:In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? options: A)34 days B)40 days C)46 days D)50 days E)None of these SOLUTION:Explanation: Less Cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) [Cows1 50 Bags 50 1]::50:x =>x∗50∗1=50∗1∗50 =>x=50 Option D #### D QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2879 C)2700 D)2797 E)2761 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer:A #### A QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(150âˆ’90)=4/5âˆ—60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150âˆ’138=12 ANSWER:D #### D QUESTION:A CAN FINISH A WORK IN 12 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK? options: A)4 B)5 1/2 C)6 D)8 E)NONE OF THESE SOLUTION:B'S 10 DAY'S WORK=(1/1510)=2/3 REMAINING WORK = (1-2/3)=1/3 NOW, 1/18 WORK IS DONE BY A IN 1 DAY 1/3 WORK IS DONE BY A IN (121/3)=4 DAYS. CORRECT OPTION:A #### A <<<Examples ends QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes? options: A)100000 B)85236 C)89562 D)90083 E)95842 SOLUTION:winners votes = 100-45 = 55% invalid votes = 83 polled votes = [(1009000)/(2*55-100)]+83 = 90083 Answer is D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)3 1/2 sec B)3 5/2 sec C)3 7/2 sec D)8 1/2 sec E)3 1/8 sec SOLUTION:D = 170 S = 72 * 5/18 = 20 mps T = 170/20 = 8 1/2 sec Answer: D #### D QUESTION:A rectangular block 15cm by 30cm by 75cm is cut into an exact number of equal cubes. Find the least possible number of cubes? options: A)6 B)40 C)15 D)10 E)22 SOLUTION:Volume of the block = 153075 = 33750 cm^3 Side of the largest cube = H.C.F of 15,30,75 = 15cm Volume of the cube = 151515 = 3375 cm^3 Number of cubes = 33750/3375 = 10 Answer is D #### D QUESTION:In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together? options: A)10!5! B)10!6! C)10! D)6!5! E)5!5! SOLUTION:The 10 letters can be grouped into 5 consonants and one set of 5 vowels. The number of ways to arrange 6 units is 6! Then, for each arrangement, the 5 vowels can be arranged in 5! ways. The total number of arrangements is 6!5! The answer is D. #### D QUESTION:How many factors of 60 are odd numbers greater than 1? options: A)3 B)4 C)5 D)3 E)7 SOLUTION:prime factors of 60 are 2^2,3^1,5^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,) = (1+1)(1+1)=4 since we need odd divisors other than 1 =>4-1 = 3 odd divisors D is the answer #### D QUESTION:Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(200) / 400 = 25% The answer is B. #### B QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:Three partners A, B, C in a business invested money such that 3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) then, The ratio of their capitals is options: A)63 : 45 : 34 B)6 : 3 : 2 C)36 : 54 : 28 D)63 : 45 : 35 E)None of these SOLUTION:Explanation: Let3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) = Rs.x Then, Aâ€™s capital = Rs x/3, Bâ€™s capital = Rs. x/6 and Câ€™s capital = Rs. x/9. A : B : C = x/3 : x/6 : x/9 6 : 3 : 2 Answer: Option B #### B QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 420=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -2.5 Prob =1/12 Answer - A #### A QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1996 has to be the ring finger Answer is (D) #### D QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?. options: A)540 m B)178 m C)936 m D)234 m E)713 m SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m. When B covers 960 m, C covers 936 m Option C #### C QUESTION:A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business? options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500 SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. 15000 x 3/10 = Rs. 4,500. B #### B QUESTION:If 75 percent of 600 is 50 percent of x, then x=? options: A)800 B)900 C)1000 D)1100 E)1200 SOLUTION:0.75 * 600 = 0.5 * x x = 7.5/5 * 600 = 900 #### B QUESTION:A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? options: A)23 Years B)21 Years C)20 Years D)25 Years E)22 Years SOLUTION:Let present age of the son =x=x years Then, present age the man =(x+24)=(x+24) years Given that, in 22 years, man's age will be twice the age of his son ⇒(x+24)+2=2(x+2)⇒x=22 ANSWER:E #### E QUESTION:The odds against ram solving the problem are 6 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try? options: A)1/4 B)5/21 C)16/21 D)23/28 E)13/18 SOLUTION:Odds against Ram are 6:3 so probability that he will solve the problem is 1/3. Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12 It will be solved means that either Ram or Krishna or both will be able to solve it. P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 7/12 - (1/3)(7/12) = 13/18 E #### E QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1â„2 C)17 D)Data inadequate E)None of these SOLUTION:12 M Ã— 18 = 12 W Ã— 18 Ã— 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 Ã— 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12Ã—18/12 2/3=17days Answer C #### C QUESTION:A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? options: A)4 sec B)6 sec C)7 sec D)3 sec E)2 sec SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 =6 sec. Answer:B #### B QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)Cannot be determined SOLUTION:It cannot be determined.As we do not know the actual value of K. however minimum value of k is sq.rt of 3^24^25^2 = 60 * any integer K=[lCM of 80 and 45] * (any integer) for value of k(60) * any integer unit value will be always zero . A #### A QUESTION:A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning? options: A)12 B)17 C)15 D)19 E)26 SOLUTION:Let the average after the 16th inning be P. So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19 Answer:D #### D QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes? options: A)6 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 11 - 1 = 10 rounds per hour. Time taken to complete one round at this speed = 1/10 hr = 6 min. A #### A QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000100/120000 = 40% Answer: option D #### D QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)2 B)1 C)7 D)6 E)4 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/10 + 10/140) = (1/14 + 1/14) = 1/7 5 women and 10 children will complete the work in 7 days. Answer:C #### C QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)3 B)5 C)6 D)4 E)9 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B #### B QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 83= 24 tubes A is the answer #### A QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? options: A)76 B)88 C)66 D)55 E)35 SOLUTION:Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 28/2 = 35 cm2 Answer:E #### E QUESTION:A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 30 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations? options: A) 2 hours, 225 miles B) 5.5 hours, 600 miles C) 4 hours, 450 miles D) 5 hours, 550 miles E) 6 hours, 650 miles SOLUTION:Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition. Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual. Equation 2 - x= 120 (t-.5) subtracted .25 hrs because it is early or took less time than usual. Now equating 12 we get 100(t+.5)=120(t-.5) => 10t +5 = 12t - 6 => 2t=11 => t= 5.5 hrs. Hence x= 100(5.5+.5) =>100 X 6 => 600 miles. Hence correct answer B #### B QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7? options: A)397 B)401 C)403 D)405 E)364 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=364. Answer: E. #### E QUESTION:What percent is 2 gm of 1 kg? options: A)0.5 % B)0.2% C)1.5% D)2% E)3% SOLUTION:1 kg = 1000 gm 2/1000 × 100 = 200/1000 =1/5 = 0.2 % B) #### B QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (1804R)/100 R = 5% Answer: A #### A QUESTION:Find the L.C.M of 2^2 * 3^3 * 5 7^211, 2^3 * 3^2* 5^2* 7^411, 2 3* 5^3* 7^411 options: A)2^3 3^3 * 5^3 * 7^4 * 11 B)2^23^35^3 * 7^4 * 11 C)2^23^35^2 * 7^4 * 11 D)2^33^35^2* 7^4 * 11 E)2^33^35^2* 7^3 * 11 SOLUTION:L.C.M= product of the highest powers of 2,3,5,7 and 11=2^3 * 3^3 * 5^3 * 7^4 * 11 Answer (A) #### A QUESTION:A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000100=15% of the remaining solution of 4,000 gallons. Answer: E. #### E QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these SOLUTION:Explanation: 80 : 5 = 105 : x x= (5×105/80) = Rs 6.56 Option A #### A QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20100/1000 = 2.0% Answer is A #### A QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.95 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.915 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33100 = 180% of 3.33. Answer: E. #### E QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x107)/(1002)) – ( (x125)/(1002)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (104% of x) / (108% of x) =104/108 =52/54 = 52:54. Answer: B #### B QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3 C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3 D. If BC = 6 , then we can have the following possibilities i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3 ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3 E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5 Thus answer is (D) #### D QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is options: A)66Â° B)18Â° C)24Â° D)60Â° E)None of these SOLUTION:In a clock, each minute makes 6Â° âˆ´ 11 minutes will make 6 Ã— 11 = 66Â° Answer A #### A QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:Evaluate 35 / .07 options: A)400 B)500 C)505 D)None of these E)506 SOLUTION:Explanation: 35/.07 = 3500/7 = 500 Option B #### B QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : options: A)8 B)9 C)4 D)18 E)None SOLUTION:Ratio of rates of working of A and B = 2 : 1 So, ratio of times taken = 1 : 2 B's 1 day's work = 1/12 Therefore A's 1 day's work = 1/6 (A + B)'s 1 day's work = (1/6 + 1/12)= 1/4 So, A and B together can finish the work in 4 days. Answer: C #### C QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/51400 = 280 560-280 = 280 Answer: E #### E QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? options: A)3. B)7. C)10. D)16. E)15. SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins Distance traveled by the bird traveling from West-Town = 4 4= 16 Answer: D #### D QUESTION:The points A(0, 0), B(0, 4a - 4) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)88 B)98 C)108 D)78 E)90 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-4=2a+6 2a=10 , a=5 Therefore, A(0,0); B(0,16); C(11,16) 1/21116=88 Answer: A #### A QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20. Answer: C. #### C QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color? options: A)a) 8 B)b) 23 C)c) 29 D)d) 32 E)e) 53 SOLUTION:Thats 29 in C. #### C QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:139 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 93+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? options: A)2015 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2014) = 2015 Ans: A #### A QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 Â· 70 and the sum of his first 5 scores is 5 Â· 75, so he received 5 Â· 75 âˆ’ 4 Â· 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:385, 462, 572, 396, 429, 671, 264 options: A)385 B)429 C)671 D)264 E)None of these SOLUTION:Solution In each number except 429,the middle digit is the sum of the other two. Answer B #### B QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)39.1 E)None SOLUTION:Sol. Therefore correct sum = ( 36 × 50 + 48 – 23) = 1825. Therefore correct mean = 1825 / 50 = 36.5. Answer C #### C QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=64=24 points 287=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 814=324 Total score to avg 87 in 6 tests = 876=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:9, 12, 11, 14, 13, ?, 15 options: A)16 B)12 C)14 D)17 E)20 SOLUTION:A 16 Alternatively, 3 is added and one is subtracted. #### A QUESTION:If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used? options: A)180 grams B)220 grams C)250 grams D)350 grams E)1400 grams SOLUTION:I too think 1400 grams should be the answer. My reasoning is The h20 content in 700 gms of water is 1 h20 content in 24% solution is 0.76 Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84 Let amount of solution be X Then the equation can be set up 7001 + 0.76X = 0.84 (X+700) 0.08X = 112 8X = 11200 X = 1400 (ANS E) #### E QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:A set consists of 12 numbers, all are even or multiple of 5. If 4 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 12 = 4 + 10 - {Both} + 0; {Both}=2(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: C. #### C QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm SOLUTION:r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 ANSWER:C #### C QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:1 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work? options: A)12/9 days B)15/4 days C)82/8 days D)22/76 days E)3/2 days SOLUTION:1M = 6W ---- 20 days 12M + 8W -----? 72W + 8 W = 80W ---? 6W ---- 20 80 -----? 6 * 20 = 80 * x => x = 3/2 days Answer:E #### E QUESTION:The price of a certain painting increased by 30% during the first year and decreased by 20% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price? options: A)102% B)105% C)120% D)135% E)104% SOLUTION:Easiest thing to do: Assume that price is 100 Price at the end of yr 1: 100+ 30 = 130 Price at the end of year 2 = 130 - 1300.20 = 1300.80 = 104 Hence required answer = (104/100)100% = 104% Answer is E. #### E QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4? options: A)288 B)173144 C)144 D)297 E)2181 SOLUTION:Explanation: If a number has to be divisible by 4, the last two digit of that number should be divisible by 4. So _ _ _ x y. Here xy should be a multiple of 4. There are two cases: Case 1: xy can be 04, 20 or 40 In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways. Case 2: xy can be 12, 24, 32, 52. In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72. Total ways = 144 Answer:C #### C QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k? options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0 SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A QUESTION:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X. options: A)16.8% B)17.4% C)17.9% D)18.5% E)19.1% SOLUTION:Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20 Selling price of an orange = 10 --> Cost price = 10/1.25 = 8 A > O 23(A) + 10(O) = 653 653 - 23(A) has to be divisible by 10 --> Units digit has to be 0 Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value Between 11 and 21, If A = 11, O = 30 --> Not possible If A = 21, O = 17 --> Possible Cost price = 2021 + 817 = 420 + 136 = 556 Profit = 653 - 556 = 97 Profit% X= (97/556)100 = 17.4% Answer: B #### B QUESTION:Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit? options: A)$8100 B)$8820 C)$8800 D)$8810 E)$8825 SOLUTION:Amount = 8000 x (1 + 5/100)^2) = 8000 x 21/20 x 21/20 =8820. Answer B)$8820 #### B QUESTION:In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ? options: A)30 B)45 C)42 D)72 E)75 SOLUTION:Let the number of benches in the class be x. Then, 6(x + 1) = 7x - 5 x = 11. Hence, number of students in the class = 6 ( x + 1) = 6 x 12 = 72. ANSWER:D #### D QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)8 B)6 C)4 D)5 E)9/2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1 When B starts: No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1 Solving the above two equations for xy x = 1/9 y = 1/9 → Total work done by AB in a day = 1/9 + 1/9 = 2/9 → No. of days to complete the work when both work together = 9/2; Answer: E #### E QUESTION:If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:1/6 = 0.1666666... (a repeating pattern one digit long) A #### A QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4, find P (E\|F) and P(F\|E)? options: A)1/4 B)1/7 C)3/7 D)4/9 E)5/11 SOLUTION:Here, E and F are events P(E\|F) = P(EnF)/P(F) = 0.4/0.4 = 1 P(F\|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4. A) #### A QUESTION:A grocer has a sale of Rs. 3435, Rs. 3920, Rs. 3855, Rs. 4230 and Rs. 3560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? options: A)500 B)1000 C)6000 D)7000 E)2000 SOLUTION:Total sale for 5 months = Rs. (3435 + 3920 + 3855 + 4230 + 3560) = Rs. 19000. Required sale = Rs. [ (3500 x 6) - 19000 ] = Rs. (21000 - 19000) = Rs. 2000 Answer: Option E #### E QUESTION:What is the greatest of 3 consecutive integers whose sum is 27 ? options: A)6 B)7 C)8 D)9 E)11 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 27; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E #### E QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9m = 150 m. ANSWER:D #### D QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)8837 C)2377 D)3772 E)3881 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer: A #### A QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is - options: A)1/5 B)1/3 C)1/4 D)118/2 E)21/4 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:Mary works in a restaurant a maximum of 60 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? options: A)300 B)420 C)560 D)320 E)400 SOLUTION:Mary receives $8(20)=$160 for the first 20 hours. For the 40 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(40)=$400. The total amount is $160+$400 = $560 Answer C 560. #### C QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.42^10=0.41024=409.6 The answer is C. #### C QUESTION:There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? options: A)21 B)25 C)16 D)22 E)20 SOLUTION:Two ball will be chosen. At least 1 blue ball Total ways = 8C2 = 28 Total without any blue ball = 4C2 = 6 Hence ways in which at least one blue will be present = 28 - 6 = 22 Correct option: D #### D QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 109876 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 109876 / 5! = 109876 5! / (5!5!) = 10! / (5!5!) Answer: Option B #### B QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls. options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7% SOLUTION:Let the cost price of 1 balls be Rs 1 Cost of 14 balls= Rs 14 Selling price of 14 balls = 9 Gain/loss = 14 - 9 = 5 %=5/14âˆ—100= 35.7 Answer: A #### A QUESTION:In a bag, there are two 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum? options: A)60 B)50 C)42 D)84 E)61 SOLUTION:As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited: 1) The minimum number on any given die is 1 2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each. With 4 dice, we could end up with any SUM between: 4 (if we rolled 1s on all 4 dice) to 64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice). Thus, there are only 61 possible sums. E #### E QUESTION:10 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ? options: A)4 hours a day B)5 hours a day C)6 hours a day D)7 hours a day E)8 hours a day SOLUTION:Explanation: More Men, Less Hours {Indirect Proportion} Less Days, More Hours {Indirect Proportion} [men 15 10 days 12 18] ::7:x =>xâˆ—15âˆ—12=10âˆ—18âˆ—7 =>x=10âˆ—18âˆ—7/ 15âˆ—12 =>x=7 Option D #### D QUESTION:1397 x 1397 = ? options: A)1951609 B)1951601 C)1951602 D)1951603 E)1951604 SOLUTION:1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer:A #### A QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage? options: A)116% B)166.66% C)60% D)100% E)150% SOLUTION:Explanation: Let the cost price of 1 litre pure milk be Re.1, then {6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only and 8 litre mixture ->SP -> 8 x 2 = Rs.16 Profit %= [16/6 -6]x100=100/6=166.66% ANSWER IS B #### B QUESTION:What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it? options: A)600 B)602 C)604 D)606 E)608 SOLUTION:The nth term is 2+3(n-1). The 201st term is 2 + 3(200) = 602 The answer is B. #### B QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,15 = 15/100 x= 8015/100 x= 12 12/10 = 1,2 = 120%, Answer C #### C QUESTION:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have? options: A)7 B)5 C)6 D)8 E)9 SOLUTION:take the example of 4... it has 3 positive divisors (1,2,4) Now, take the example of 64... it has only 7 divisors.. so A is the ans #### A QUESTION:There are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution. options: A)1 B)2 C)3 D)4 E)9 SOLUTION:145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A. #### A QUESTION:Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was? options: A)Rs. 692.80 B)Rs. 820 C)Rs. 990 D)Rs. 1385 E)None SOLUTION:Answer Income of the deceased = Total income of 4 members - total income of remaining 3 members. = 735 x 4 - 550 x 3 Rs. = 1290 Rs. Correct Option: E #### E QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 23 x = 6 Answer is E #### E QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together? options: A)120 B)110 C)105 D)140 E)135 SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8C6 + (8C5 * 2C1) this is 28 + 112=140 Answer : D #### D QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? options: A)30% B)40% C)50% D)60% E)65% SOLUTION:Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy C #### C QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle? options: A)13π B)26π C)262√π D)52π E)4π SOLUTION:The distance between the two points is sqrt(8) radius = sqrt(8)/2 Area= pi(sqrt(8)/2)^2 E.4π #### E QUESTION:A train of 30 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)6 B)3.3 C)4 D)9 E)2 SOLUTION:D = 30 60 + 1500 = 3300 m T = 3300/60 * 18/5 = 198 sec = 3.3 mins Answer:B #### B QUESTION:If ab-a-b=265 bc-b-c=155 ac-c-a=150 then find a? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:(A-1)(B-1)=AB-A-B+1=265+1=266..(1) (B-1)(C-1)=BC-B-C+1=155+1=156..(2) (C-1)(A-1)=CA-C-A+1=150+1=151..(3) (1)/(2) gives..(A-1)/(C-1)=266/156..(4) (3)(4) gives..(A-1)^2=257.47...A=17.04 Solving other equations..B=17.58 and C=10.4 ANSWER:B #### B QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)? options: A) 1 B) 21 C) 26 D) 52 E) 1014 SOLUTION:x = 14 + 16 + ... + 54 = (largest + smallest)/2 (# of terms) = (14 + 54)/221= 3421. GCD of 21 and 34*21 is 21 Answer: B. #### B QUESTION:In an examination a pupil's average marks were 63 per paper. If he had obtained 26 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination? options: A)8 B)9 C)10 D)14 E)12 SOLUTION:Let the number of papers be x. Then, 63x + 26 + 2 = 65x = 2x = 28 = x = 14. ANSWER:D #### D <<<Examples ends QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? options: A)4 B)5 C)56 D)12 E)7 SOLUTION:Explanation: Let the price be = Rs.100, and number of units sold = 100 Then, sale value = Rs.(100 × 100) = Rs.10000 New sale value = Rs.(140 × 80) = Rs.11200 Increase% = 1200/10000 × 100 = 12% Answer: D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.9 km C)3.4 km D)1.9 km E)5.6 km SOLUTION:Explanation: Speed in still water = 4 kmph Speed of the current = 1 kmph Speed downstream = (4+1) = 5 kmph Speed upstream = (4-1) = 3 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/5+x/3=1 â‡’3x+5x=15 â‡’8x=15 â‡’x=1.9 km Answer: Option D #### D QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)- 10% B)- 16 2/3 % C)- 52.38% D)- 25% E)- 183 1/3% SOLUTION:Assume 100 enrollments present in 1990 210 % of 1990 = enrollments on 1980 enrollments on 1980 = 210 % change = (enrollment in 1990 - enrollment in 1980)100/(enrollment in 1980) =(100 - 210) 100 / 210 = -11000 / 210 = - 52.38 % Ans - C #### C QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)27% B)25% C)21% D)85% E)24% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer:B #### B QUESTION:If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in: options: A)12 years B)18 years C)16 years D)14 years E)19 years SOLUTION:Explanation: The sum P becomes 3P in 4 years on compound interest 3P = P(1+R/100)4 â‡’ 3 = (1+R/100)4 Let the sum P becomes 81P in n years 81P = P(1+R/100)n â‡’ 81 = (1+R/100)n â‡’ (3)4 = (1+R/100)n â‡’ ((1+R/100)4)4 = (1+R/100)n â‡’ (1+R/100)16 = (1+R/100)n n=16 i.e, the sum will become 81 times in 16 years ANSWER IS C #### C QUESTION:Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are: options: A)7, 6 B)5, 1 C)6, 3 D)8, 7 E)None of these SOLUTION:Explanation : Let A and B be such sets, i.e., n (A) = m, n (B) = n So, n (P(A)) = 2m and n (P(B)) = 2n Thus n (P(A)) – n (P(B)) = 56, i.e. 2m – 2n = 56 ⇒ 2n (2m-n - 1) = 23 x 7 ⇒ n = 3 , 2m-n – 1 = 7 ⇒ m = 6 Answer : C #### C QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount. options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500 SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. B #### B QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: options: A)173 m B)200 m C)273 m D)300 m E)None of these SOLUTION:xplanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, <ACB = 30º and <ADB = 45º. AB/AC=tan30 Answer: C #### C QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =316250/20 =600 Answer : C #### C QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/251/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:A car covers a distance of 630 km in 6 hours. Find its speed? options: A)105 B)7778 C)266 D)288 E)121 SOLUTION:624/6 = 105 kmph Answer:A #### A QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop. The cost of the bomber is quite interesting. The Cost of 1st bomber is: 2 The Cost of 2nd bomber is: 4 The Cost of 3rd bomber is: 6 The Cost of 4th bomber is: 8 The Cost of 5th bomber is: 10 i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins. How many bombers can you buy using 1000 coins ? ? options: A)61 B)62 C)63 D)64 E)65 SOLUTION:Solution 62 The Cost of 1st bomber is: 2 i.e Total coins spend: 2 The Cost of 2nd bomber is: 4 i.e Total coins spend: 6 The Cost of 3rd bomber is: 6 i.e Total coins spend: 12 The Cost of 4th bomber is: 8 i.e Total coins spend: 20 The Cost of 5th bomber is: 10 i.e Total coins spend: 30 The Cost of 6th bomber is: 12 i.e Total coins spend: 42 The Cost of 7th bomber is: 14 i.e Total coins spend: 56 The Cost of 8th bomber is: 16 i.e Total coins spend: 72 The Cost of 9th bomber is: 18 i.e Total coins spend: 90 The Cost of 10th bomber is: 20 i.e Total coins spend: 110 The Cost of 11th bomber is: 22 i.e Total coins spend: 132 The Cost of 12th bomber is: 24 i.e Total coins spend: 156 The Cost of 13th bomber is: 26 i.e Total coins spend: 182 The Cost of 14th bomber is: 28 i.e Total coins spend: 210 The Cost of 15th bomber is: 30 i.e Total coins spend: 240 The Cost of 16th bomber is: 32 i.e Total coins spend: 272 The Cost of 17th bomber is: 34 i.e Total coins spend: 306 The Cost of 18th bomber is: 36 i.e Total coins spend: 342 The Cost of 19th bomber is: 38 i.e Total coins spend: 380 The Cost of 20th bomber is: 40 i.e Total coins spend: 420 The Cost of 21st bomber is: 42 i.e Total coins spend: 462 The Cost of 22nd bomber is: 44 i.e Total coins spend: 506 The Cost of 23rd bomber is: 46 i.e Total coins spend: 552 The Cost of 24th bomber is: 48 i.e Total coins spend: 600 The Cost of 25th bomber is: 50 i.e Total coins spend: 650 The Cost of 26th bomber is: 52 i.e Total coins spend: 702 The Cost of 27th bomber is: 54 i.e Total coins spend: 756 The Cost of 28th bomber is: 56 i.e Total coins spend: 812 The Cost of 29th bomber is: 58 i.e Total coins spend: 870 The Cost of 30th bomber is: 60 i.e Total coins spend: 930 The Cost of 31st bomber is: 62 i.e Total coins spend: 992 Answer B #### B QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 91 min C)6 hrs 01 min D)6 hrs 23 min E)3 hrs 21 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed? options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:Work done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the Printer were operating. Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm B #### B QUESTION:Half of 2 percent written as decimal is options: A)5 B)0.01 C)0.05 D)0.005 E)None of these SOLUTION:Explanation: It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01 Answer: Option B #### B QUESTION:A customer pays 40 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)50 B)40 C)70 D)60 E)20 SOLUTION:Let x be the original price. x - 20 = 40 x - 20 + 20 = 40 + 20 x + 0 = 60 x = 60 Answer is D #### D QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:Rs.6160 were divided among B, C & D in such a way that B had Rs.320 more than C and D had Rs 240 more than B . How much was Câ€™s share? options: A)Rs.2300 B)Rs.2310 C)Rs.2320 D)Rs.2330 E)Rs.2340 SOLUTION:Let C gets Rs x. Then We can say B gets Rs (x + 320 ) and D gets Rs ( x + 280) . x + 320 + x + x + 560 = 6160 3x = 5280 x = 1760 . Câ€™s share = Rs ( 1760+560 ) = Rs.2320 C #### C QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value? options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)55 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 100/((x+5)×5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55 Speed of the train is 55 kmph. Answer: Option C #### C QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48 SOLUTION:First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4) So now as above we have three events A,BC. 1st method(This is lengthy method) Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1.ABC= 1/25/63/4 OR 2.ABC= 1/21/63/4 OR 3.ABC= 1/25/61/4 OR 4.ABC= 1/21/63/4 OR 5.ABC= 1/25/61/4 OR 6.ABC= 1/25/61/4 OR 7.ABC= 1/21/61/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 Answer : B #### B QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over? options: A)60 B)70 C)B=75 D)B=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 10010=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options? Your approach: total 10 options, 5c3. Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together. This gives us 10-3-3=4 as the answer. Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE. D #### D QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is options: A)100 B)250 C)260 D)416 E)None of these SOLUTION:Explanation: Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 × 32 = 416. Answer: D #### D QUESTION:If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D? options: A)55 B)61 C)69 D)90 E)97 SOLUTION:c + d = 11 5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15 D=15 c+d=9=C+15=9=C=9-15=-6 C=-6 5C + 8D=5(-6)+8(15)=-30+120=90 Hence, D is the right answer. #### D QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 2006 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 12=45,0008 1:1 Madhu's share=1/260,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:A girl has exactly 5 quarters, 9 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%. P(not drawing a quarter with 2 coins) = 19/24 18/23 = 57/92 > 50% P(not drawing a quarter with 3 coins) = 57/92 * 17/22 = 969/2024 < 50% The answer is B. #### B QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? options: A)7⁄19 B)2⁄3 C)3⁄4 D)9⁄21 E)None of these SOLUTION:If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways. ∴ Reqd probability = 7⁄21 = 1⁄3 Answer E #### E QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students. options: A)1200 B)120 C)360 D)168 E)None of these SOLUTION:Explanation : Let the original no. of students be x. According to situation, 46x + 12032 = (x + 120)36 ⇒ x = 48 So, Required no. of students after joining the new students = x + 120 = 168. Answer : D #### D QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25Ã—26/2=325 Correct Option: B #### B QUESTION:Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each? options: A)20 B)27 C)18 D)23 E)30 SOLUTION:A1P1=A2P2 1815=A210 => A2=27 Answer:B #### B QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1. What is the dividend? options: A)48 B)49 C)96 D)97 E)72 SOLUTION:D = d Q + R D = 12 * 4 + 1 D = 48 + 1 D = 49 Answer: B #### B QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:60% is 20%-points above 40% and 20%-points below 80%. Thus the ratio of "the first 30 games" to "remaining games" is 1:1. So the team played a total of 30+30 = 60 games. The answer is B. #### B QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A? options: A)2 B)3 C)5 D)6 E)8 SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize. 14n/60 If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have (27n)/(2^235) Simplifying 7n/(235) The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7. The number could be 235, or 2352, or 235..... However to be less than 200 we can not add any prime number. 235 = 120 If we added the next prime factor 7, we would have A=2357 = 840 Thus, answer B #### B QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:219C2 = 2171 = 342 The answer is B. #### B QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4100 So, % increase is 21% Answer will be (E) #### E QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6d B) 7/3d C) 10/3d D) 7/2d E) 9/2d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit. options: A)487 B)15 C)76 D)29 E)12 SOLUTION:If x is speed limit, Speed of first person = x + 10 Speed of 2nd person = x + 20 But speed of 2nd person = 35 kmph x + 20 = 35 x = 15 kmph. so speed limit is 15 kmph option D Answer: B #### B QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B? options: A)100 B)120 C)140 D)160 E)180 SOLUTION:After two hours, Train A is ahead by 60 miles. Train B can catch up at a rate of 15 miles per hour. The time to catch up is 60/15 = 4 hours. In 4 hours, train A travels another 304 = 120 miles for a total of 180 miles. The answer is E. #### E QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$788 B)$812 C)$864 D)$878 E)$912 SOLUTION:After one year: 1.2 $500 After two years: (1.2)^2 * $500 After three years: (1.2)^3 * $500 = $864 The answer is C. #### C QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends? options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65 SOLUTION:Praveen spent and gave to his two friends a total of 12.25 + 2x= $4.65, x is the amount spent to one friend. Money left 50.50 -2x = $31.85. Then 2x=$18.65. correct answer is B) $ 18.65 #### B QUESTION:The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers : options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer: B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was? options: A)18years B)19years C)20years D)21years E)22years SOLUTION:Let the son's present age be x years. Then, (50 - x) = x 2x = 50. x = 25. Son's age 5 years back (25 - 5) = 20 years. C) #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)288 B)165 C)881 D)1277 E)121 SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 25 = 375 m. Let the length of the platform be x m . Then, (x + 375)/36 = 15 => x = 165 m. Answer: B #### B QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 185x+152x=180 x=180/215 x=0.837209 time taken for type A problem=1520.837209=25.11628min ANSWER:B #### B QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? options: A)30days B)35days C)40days D)44days E)45days SOLUTION:Explanation: (A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5 A complete remaining work in 2/550 = 20 Total work = 10+20= 30days Answer: Option A #### A QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:B and C started a business investing Rs. 72,000 and Rs. 45,000 respectively. In what ratio the profit earned after 7 years be divided between B and C respectively? options: A)7:5 B)5:8 C)5:7 D)8:5 E)None of these SOLUTION:B:C = 72000 : 45000 = 8:5. ANSWER:D #### D QUESTION:Which is greater than 16 options: A)1.6 B)66 C)6 D)-6 E)6.1 SOLUTION:66 greater than 16. Answer: B #### B QUESTION:A reduction of 30% in the price of apples would enable a man to obtain 54 more for Rs.30, what is reduced price per dozen? options: A)1 B)2 C)6 D)7 E)10 SOLUTION:B 30(30/100) = 9 --- 54 ? --- 12 => Rs.2 #### B QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 Ã— 9 Ã— 9 Ã— 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint? options: A)10 B)20 C)28 D)14 E)19 SOLUTION:number of statues=all the paint÷amount used per statue =7/8 ÷ 1/16 =7/816/1 =112/8 =14. Answer is D. #### D QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? options: A)62% B)69.45% C)70% D)71% E)72% SOLUTION:Required percentage = [ (288 + 98 + 3.00 + 23.4 + 83) x 100 ] % (420 + 142 + 3.96 + 49.4 + 98) = [ 495.4 x 100 ] % 713.36 ~= 69.45%. B) #### B QUESTION:A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is? options: A)90 B)45 C)110 D)40 E)50 SOLUTION:Explanation: milk:water = 6:3 6x : 3x + 10 = 6 : 5 5[6x] = 6[3x + 10] 30x = 18x + 60 30x - 18x = 60 12x = 60 x = 5 The quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9x = 45 Short cut method - 2 : for Only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio -------> 10 liters 9part of ratio -------> 45 liters Answer: Option B #### B QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 16 = 960 km ANSWER A #### A QUESTION:Pipe A that can fill a tank in an hour and pipe B that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe B is shut 10 minutes before the tank overflows. When will the tank overflow? options: A)37 mins B)35 mins C)40 mins D)32 mins E)36 mins SOLUTION:The last 10 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 10 minutes it fills 1/5th of the tank, thus 5/6 of the tank is filled with both pipes open. The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 5/6th of the tank they need (time) = (work)/(rate) = (5/6)/3 = 5/18 hours = 27 minutes. Total time = 10+ 27= 37 minutes. Answer: A. #### A QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)891 E)1,001 SOLUTION:James = (0.5/100)2000 = 10 Votes to win = (45/100)Total Votes +1 = (45/100)2000 +1 = 901 Remaining Voted needed to win election = 901 - 10 = 891 Answer: option D #### D QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(490+x)/5=92 x=(592)-(490) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream? options: A)19 B)88 C)14 D)12 E)17 SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 57/3 = 19 kmph. Answer:A #### A QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:During the months May through October, Teddy the bear triples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976? options: A)9m−1300 B)9m−300 C)4m−1200 D)3m−300 E)m−1300 SOLUTION:Nov ' 73 = m April ' 74 = m - 100 Oct ' 74 = 3m - 300 April' 75 = 3m - 400 Oct' 75 = 9m - 1200 April'76 = 9m - 1300 Hence answer will be (A) 9m - 1300 #### A QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 7:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/84=1/2, as it quadruples every hour then container was one-eighth full at 7:00 a.m -1 hour = 6:00 a.m. Answer: C. #### C QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:A sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:w:x:y = 100:30:20 20:6:4 20 --- 10 30 --- ? => 15 Answer:D #### D QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:A 160 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train? options: A)48 kmph B)54 kmph C)92 kmph D)86 kmph E)76 kmph SOLUTION:S = 160/12 18/5 = 48 kmph ANSWER:A #### A QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is- options: A)42 B)32 C)48 D)28 E)38 SOLUTION:X/63 = 24. X = 24 63. So correct answer would be, (24 63) /36 = 42. ANSWER : A #### A QUESTION:A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)7 km D)5 km E)2 km SOLUTION:Let the total distance be 3x km. Then, x/8 + x/9 + x/10 = 47/60 x/3 = 47/60 => x = 2.33. Total distance = 3 * 2.33 = 6.99 km. Answer:C #### C QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:How many integers between 4000 and 5000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 445_ --> 4 446_ --> 3 447_ --> 2 448_ --> 1 456_ --> 3 457_ --> 2 458_ --> 1 467_ --> 2 468_ --> 1 478_ --> 1 Number of integers =20 D #### D QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages. options: A)20,35,45 B)8,20,28 C)16,28,36 D)16,28,46 E)None of these SOLUTION:Let the present ages of three persons be 4K,7K and 9K respectively. (4K - 8) + (7K - 8) + (9K - 8) = 76 20K = 100 K = 5 Therefore, then present ages are 20,35,45. ANSWER:A #### A QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)50 B)88 C)77 D)66 E)55 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in: options: A)14 hrs B)15 hrs C)10 hrs D)8 hrs E)9 hrs SOLUTION:work done by leak in 1 hr = (1/2-3/7)=1/4 =>14 hrs ANSWER A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =âˆšb : âˆša = âˆš25 : âˆš36 = 5 : 6 Answer D #### D QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k? options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0 SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A QUESTION:9, 35, 91, 189, 341, ? options: A)502 B)521 C)559 D)611 E)712 SOLUTION:Explanation : 13 + 23 = 9 23 + 33 = 35 33 + 43 = 91 43 + 53 = 189 53 + 63 = 341 63 + 73 = 559 Answer : Option C #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y? options: A)2 B)1 C)0 D)5 E)6 SOLUTION:Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x can not equal 0 D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer. Answer A #### A QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:2512: 3012: 358 15:18:14 14/47 47000 = 14000 ANSWER:D #### D QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges? options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2 SOLUTION:The cost of one orange=5/12=0.416 The cost of ten oranges= 0.416x10= $ 4.16 Answer: B #### B QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 7) years. (x+7+10)=2(x—10) hence x=37. Present age of B = 37 years Answer: Option B #### B QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37 options: A)13 B)18 C)40 D)37 E)25 SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong. Answer : D #### D QUESTION:How much is 90% of 40 is greater than 4/5 of 25? options: A)29 B)776 C)66 D)16 E)99 SOLUTION:(90/100) * 40 – (4/5) * 25 36 - 20 = 16 Answer: D #### D QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers options: A)9 B)10 C)15 D)18 E)17 SOLUTION:The only possible sum for 4 different squares of an integer with total sum number is 95 are : 49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17) or 81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15) hence the answer is (E) #### E QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 79 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/38 B)8/32 C)8/35 D)8/31 E)6/38 SOLUTION:Explanation: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)P(B) = 2/5 4/7 = 8/35 ANSWER: C #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:In a throw of dice what is the probability of getting number greater than 5 options: A)1/7 B)1/6 C)1/11 D)1/13 E)2/9 SOLUTION:Number greater than 5 is 6, so only 1 number Total cases of dice = [1,2,3,4,5,6] So probability = 1/6 B) #### B QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? options: A)525 B)665 C)412 D)235 E)856 SOLUTION:Answer: Option B 8 * 84 = 672 â€“ 7 = 665 #### B QUESTION:Which of the below fractions has the highest value? options: A)A)23/77 B)B)23/78 C)C)23/84 D)D)23/87 E)E)23/40 SOLUTION:23/40. Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator. Answer (E). #### E QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers? options: A)200 B)150 C)160 D)170 E)180 SOLUTION:L.C.M of two numbers is given by (Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200. ANSWER:A #### A QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A QUESTION:161?85?65?89=100 then use + or - in place of ? and take + as m,- as n then find value of m-n options: A)3 B)-1 C)1 D)-3 E)2 SOLUTION:161-85-65+89=100 so m=1, n=2 => (m-n)=-1 ANSWER:B #### B QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways SOLUTION:The boy can select one trouser in thirteen ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 13 * 15 = 195 ways. Answer:D #### D QUESTION:[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to options: A)7 / 30 B)11 / 30 C)13 / 30 D)17 / 30 E)None SOLUTION:Answer Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30 Correct Option: A #### A <<<Examples ends QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 10'o clock. options: A)60sec B)62sec C)66sec D)64sec E)54sec SOLUTION:At 6'0 clock, clock ticks 6 times. So, there must be 5 intervals between clock ticks. Time Between first and last ticks = 30sec So, 1 interval = 30/5 = 6sec So 6'o clock 5 6=30sec 7'o clock 6 6=36sec . . 9'o clock 8 6=48sec 10'o clock 9 6=54sec So, 54sec at 10'o clock. ANSWER:E #### E QUESTION:A boat having a length 7 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: options: A)100 kg B)120 kg C)89 Kg D)80 Kg E)210 Kg SOLUTION:Volume of water displaced = (7 x 3 x 0.01) m3 = 0.21 m3. Mass of man = Volume of water displaced x Density of water = (0.21 x 1000) kg = 210 kg. Answer: E #### E QUESTION:In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways SOLUTION:6 people can be prized with distinct prizes in 6^6 ways ANSWER:A #### A QUESTION:In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is? options: A)35yrs B)40yrs C)50yrs D)60yrs E)70yrs SOLUTION:Let B's present age = x years Then A's present age = x+10 years x+10+20 = 2(x-20) x + 30 = 2x - 40 x = 70years Answer is E #### E QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17 SOLUTION:Explanation : Let two digit number that Shiwani thought be 'xy', where x and y are single digit number. Therefore, 10x+y=p(x+y)+3, where p is a natural number p=10x+y−3x+y. Also, y+x>3. Possible values of x and y for which p is a natural number are :- (x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9), (x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null), (x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4) There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits. Probability that Devesh thought of the same number as Shiwani = 1/14 Answer : B #### B QUESTION:The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least? options: A)18 hours B)22 hours C)25 hours D)26 hours E)20 hours SOLUTION:Let the persons be A, B, C. Hours worked: A = 290/9 = 20 hours B = 390/9 = 30 hours C = 490/9 = 40 hours C is the hardest worker and A worked for the least number of hours. So the difference is 40-20 = 20 hours. Answer : E #### E QUESTION:A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? options: A)77 days B)21 days C)88 days D)55 days E)44 days SOLUTION:WC = 1:2 2x + x = 1/14 => x = 1/42 2x = 1/21 => 21 days Answer: B #### B QUESTION:The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square? options: A)277 B)268 C)287 D)480 E)281 SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D #### D QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:In an election between two political leaders 10% of the voters did not cast their vote. 10% of the votes polled were found invalid. The successful political leader got 54% of the valid, votes and won by a majority of 3240 votes. The number of voters enrolled on the voters list was : options: A)30000 B)50000 C)33000 D)40000 E)45000 SOLUTION:Explanation : Solution: Let the number of voters be x. then, votes polled = 90% of x. Valid votes = 90% of(90% of x) .'. 54% of[90% of(90% of x)] - 46% of[90% of(90% of x)] = 3240. 8% of[90% of(90% of x)] = 3240. 8/100 90/100 * 90/100 * x = 3240 x = (3240100100100)/(89090) = 50000 Answer : B #### B QUESTION:The number of positive integer solutions for the equation x +y +z + t = 18 is options: A)640 B)780 C)380 D)540 E)680 SOLUTION:The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k (k-1)C(n-1)- where k is the number and n is number of variable in the equation. 18-1 C 4-1 = 17C3 = 680 Answer : E #### E QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^327 + 26^5. Answer: D. #### D QUESTION:(1/5)^q * (1/4)^18 = 1/(2(10)^35). What is q? options: A)17 B)18 C)34 D)35 E)36 SOLUTION:We need to arrive at a common base. --> (5)^(-q) * 2^(-36) = 2^(-36)5^(-35) 5^(-q)=5^(-35) -q=-35 q=35=D #### D QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)88.6 C)81.1 D)81.5 E)81.2 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector? options: A)1/120 B)1/100 C)1/80 D)1/60 E)1/40 SOLUTION:The largest angle is 87. Let d be the difference between any two angles in the progression. The sum of all the angles will be: 87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d The sum of all the central angles in a circle = 360 696 - 28d = 360 d = 336/28 = 12 The smallest sector is (87-7d) = 87-712 = 3 3/360 = 1/120 The answer is A. #### A QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)100=10% Answer:A #### A QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr SOLUTION:still in water=1/2(98+10)km/hr =54km/hr correct option is :B #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:If x is a positive integer, which of the following must be odd? options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3 SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD] C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD Hence C. #### C QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 45678=6720. ANS:A #### A QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is options: A)not an even B)an even C)a perfect square D)an odd E)a prime SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1 y = x^2 - x - 2 y = (x-2)(x+1) (Note that one factor is even and one factor is odd.) Then y must be even. The answer is B. #### B QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300 SOLUTION:Let the cost of one toy = X. Then, cost of 18 toys = 18X. Gain = 3X. SP of 18 toys = Rs. 27300. Gain = SP â€“ CP 3X = 27300 â€“ 18X 21X = 27300 X = Rs. 1300. ANSWER : OPTION E #### E QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)12 B)15 C)20 D)24 E)30 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 60 / (60+x) = 4/5 x = 15 The answer is B. #### B QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600 SOLUTION:let investment is x... den remaining investment is (9800-x) x9/75= (9800-x)10/80 x=4800 9800-x=5000 ANSWER:B #### B QUESTION:Evaluate 28% of 550 + 45% of 280 options: A)232 B)242 C)252 D)262 E)280 SOLUTION:Explanation: = (28/100) 550 + (45/100) * 280 = 154 + 126 = 280 Answer: Option E #### E QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago? options: A)2 B)4 C)6 D)8 E)16 SOLUTION:j= 3s after 6 years j +6 = 2(s+6) j= 2s+6 2s +6 = 3s s= 6 four years ago s= 6-4= 2 A is the answer #### A QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed Ã— time =9Ã—4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:A city with a population of 173,460 is to be divided into 9 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)17,400 B)17,500 C)17,600 D)17,700 E)17,800 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 173,460 = p + 8(1.1)p 9.8p=173,460 p = 17,700 The answer is D. #### D QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel? options: A)400 B)450 C)500 D)550 E)600 SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour. The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours. The answer is A. #### A QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 1000.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit? options: A)750 B)800 C)850 D)860 E)890 SOLUTION:Let ‘x’ be the CP of the article; Then 900 – x = 2(x – 450); :. x= 600. 25% of 600 = 150 :. New SP = 600 + 150 = 750 Option 'A' #### A QUESTION:If logx y = 10 and log2 x = 1000, what is the value of y? options: A)210002 B)277889 C)210000 D)27788 E)788291 SOLUTION:Explanation: log2 x = 1000 => x = 21000 logx y = 10 => y = x10 = (21000)10 = 2(1000 × 10) = 210000 Answer: Option C #### C QUESTION:In a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal? options: A)41 B)30 C)35 D)33 E)36 SOLUTION:D 33 There is a meal for 200 children. 140 children have taken the meal. Remaining meal is to be catered to 60 children. Now, 200 children 110 men. 60 children = (110/200)x 60= 33 men. #### D QUESTION:Jimmy has 20% more cookies than Janice. What percentage of cookies should Jimmy give to Janice so that both Jimmy and Janice have the same number of cookies? options: A)7.5% B)7.7% C)7.9% D)8.1% E)8.3% SOLUTION:An easy way to solve this question is by number plugging. Assume Janice has 100 cookies then Jimmy has 120 cookies. Now, for both Jimmy and Janice to have equal amounts of cookies we should give Janice 10 of Jimmy's cookies, which is 10/120=~8.3% of Jimmy's cookies. Answer: E. #### E QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 23x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 44000 = 16,000 Answer (E) #### E QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 * 672 = 256 Answer: A #### A QUESTION:Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)s.225 B)s.288 C)s.485 D)s.279 E)s.282 SOLUTION:Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5 SP = CP[(100 + profit%)/100] = 232.5 * [(100 + 20)/100] = Rs.279. Answer:D #### D QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay? options: A)m/(5d) B)20d C)5d D)5dm E)20d/m SOLUTION:Total income of Sara in a month = d5m dollars. = d5m = 5dm Answer is D #### D QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages? options: A)25 years B)28 years C)32 years D)26 years E)28 years SOLUTION:let rhea age be x rick age be y given x-8=1/2(y-8)......a also given x/y=(3/4) =>x=3/4(y).......b by solving a and b we get y=16 x=12 then x+y=12+16=28 ANSWER:B #### B QUESTION:If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4? options: A)1/4 B)3/8 C)1/2 D)5/8 E)3/4 SOLUTION:I get 5/8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers E O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8 O E O / 4 = Not Integer We cannot forget multiples of 8 from 1 to 96 We have 24 numbers that are multiple of 4 Therefore, 48/96 + 24/96 = 72/96 = 3/4 answer : E #### E QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:Find the smallest four-digit number which is a multiple of 112. options: A)896 B)1008 C)1120 D)1024 E)None of these SOLUTION:The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104. 112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112. ANSWER:B #### B QUESTION:There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work? options: A)5 1⁄2 days B)5 1⁄3 days C)5 1⁄6 days D)6 1⁄6 days E)7 1⁄6 days SOLUTION:Work completed in 1st day = 1/16 Work completed in 2nd day = (1/16) + (1/16) = 2/16 Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16 … An easy way to attack such problems is from the choices. You can see the choices are very close to each other. So just see one by one. For instance, The first choice given in 3 1⁄4 The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16 The work done in 4 days = (1+2+3+4)/16 = 10/16 The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it? The work done in 6 days = (1+2+3+4+5+6)/16 > 1 Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days. (Just for your reference, work done in 5 days = 15/16. Pending work in 6th day = 1 – 15/16 = 1/16. In 6th day, 6 people are working and work done = 6/16. To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days. Hence total time required = 5 + 1/6 = 5 1⁄6 days C #### C QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days SOLUTION:A 6.4 days 1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300 So, all three together will complete the work in 300/47 = 6.4 days.- #### A QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be. options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=ST=485/6=40km time=45/60hr=3/4hr New speed = 40* 4/3 kmph= 53kmph Answer : B #### B QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1200 B)1256 C)1349 D)1456 E)1590 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C? options: A)127 B)150 C)177 D)167 E)122 SOLUTION:A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer:B #### B QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)30/13 hours E)60/29 hours SOLUTION:Speed downstream = 20 + 9 = 29 kmph. Time required to cover 60 km downstream = d/s = 60/29 = 60/29 hours. Answer: E #### E QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n? options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2 SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2. In an AP, Last term = First term + (n-1)common difference w = First term + (n-1)2 First term = w - 2(n-1) ANSWER:C #### C QUESTION:a goes to place x and b goes to place y. after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y? options: A)900km B)540km C)720km D)820km E)920km SOLUTION:let speed of A be-------Sa let speed of B be--------Sb let the distance covered by B while going to position XY be-----------x so distance covered by A in same time while going to XY is----------180 +x(it's given in the question) so total distance b/w X and Y is=x+(x+180) while going to position XY :- time taken by A = time taken by B (x+180)/Sa= x/Sb Sa/Sb=(x+180)/x---------------------1 After lunch:- A.C.T(according to question) Sa=x/2 Sb=(x+180)/4.5 dividing Sa/Sb=(x4.5) / ((x+180)2)--------------------2 equating equations 1 and 2 9/4 = (x+180)^2 / x^2 now taking square root on both sides we get 3/2 = (x+180) / x x=360 therefore distance between x and y =x+(x+180)=900km ANSWER:A #### A QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)(1/5) So it takes 25 men to complete this job = 25 * (1/25) = 1 Answer: C #### C QUESTION:In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)170 C)C)190 D)D)210 E)E)1663200 SOLUTION:11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200 Option 'E' #### E QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:What will come in place of the x in the following Number series? 75, 225, x, 2025, 6075 options: A)675 B)752 C)300 D)400 E)1200 SOLUTION:(A) 25 x 3 = 75, 75 x 3 = 225 , 225 x 3 = 675, 1675 x 4 = 2025. #### A QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? options: A)1/5 B)2/7 C)2/9 D)3/10 E)4/11 SOLUTION:The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9. The answer is C. #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases Answer: option C #### C QUESTION:One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? options: A)120 % B)140 % C)162/3 % D)20 % E)None SOLUTION:Sol. CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain. Answer D #### D QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400? options: A)8100 B)3388 C)7767 D)2009 E)22888 SOLUTION:6400* 9/8 * 9/8 = 8100 Answer: A #### A QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour? options: A)6 metre B)12 metre C)120 metre D)1200 metre E)2200 metre SOLUTION:Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600 :. Distance moves = (600 20) cms = 12000 cms In metres = 120 metre Answer: C #### C QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:What is 30% of 210? options: A)61 B)63 C)65 D)67 E)69 SOLUTION:X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 #### B QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L? options: A)6 B)-1 C)-2 D)-6 E)-10 SOLUTION:We need to find out the value of p and L to get to the slope. Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving 5 = -p2 +9 p2 = 4 p = + or - 2 simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7. -7 = -t2+9 t = +or - 4 considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1 IMO option B is correct answer. #### B QUESTION:If n = 3^6 – 2^6 which of the following is NOT a factor of n? options: A)97 B)7 C)35 D)5 E)19 SOLUTION:3^6 - 2^6 = (3^3)^2 - (2^3)^2 =(3^3 + 2^3)(3^3 - 2^3) =(27+8)(27-8) =3519 =7519 Therefore, 97 is Not a factor of n. A #### A QUESTION:(8^16)+(16^10)+(4^24) = ? options: A)(4)(2^29+1) B)(6)(2^48) C)(9)(2^49) D)(28)(2^53) E)2^148 SOLUTION:I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ) So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents. Here's how my brain works with this one, Step 1: Recognize a common base. (8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48) Step 2: Recognize the factor and pull out of the equation. = (2^48)(1 + (2^4) + 1) = (2^48)(1 + 16 + 1) = (2^48)(18) Step 3: Recognize this is not an answer and adapt. (2^48)(18) = (2^48)(2)(9) = 2^148 Answer is E. #### E QUESTION:What is the probability of flipping a fair coin five times and the coin landing on heads on at least two flips? options: A)5/8 B)7/8 C)11/16 D)13/16 E)27/32 SOLUTION:The number of possible outcomes is 2^5=32. 0 heads: There is 1 way to have all tails. 1 head: There are 5 ways to have one head. P(0 or 1 head)=6/32=3/16 P(at least 2 heads)=1 - 3/16 = 13/16 The answer is D. #### D QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true? (i) x is prime (ii) y is even (iii) xy is positive options: A)ii only B)iii only C)i and iii only D)ii and iii only E)i, ii and iii SOLUTION:Effectively y = 36x/41 (i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime. (ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN. (iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:B #### B QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the R odds that x^2+y^2>1? options: A)1. pi/4 B)2. R=pi/16 C)3. R=1-pi/4 D)4. 1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 5 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 8 a.m. Answer: C #### C QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x â€“ 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have? options: A)5 B)10 C)30 D)40 E)50 SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)100% = 60% Now by Alligation Rule: A . ......... B 20% . . . 80% . . 60% . . (80-60) . (60-20) =20 : =40 Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration) So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%) So as per above ration Qty B mixed will be 50 gallons. Qty of water in mixture B = 20% of 50 = 10 gallons. ANSWER:B #### B QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ? options: A)160 B)180 C)200 D)220 E)None SOLUTION:Answer Let the number be N. Then, (N/5) + 4 = (N/4) - 4 â‡’ (N/4) - (N/5) = 8 â‡’ (5N - 4N)/20 = 8 âˆ´ N = 160 Option: A #### A QUESTION:A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square? options: A)148/29 B)168/29 C)168/26 D)158/29 E)198/29 SOLUTION:By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle. Then s = ½(10 + 17 + 21) = 24, and A = 84. A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21. Now drop a perpendicular of length h onto the side of length 21. We also have A = ½ × base × perpendicular height. Hence A = 21h/2 = 84, from which h = 8. Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.) Let the square have side of length d. Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1. Therefore the length of the side of the square is 168/29. ANSWER:B #### B QUESTION:If SAGE is coded as 4657 and COT is coded as 333. How is GATE coded? options: A)5637 B)5367 C)5763 D)6573 E)6753 SOLUTION:g-5 a-6 e-7 from the code gate t - 3 from bat ANSWER:A #### A QUESTION:A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 210, how much must C pay as his share of rent? options: A)45 B)50 C)54 D)65 E)none SOLUTION:Sol. A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9. âˆ´ Câ€™s rent = Rs. [210* 9/35] = Rs. 54. Answer C #### C QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|C\| = -c \|b - 4\| + \|ab - b\| = ? options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab - b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab - b =ab - 2b + 4 Answer: Option B #### B QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)34 B)97 C)37 D)80 E)22 SOLUTION:1/2 * d (10 + 6) = 640 d = 80 Answer: D #### D QUESTION:If P * Q implies (P2 + Q2), 8 * (3 * 2) = ? options: A)239 B)278 C)233 D)2697 E)771 SOLUTION:Explanation: We have, P * Q = (P2 + Q2) ......... Given 8 * (3 * 2) = ? 8 * 13 = (64 +169) = 233 ANSWER: C #### C QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for? options: A)160 B)175 C)180 D)195 E)215 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 X 8 X 4) = 160. 160 X 2.40 + x X 3.20 = 432 3.20 X = 432 - 384 = 48 x = 15. Hence, total hours of work = (160 + 15) = 175 Answer: Option B #### B QUESTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? options: A)5 B)T=9 C)T=10 D)T=20 E)30 SOLUTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? 9^10 = (3^2)^10 = 3^20 D. 20 #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^102^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)\|x - 1\| < 7 B)\|x + 2\| < 6 C)\|x + 3\| < 5 D)\|x - 2\| < 6 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => \|x-2\| < 6. Hence, answer is D #### D QUESTION:Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other? options: A)4: 45 p.m. B)2: 20 p.m. C)5: 20 p.m. D)5: 35 p.m. E)6: 00 p.m. SOLUTION:the distance travelled by the train A in first 20 minutes will be 10. The distance which will be remaining is 80. Now both trains are running in opposite direction.Their speed will be added so 40. Time at which they will meet =80/40=2 time of train B will be 0:20 +2=2:20 Hence answer is B.Hope i am correct #### B QUESTION:In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? options: A)65 B)66 C)67 D)131 E)130 SOLUTION:The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ... The number of 1 letter words (X) that can be made from 65 letters is 65; The number of 2 letter words (XX) that can be made from 65 letters is 6565, since each X can take 65 values. Total: 65+6565. Similarly: The number of 1 letter words (X) that can be made from 64 letters is 64; The number of 2 letter words (XX) that can be made from 64 letters is 6464, since each X can take 64 values. Total: 64+6464. The difference is (65+6565)-(64+6464)=130. Answer: E. #### E QUESTION:There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg. options: A)29.23 kg B)32.56 kg C)35.66 kg D)37.25 kg E)NONE OF THE ABOVE SOLUTION:Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg 1) First find the total weight of all students - Weight of batch A = (36 x 40) = 1440 - Weight of batch B = (44 x 35) = 1540 Total weight of all students = (1440 + 1540) = 2980 kg 2) Find average weight of whole class (Batch A + Batch B) students = (36 + 44) = 80 students Average Weight = Total weight of all the students / No. of Students = 2980 / 80 = 37.25 kg ANSWER IS D #### D QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? options: A)6 B)7 C)8 D)2 E)9 SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class. We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24 x+9(24−x)=3⋅24x+9(24−x)=3⋅24 x+216−9x=72x+216−9x=72 216−72=8x216−72=8x 1448=x1448=x x=18x=18 So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. Answer:A #### A QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __? options: A)276 B)277 C)278 D)279 E)None of these SOLUTION:Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B #### B <<<Examples ends QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is: options: A)3 months B)4 months C)5 months D)6 months E)7 months SOLUTION:S.I. on Rs. 1600 = T.D. on Rs. 1680. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%. Time = (100x80)/(1600x15)= 1/3 year = 4 months answer : B #### B QUESTION:what is the radius of a circle that has a circumference of 3.14 meters? options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr. 2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A QUESTION:What will be the product of (50-1)(50-2)(50-3)..............(50-79)(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)7 C)9 D)11 E)15 SOLUTION:223 + 43 = 266/17 = 11 (Remainder) D #### D QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips? options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128 SOLUTION:P(HHHHTT) = 1/21/21/21/21/21/2 = 1/64 The answer is D. #### D QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 Â½ = 75 km RS = 75 â€“ 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6 SOLUTION:x – y = 5 4x – 6y = 6 x = 12 y = 7 ANSWER:C #### C QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)34 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:D #### D QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies options: A)250 B)150 C)100 D)50 E)200 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 ANSWER E #### E QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:The total number of books the students borrowed is 202=40. The students who borrowed zero, one, or two books borrowed 81+32=14 books. The 7 students who borrowed at least three books borrowed 40-14=26 books. If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books. The answer is A. #### A QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4 SOLUTION:Method- 1 There are 9 fine pieces of pen and 3 defective in a lot of 16 pens i.e. Probability of first pen NOT being defective = (13/16) i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective] Probability of Both pen being NON-defective = (12/15)(13/16) = 13/20 Answer: option D #### D QUESTION:A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total? options: A)220 B)250 C)280 D)300 E)340 SOLUTION:Let the total number of ounces in the drink be x. % of orange = 25% % of watermelon = 40% % of grape = 100% - 65% = 35% 0.35x = 105 x = 300 Therefore there are a total of 300 ounces in the drink. The answer is D. #### D QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell? options: A)111 B)75 C)29 D)128 E)96 SOLUTION:E 96 Joshua sold 90 phones. Rob sold 30 % more phones than Joshua Rob = 90 + 90 × 30% = 90 + 90 × 0.30 = 90 + 27 = 117 Prerna sold 11 more phones than Rob Prerna = 117 + 11 = 128 Declan sold 3/4 of what Prerna sold. Declan= 128 x 3/4 =96 Declan sold 96 phones. The correct answer is E. #### E QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 3200 = 400.Answer: D #### D QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:250/15 = 16 (plus remainder) so there are 16 multiples of 15 250/14 = 17 (plus remainder) so there are 17 multiples of 14 We need to subtract 1 because 1514 is a multiple of both so it was counted twice. The total is 16+17-1 = 32 The answer is C. #### C QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty five paise coins are in the ratio of 3:2:4, add up to Rs 75. Then how many 1 rupee coins he have? options: A)10 B)20 C)45 D)128 E)49 SOLUTION:Explanation : Given ratio = 3:2:4. Let us assume that there are 3 one rupee coins,2 fifty paise coins and 4 twenty-five paise coins in all. Their value=(31)+(2.50)+(4.25)=3+1+1=Rs 5 If the total is Rs 5, number of 1 rupee coins are 3. If the total is Rs 75, number of 1 rupee coins would be 753/5=45. Answer : C #### C QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg SOLUTION:let c=coach's avg. weight original total weight=(30 friends)(30 kg avge)=900kg (900+3c)/(30+3)=33 kg avg. c=63 kg Answer B #### B QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:Find the area of a parallelogram with base 20 cm and height 10 cm? options: A)287 cm2 B)887 cm2 C)200 cm2 D)250 cm2 E)668 cm2 SOLUTION:Area of a parallelogram = base height = 20 * 10 = 200 cm2 Answer: C #### C QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these SOLUTION:Explanation: We know perimeter of square = 4(side) So Side of first square = 40/4 = 10 cm Side of second square = 32/4 = 8 cm Area of third Square = 1010 - 88 = 36 cm So side of third square = 6 [because area of square = sideside] Perimeter = 4Side = 46 = 24 cm Option B #### B QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is? options: A)11 B)72 C)36 D)99 E)27 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240)/12 => x = 20 Speed of each train = 20 m/sec. = 20 18/5 =72 km/hr. Answer: B #### B QUESTION:The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch? options: A)51% B)52% C)53% D)54% E)55% SOLUTION:let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16 so total 52 students takes lunch out of 100 students..so required % is 52% ANSWER:B #### B QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be options: A)7744 B)2388 C)3778 D)2992 E)2888 SOLUTION:Explanation: length of wire = {\color{Blue}2 \Pi r}= 2 (22/7 )56 = 352 cm side of the square = 352/4 = 88cm area of the square = 8888 = 7744sq cm Answer: A) 7744 #### A QUESTION:If n = 20! + 15, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:15 divides 20! so 15 also divides 20! + 15. 17 and 19 divide 20! so they do not divide 20! + 15. The answer is A. #### A QUESTION:The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is? options: A)6.06% B)6.07% C)6.08% D)6.09% E)6.19% SOLUTION:Amount of Rs. 100 for 1 year when compounded half-yearly = [100 (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% ANSWER:D #### D QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ? options: A)148 B)134 C)156 D)144 E)None SOLUTION:Solution: Ratio of Ducks and Frogs in Pond, = 37 : 39. Average of Ducks and Frogs in Pond, = 132. So, total number of Ducks and Frogs in the Pond, = 2* 132 = 262. Therefore, Number of Frogs, = (26239)/76 = 134. Answer: Option B #### B QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 83= 24 tubes A is the answer #### A QUESTION:A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight? options: A)20 lb B)11 lb C)10 lb D)15 lb E)5 lb SOLUTION:Sol. 66÷6 = 11. Answer : B #### B QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State? options: A)7000 B)7200 C)7400 D)7600 E)8000 SOLUTION:State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 E) #### E QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:The rate of the pump + leak = 5/14 1/2 - leak's rate = 5/14 leak's rate = 1/2 - 5/14 = 1/7 The leak will empty the tank in 7 hours. The answer is D. #### D QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? options: A)21, 12 B)9, 0 C)15, 6 D)10, 1 E)14, 5 SOLUTION:the larger number: x the smaller number: y twice the larger: 2x three more than five times the smaller: 5y + 3 relationship between ("is"): 2x = 5y + 3 four times the larger: 4x three times the smaller: 3y relationship between ("sum of"): 4x + 3y = 71 Now I have two equations in two variables: 2x = 5y + 3 4x + 3y = 71 I will solve, say, the first equation for x: x = (5/2)y + (3/2) Then I'll plug the right-hand side of this into the second equation in place of the "x": 4[ (5/2)y + (3/2) ] + 3y = 71 10y + 6 + 3y = 71 13y + 6 = 71 13y = 65 y = 65/13 = 5 Now that I have the value for y, I can solve for x: x = (5/2)y + (3/2) x = (5/2)(5) + (3/2) x = (25/2) + (3/2) x = 28/2 = 14 Answer: E #### E QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number? options: A)4 B)10 C)11 D)12 E)15 SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5 So we have 5,15,25,35,45,55,65,75,85,95 =10 Ans B #### B QUESTION:Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? options: A)21 B)16 C)16 D)28 E)12 SOLUTION:Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 4 --------- ? è 28 m Answer: D #### D QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4side = 4 (3p/5) = 12p/5 Answer is C. #### C QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77 SOLUTION:Solution P( None is defective) = 18C2 / 22C2 = 51/77 P( at least one is defective) = (1- 51/77) = 26/77. Answer E #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4? options: A)2:8 B)2:1 C)2:2 D)2:3` E)2:7 SOLUTION:Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5  Milk in 1 lit mixture in A = 8/13 lit  C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2  milk in 1 litre mixture in B – 5/7 lit  C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4  milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13  Required ratio = 2/91 : 1/13 = 2:7 Answer:E #### E QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)16 sec B)13 sec C)17 sec D)21 sec E)23 sec SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/20 = 6 m/sec. Relative speed = 12 + 6 = 18 m/sec. Required time = (120 + 120)/18 = 13 sec. Answer: B #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000? options: A)6620 B)2888 C)2776 D)2997 E)5958 SOLUTION:A = 18000(11/10)^3 = 23958 = 18000 ---------- 5958 Answer: E #### E QUESTION:A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make? options: A)100% B)90% C)140% D)115% E)120% SOLUTION:The total CP = Rs. 18000 + Rs. 5000 = Rs. 2300 and SP = Rs. 46000 Profit(%) = (46000 - 23000)/23000 * 100 = 100% Answer:A #### A QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. Answer:B #### B QUESTION:How many 9 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if the repetition is allowed? options: A)77 B)26 C)88 D)27 E)99 SOLUTION:: If A number has to be divisible by 4, the last two digits must be divisible by 4. So possibilities are, 12, 24, 32, 44, 52. And the of the remaining 7 places, each place got filled by any of the five digits. So these 7 places got filled by 5 x 5 x .....(7 times) = 5757 ways. So total ways are 5 x 5757 = 5/8 Answer:A #### A QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.) options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360 SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit. OR For every $1 loss in the benefit, the recipient earns $3 above $9360 If earning is; 9360+3x Benefit = 12000-x Or the vice versa If benefit is 12000-x, the earning becomes 9360+3x He lost 50% of the benefit; Benefit Received= 12000-0.5512000 = 12000-6600 x=5400 Earning becomes 9360+3x=9360+35400=25560 Ans:C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is? options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3 SOLUTION:Correct sum = (36 * 50 + 48 - 23) = 1825. Correct mean = 1825/50 = 36.5 Answer:C #### C QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 7) years. (x+7+10)=2(x—10) hence x=37. Present age of B = 37 years Answer: Option B #### B QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20? options: A)276 B)84 C)88 D)90 E)342 SOLUTION:Required Number = (LCM of 5, 10, 15 and 20) + 24 = 60 + 24 = 84 Option B #### B QUESTION:A shop keeper marked 30% above the cost price and offered 20% discount then find it's net profit? options: A)2% B)2.5% C)3.7% D)4.6% E)5% SOLUTION:Net profit = 30-20 + (30(-25)/100) = 2.5% Answer is B #### B QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 35 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)45 E)01 SOLUTION:Explanation: As there is meal for 70 adults and 35 have their meal, the meal left can be catered to 35 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 35 adults = 45 children Hence, the meal can be catered to 45 children. ANSWER: D #### D QUESTION:A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 5/18 = 20 = 400 â€“ 250 = 150m ANSWER:A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7 SOLUTION:Total number of balls = 8+3 = 11 number of white balls = 8 Probability = 8/11 = 8/11 Answer is C #### C QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 34/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 1860 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)1/2 B)1/2 C)8/15 D)9/20 E)9/24 SOLUTION:Explanation : Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20 Answer : D #### D QUESTION:In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? options: A)36 B)2^43 C)24 D)38 E)47 SOLUTION:Working backward from the day it's covered: day 39: fully covered day 38: half covered So 38 days ANSWER:D #### D QUESTION:850 - (1500 ÷ ?) × 8/15 = 770 options: A)A)31 B)B)10 C)C)15 D)D)26 E)E)17 SOLUTION:Explanation: => 850 - (1500 ÷ ?) × 8/15 = 770 => 850 - 770 = (1500 ÷ ?) × 8/15 => 80 = (1500 ÷ ?) × 8/15 => 80 × 15/8 = (1500 ÷ ?) = 150 => 1/? = 150/1500 = 1/10 => ? = 10 Answer: Option B #### B QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 Ã— 9 Ã— 9 Ã— 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)5 B)6 C)21 D)8 E)9 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [385 * 3/55] sec = 21 sec Answer: C #### C QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is? options: A)48 B)49 C)50 D)51 E)52 SOLUTION:Excluded number = (27 * 5) - (21 * 4) = 135 - 84 = 51. Answer: D #### D QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/5 B)2/5 C)3/10 D)3/7 E)1/7 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 years B)9 years C)4 years D)6 years E)2 years SOLUTION:Explanation: 100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer: Option D #### D QUESTION:If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar? options: A)45 B)67 C)75 D)83 E)150 SOLUTION:We are told that 15 percent discount from the original price is more than $10: 0.15{price} > 10; {price} > 1,000/15; {price} > 66 2/3. Answer: B. #### B QUESTION:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert? options: A) 20% B) 25% C) 40% D) 60% E) 75% SOLUTION:could you use a venn diagram and just go with the number 100. 60 people order dessert and coffee... which is the union of D and C. T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither. B 25% #### B QUESTION:How many 0's are there in the binary form of 61024 + 464 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:61024 + 464 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:0.40 represents what percent of 0.008? options: A)0.05% B)0.5% C)5% D)500% E)5000% SOLUTION:One more method 0.40 represents what percent of 0.008? Adjusting the decimal 400 represents what percent of 8? Divide by 8 50 represents what percent of 1? Answer = 50100 = 5000% = E #### E QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)350 B)250 C)450 D)550 E)650 SOLUTION:The number of chocolate bars is equal to 18 ? 25 = 450 correct answer C #### C QUESTION:How many different positive integers are factors of 196 ? options: A) 1 B) 2 C) 3 D) 49 E) 36 SOLUTION:15, 14×15, 14=7^2 × 2^2 So total factors = (6+1)(6+1) = 49 Answer: D #### D QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=66 = 36 (6^3)= 366 = .16 (6^4)= .166 = ..96 (6^5) = ..966 = ..76 (6^6) = ..766 = ...56 (6^7) = ....566 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:Health insurance Plan Q requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$600 B)$1000 C)$3800 D)$5300 E)$6200 SOLUTION:0.5 * 600 = 300 where Q = B #### B QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area? options: A)1320 sq.metres B)4260 sq.metres C)6870 sq.metres D)7875 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 360 â‡’ x = 15 Area = 7 Ã— 15 Ã— 5 Ã— 15 = 7875 sq.m. Answer D #### D QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C 100 =50% Answer A #### A QUESTION:which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2 options: A)II only B)I only C)III only D)I,II only E)I,III only SOLUTION:10=25 15=35 GCF =5 Answer : B #### B QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A) $ 165 B) $ 145 C) $ 175 D) $ 180 E) $ 170 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by (B)$ 145. #### B QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years? options: A)Between 20 and 21 B)Between 21 and 22 C)Between 22 and 23 D)Between 23 and 24 E)None of these SOLUTION:Required sum = 20(1+8/100)2=20×27×27/25×25=23.3 Answer D #### D QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:7+2=56 6+3=48 5+5=45 2+1=4 4+9=?? Solve it? options: A)92 B)48 C)42 D)38 E)72 SOLUTION:x+y=x[y+(x-1)]=x^2+xy-x 7+2=7[2+(7-1)]=49+14-7=56 6+3=6[3+(6-1)]=36+18-6=48 5+5=5[5+(5-1)]=25+25-5=45 2+1=2[1+(2-1)]=4+2-2=4 4+9=4[9+(4-1)]=16+36-4=48 Answer :B #### B QUESTION:If the cost price of 60 boxes is equal to the selling price of 50 boxes, the gain percent is options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let C.P. of each box be Re. 1. Then, C.P. of 50 boxes = Rs. 50; S.P. of 50 boxes = Rs. 60. Gain % = 10/50 100 = 20% Answer:D #### D QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b â€“ d) d (80 + 60 â€“ 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is options: A)3Â° B)18Â° C)24Â° D)90Â° E)None of these SOLUTION:In a clock, each minute makes 6Â° âˆ´ 15 minutes will make 6 Ã— 15 = 90Â° Answer D #### D QUESTION:A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2? options: A)Rs.45 B)Rs.48 C)Rs.44 D)Rs.43 E)Rs.41 SOLUTION:π (152 - 132) = 176 176 * 1/4 = Rs.44 Answer:C #### C QUESTION:A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, A receives : options: A)14700 B)24703 C)29400 D)33777 E)34778 SOLUTION:Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=> x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. A's share = Rs. (70000 * 21/50 ) = Rs. 29,400. Answer: C) #### C QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Minimuum should be 1 Maximum should be 4: 1 out of a or b to make the multiplication negative 3 out of c, d, e or f to make the multiplication negative. Negative+Negative<0 Answer:C maximum will be 5.. you dont require both the multiplicatin to be negative for entire equation to be negative... any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers... actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation.. ans D #### D QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:According to a survey, at least 60% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? options: A)15% B)20% C)25% D)0% E)35% SOLUTION:It seems that something is wrong with your answer options. 1) minimum applesbananas: [XXXXXXXXXXXXXX------] - apples [-----XXXXXXXXXXXXXXX] - bananas mimimum ab = 60 - (100-75) = 35% 2) minimum (applesbananas)cherries: [XXXXXXXXX-----------] - applesbananas [----XXXXXXXXXXXXXXXX] - cherries mimimum ab = 35 - (100-80) =15% A #### A QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (512/5)/100] P= 1000 Answer: A #### A QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)28 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (14000 × 7) + 6000 ( x – 7) ‹=› 2000x = 56000 ‹=› x = 28. Answer D #### D <<<Examples ends QUESTION:Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 35%. What fraction of the original paint was replaced? options: A)1/35 B)1/5 C)2/3 D)3/5 E)4/5 SOLUTION:35% is 10%-points above 25% and 15%-points below 50%. Thus the ratio of 25%-solution to 50%-solution is 3:2. 3/5 of the original paint was replaced. The answer is D. #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4 SOLUTION:Method- 1 There are 9 fine pieces of pen and 3 defective in a lot of 16 pens i.e. Probability of first pen NOT being defective = (13/16) i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective] Probability of Both pen being NON-defective = (12/15)(13/16) = 13/20 Answer: option D #### D QUESTION:A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples? options: A)1:7 B)1:5 C)1:4 D)1:2 E)2:5 SOLUTION:To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars. To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these. 45 split in the ratio 1:4 gives 9 and 36. 9 apples split into 3 apples each will give $3. 36 apples split into 6 apples each will give $6. They add up to $9 so we have hit the right answer. Answer (C) #### C QUESTION:man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)34 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 36) + 2 = 2(x + 2) x + 38 = 2x + 4 x = 34. answer :D #### D QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely? options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec SOLUTION:Explanation: D = 250 m + 250 m = 500 m RS = 80 + 40 = 120 5/18 = 100/3 T = 500 * 3/100 = 15 sec Answer: Option A #### A QUESTION:If 0.5% of A =85 paise, then the value of A is ? options: A)Rs. 170 B)Rs. 17 C)Rs. 1.70 D)Rs. 4.25 E)None SOLUTION:Answer ∵ 0.5/100 of A = 85/100 ∴ A = Rs. (85 / 0.5) = Rs. 170 Correct Option: A #### A QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D QUESTION:How many multiples of 5 are there between 50 and 500 ? options: A)128 B)91 C)89 D)61 E)60 SOLUTION:It should be mentioned whether 50 and 500 are inclusive. If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91. If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89. Since OA is C, then we have NOT inclusive case. #### C QUESTION:The present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)25,30,20 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 5x, 6x and 4x years respectively. Then, (5x - 5) + (6x - 5) + (4x - 5) = 60 15x-15 = 60 x = 5 Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively. Answer: C #### C QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:Ravi can do a piece of work in 15 days while Prakash can do it in 30 days. In how many days will they finish it together? options: A)11 days B)9 days C)8 days D)12 days E)10 days SOLUTION:1/15 + 1/30 = 3/30 10/1 = 10 days ANSWER:E #### E QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (11) = 2. 2(result) + (22) = 6. 6(result) + (33) = 15. 15(result) + (44) = 31. 31(result) + (55) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Answer:D #### D QUESTION:A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum? options: A)22887 B)2677 C)2987 D)8925 E)17711 SOLUTION:Principal = (100 4016.25) / (9 * 5) = Rs. 8925. Answer:D #### D QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions. = 1500 * 2 * 22/7 * 22.4 = 211200 cm = 2112 m Answer: A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+52)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:575.104 x 15.98 Ã· 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 Ã· 9.001 + 21.25 â‰ˆ (575.104 x 16/9) + 21.25 â‰ˆ 1022.40 + 21.25 â‰ˆ 1043.65 Answer: Option B #### B QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A? options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440 SOLUTION:LCM = 180 Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c = (180/15)/(180/15 +180/20 + 180/45) = (12/25) * 500 = Rs.240 ANSWER:A #### A QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1 options: A)I,III only B)III only C)I only D)II only E)II,III only SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+36=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1; I. y<3x --> is not always true. Answer: E #### E QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2 SOLUTION:P(at least one graduate) = 1 - P(no graduates) = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 5 * 4)/(10 * 9 * 8) = 5/6 Answer: D #### D QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is: options: A)180 B)1800 C)18 D)18000 E)1350 SOLUTION:Area of the hall= 36001500 Area of each stone= (8050) Therefore, number of stones= (36001500/ 8050)= 1350 ANSWER:E #### E QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? options: A)40 B)45 C)35 D)50 E)55 SOLUTION:A is one third of the sum of B and C.. or A=1/3(B+C)... But A+B+C=60 so 1/3(B+C)+B+C=60 4(B+C)/3= 60 B+C =603/4 = 45 A=60-45=15 2)B is one fifth of the sum of A and C or B=1/5(A+C)... But A+B+C=60 so 1/5(A+C)+A+C=60 A+C=605/6=50 but A=15, so C=50-15=35 Answer :C #### C QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)22 B)45 C)66 D)88 E)12 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/155297 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass? options: A)6 B)9 C)8 D)7 E)5 SOLUTION:B = 9 2/3x= 20 x=30 for 80% approval we need 24 garments approved. already approved = 18 we need 6 more. Answer : A #### A QUESTION:If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true? I. a + b + c > a^3 II. a × b × c < a^3 III. 5b > bc options: A)I only B)II only C)III only D)II and III E)I, II, and III SOLUTION:Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4 Putting the values in the answers only 'A' seems valid. #### A QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together? options: A)89! B)88! C)79! D)98! E)None SOLUTION:Solution: No. of ways in which 10 paper can arranged is 10! Ways. When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers. These 9 papers can be arranged in 9! Ways. And two papers can be arranged themselves in 2! Ways. No. of arrangement when best and worst paper do not come together, = 10!- 9!.2! = 9!(10-2) = 8.9!. Answer A #### A QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:an article with cost price of 192 is sold at 25% profit. what is the selling price? options: A)198 B)200 C)204 D)240 E)210 SOLUTION:sp=1.25192=240 ANSWER:D #### D QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. Aâ€™s 1 dayâ€™s work = (1/20) (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:In the coordinate plane, points (x, 1) and (12, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y = options: A) 4.5 B) 7 C) 8 D) 11 E) 12 SOLUTION:Line k passes through the origin and has slope 1/2 means that its equation is y=1/2x. Thus: (x, 1)=(2, 1) and (12, y) = (12,6) --> x+y=2+6=8. Answer: C. #### C QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is options: A)91 B)81 C)1001 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 891 and 810. â€¹=â€º 81. Answer B #### B QUESTION:A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet? options: A)6 B)3 C)2 D)4 E)5 SOLUTION:Total fleet--20 End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new). End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new). Answer is C--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet. #### C QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. options: A)15 B)25 C)30 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:C #### C QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c11c11c1)/5c3 =3/10 ANSWER:A #### A QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was? options: A)320000 B)120029 C)187899 D)178968 E)789698 SOLUTION:X * (105/100) * (105/100) * (105/100) = 370440 X = 370440/1.157625 X = 320000 Answer:A #### A QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All two 2. One symmetry and other two non 4. All the two letters can be arranged in 2 ways ( 11c2+ 11c1 * 15c2) 2 ( 1110/ 2 + 11 * 15 * 14 / 2 ) * 2 2420 IMO option D is the correct answer.. OA please...will correct if I missed anything..D #### D QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:A local bank that has 8 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 8 codes? options: A)4 B)6 C)5 D)3 E)7 SOLUTION:Pick any two integer. Integers: 12 Code: 11, 12, 21, 22 = 4 Codes Add one more integer: 3 13, 31, 33, 23, 32 = 5 Codes Total = 9 Codes. Enough. Answer: D #### D QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 182 cm. Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm = 182 cm - 1.71 cm = 180.29 cm. Answer: B #### B QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17 SOLUTION:Explanation : Let two digit number that Shiwani thought be 'xy', where x and y are single digit number. Therefore, 10x+y=p(x+y)+3, where p is a natural number p=10x+y−3x+y. Also, y+x>3. Possible values of x and y for which p is a natural number are :- (x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9), (x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null), (x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4) There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits. Probability that Devesh thought of the same number as Shiwani = 1/14 Answer : B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown? options: A)26 B)19 C)11 D)8 E)6 SOLUTION:No of dogs=45 Long fur=36 Brown=27 Neither long fur nor brown=8 Therefore, either long fur or brown=45-8=37 37=36+27-Both Both=26 Answer A #### A QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4 SOLUTION:P1 takes 12 hrs Rate for P2P3 together = 1/16 + 1/18 = 17/144 Therefore they take 144/17 Ratio = 144/17 = D #### D QUESTION:One pump drains one-half of a pond in 5 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone? options: A)1 hour B)1.2 hour C)3 hours D)5 hours E)1.1 hours SOLUTION:The tricky part here, I believed is one half hour = 1/2. Then everything would be easy. We have the 1st pump working rate/hour = 1/2 : 5 = 1/10 Working rate of 2 pumps: 1/2 : 1/2 = 1. Working rate of 2nd pump: 1 -1/10 = 9/10 --> Time taken for the 2nd pump to finish: 1 : 9/10 = 10/9 = 1.1 hours. E #### E QUESTION:Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months. options: A)Rs. 9009 B)Rs. 9008 C)Rs. 9002 D)Rs. 9202 E)Rs. 9001 SOLUTION:Explanation: P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years Therefore, S.I = (PRT)/100 = (78000* 77/5 * ¾ * 1/100) = Rs. 9009 ANSWER: A #### A QUESTION:Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3? options: A)2 B)5 C)3 D)1 E)4 SOLUTION:{4^1} / 3 =4/3 remainder 1 {4^2} / 3 = 16/3 remainder 1 {4^3} / 3 = 64/3 remainder 1 {4^4} / 3 = 256/3 remainder 1 Actually the same remainder keeps repeating ..... Try with a diff no, say 2 {2^1}/3 = remainder 2 {2^2}/3 = remainder 1 {2^3}/3 = remainder 2 {2^4}/3 = remainder 1 Answer : D #### D QUESTION:In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women? options: A)63 B)67 C)70 D)90 E)80 SOLUTION:We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this = 6C4 × 4C2 90 D) #### D QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,55x+44x+2x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A? options: A)29491 B)28491 C)39491 D)49491 E)59491 SOLUTION:Compound ratio of A:B:C A:B = 3:4 B:C = 5:6 ---------- A:B:C = 15:20:24 We can divide Rs.116000 in this ratio. Share of A = 15/59 116000 = 29491 ANSWER:A #### A QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last? options: A)9 B)5 C)6 D)2 E)4 SOLUTION:I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p: In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last? Water required is 2005=1000 (mn) Water available is 2000 (p) It will last 2 months (p/mn) Ans : D #### D QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 1000.70.60.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. options: A)Rs.240 B)Rs.350 C)Rs.340 D)Rs.390 E)Rs.370 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 * 630 = 240 ANSWER IS A #### A QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse? options: A)A)5 B)B)8 C)C)10 D)D)15 E)E)30 SOLUTION:Total number of ways to choose 6 chairs from 5= 6C2=15 Total number of combination=150 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C3=10..... 1015=150 Answer is 5... A #### A QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.6 D)5.7 E)6.5 SOLUTION:if $x$ is the number, x/6 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 205 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these SOLUTION:Explanation: 80 : 5 = 105 : x x= (5×105/80) = Rs 6.56 Option A #### A QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)6 B)(P-7)5 C)(P-7)2 D)(P-7)3 E)(P-7)4 SOLUTION:M/84 =(P-7)/21 M = (P-7)84/21 =(P-7)4 E #### E QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer: Option D #### D QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty? options: A)36 B)39 C)42 D)48 E)24 SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS. We're told 3 facts about the relative ages of 3 people: 1) Carol's age is 4 times Alice's age 2) Carol's age is 2 times Betty's age 3) Carol is 36 years older than Alice We're asked for BETTY'S age. Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first. IF.... Betty = 24 Then Carol = 2(24) = 48 Then Alice = 48 - 36 = 12 AND 48/4 =12 All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24 E #### E QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:In how many K ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6666= 1296 ------(1) Total number of passwords in which no letter repeats = 6C44!= 1524=360------(2) therefore required value K= (1)-(2)= 1296-360=936.D #### D QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:The least common multiple is 222357=840. 3600 seconds / 840 = 4 + remainder. The answer is A. #### A QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/1001000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)8.3% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100100=10,000. Now, the area obtained with wrong measurements would be 11495=10,830, which is 8.3% greater than the actual area. Answer: C. #### C QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A? options: A)2 B)3 C)5 D)6 E)8 SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize. 14n/60 If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have (27n)/(2^235) Simplifying 7n/(235) The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7. The number could be 235, or 2352, or 235..... However to be less than 200 we can not add any prime number. 235 = 120 If we added the next prime factor 7, we would have A=2357 = 840 Thus, answer B #### B QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? options: A)6 B)8 C)6 D)5 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged? options: A)6 B)48 C)36 D)24 E)12 SOLUTION:Dhoni have to sit at either of the ends. If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24 David can also sit on the other end, then another 4! ways we can arrange. So total number of ways = 24+24 = 48 Answer : B #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture? options: A)1/2 B)1/3 C)1/4 D)1/6 E)1/5 SOLUTION:Do not need any computation 30%-----------21%---------12% if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times only possibility is 1/6 D #### D QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:The sum of three consecutive numbers is 87. The greatest among these three numbers is : options: A)22 B)24 C)26 D)30 E)44 SOLUTION:Sol. Let the numbers be x, x + 1 and x + 2. Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28. Greatest number = (x + 2) = 30. Answer D #### D QUESTION:Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Time taken for Jemma to reach buoy B is 2 hours. The distance between the buoys is 4 miles. Distance travelled/time taken = Average speed Hence the average speed to travel the distance is 2m/hr Now, she would have to travel 6 miles . However as she is tired the speed is half or 1m/hr Hence, it will take her 6 hours (Option C) #### C QUESTION:Two numbers are in the ratio of 1 : 2. If 8 be added to both, their ratio changes to 3 : 5. The greater number is options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let the ratio be X : Y, Given X/Y = 1/2 , (X + 8)/(Y + 8) = 3/5 => X = 16 And Y = 32 ANSWER:D #### D QUESTION:If 50 percent of the members of a certain organization are women and 5/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)I B)II C)III D)I,II & III E)I,II SOLUTION:5/10 (50%) of the members are women and 5/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 5/1080 = 40 women; 80 - 40 = 40 men; 5/840 = 25 married men; 40 - 25 = 15 unmarried men. So, option I,II is true. Answer: E #### E QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =250=100m ANSWER:D #### D QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? options: A)25 B)21 C)20 D)10 E)15 SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B respectively Quantity of A in mix. left =[7x –7/12 9 ] =[7x –21/4] Quantity of B in mix. left =[5x –5/12 9 ] = [ 5x - 15/4 ] Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9 [5x-15/4]+9 20x+21 252x -189 =140x+147 or 112x =336 , x = 3. Quantity of A in the can initially =73 =21 ANSWER:B #### B QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ? options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5 SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7 = 2 (2^7) + 3 (3^7) = 2^1 (2^7) + 3^1 (3^7) = 2^(1+7) + 3^(1+7) = 2^8 + 3^8 Ans: A #### A QUESTION:If k^3 is divisible by 60, what is the least possible value of integer k? options: A)12 B)30 C)60 D)90 E)120 SOLUTION:60 = 2^235 Therefore k must include at least 2 * 3 * 5 = 30. The answer is B. #### B QUESTION:A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long options: A)6 ½ sec B)7 ½ sec C)8 sec D)13 ½ sec E)9 sec SOLUTION:Explanation: Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (200 + 295) m = 495 m. Time taken =495 ×(3/110) sec =27/2 sec = 13 ½ sec Answer: Option D #### D QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days? options: A)18 B)09 C)07 D)19 E)12 SOLUTION:3 M + 10 B ----- 09 days 7 M + 7 B ------- 8 days 9 M + 9 B -------? 21 M + 70 B = 63 M +63 B 7 B= 42 M => 6 M = 1 B =>1 B =6 M 3 M + 60 M = 63 M ---- 9 days 9 M + 54 M = 63 M -----? => 9 days Answer: B #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score? options: A)662 B)672 C)652 D)646 E)721 SOLUTION:8 * 82 = 656 – 10 = 646 ANSWER:D #### D QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 5/7 . 2/5 P (A n B) = 2/7. D #### D QUESTION:A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face? options: A)52.9% B)55.4% C)58.3% D)61.7% E)64.5% SOLUTION:There are a total of 999 = 729 cubes. All the exterior cubes will have at least one face painted red. The interior is formed by 777 = 343 cubes. The number of cubes with at least one side painted red is 729 - 343 = 386 cubes The probability that a cube has at least one side painted red is 386/729 which is about 52.9% The answer is A. #### A QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next? options: A)52 B)56 C)96 D)128 E)None SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8. Answer: Option B #### B QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? options: A)150 B)88 C)270 D)62 E)52 SOLUTION:Length of the train be â€˜Xâ€™ X + 120/15 = X + 250/20 4X + 480 = 3X + 750 X = 270m Answer: C #### C QUESTION:The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? options: A)s.1014 B)s.1332 C)s.999 D)s.1085 E)s.1020 SOLUTION:a2 = 3136 => a = 56 56 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 ANSWER:B #### B QUESTION:In a family 16 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family? options: A)28 B)26 C)22 D)31 E)21 SOLUTION:Total people eat veg = only veg + both veg and non veg Total= 16+12= 28 Answer = A #### A QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 654321 = 720 ANSWER:B #### B QUESTION:1 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work? options: A)12/9 days B)15/4 days C)82/8 days D)22/76 days E)3/2 days SOLUTION:1M = 6W ---- 20 days 12M + 8W -----? 72W + 8 W = 80W ---? 6W ---- 20 80 -----? 6 20 = 80 * x => x = 3/2 days Answer:E #### E QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:The smallest value of n, for which n+2 is not a prime number, is options: A)1,2 B)4,6 C)2,4 D)8,12 E)9,6 SOLUTION:(1 + 2) = 3. (2 + 2) = 4. (3 + 2) = 5. (4 + 2) = 6. which is not prime , n=2,4. ANSWER:C #### C QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected? options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9) SOLUTION:x red balls y green balls x+4+y+5 is the total =x+y+9 x+5 is the number of red balls so (x + 5)/(x + y + 9) the answer is C #### C <<<Examples ends QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 76 = 42 litres of 2% solution and 36 = 18 litres of 12% solution. Answer (E) #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km. options: A)3 B)4 C)5 hrs. D)6 E)2 SOLUTION:US =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C #### C QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q\|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q\|Q) = 3/51 P(A\|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A\|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q\|Q) P(A\|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:What is the unit’s digit of 7^5 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:7^1=7 7^2=49 7^3=343 7^4=1(last digit) 7^5=7(last digit) and the cycle repeats after every 4 powers Therefore, last digit of 7^5=7 Answer D #### D QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ? options: A)5 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 15 x 10 ) / (15 +10 ) km/hr. = 12 km/hr. Correct Option: B #### B QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1? options: A)28% B)40% C)68% D)70% E)72% SOLUTION:Let initial price be 1000 Price in day 1 after 10% discount = 900 Price in day 2 after 15% discount = 765 Price in day 3 after 20% discount = 612 So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900100 => 68% Answer will definitely be (C) #### C QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d? options: A) 16% B) 32% C) 48% D) 84% E) 92% SOLUTION:16% ________________________________________________ a+d 34% ________________________________________________ a 34% ________________________________________________ a-d 16% since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a. thus 16% lie below a-d and 16% lie above a+d now below a+d = 16+34+34 = 84% hence D #### D QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women? options: A)266 B)86400 C)11760 D)5040 E)None of these SOLUTION:Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in 8C5 × 10C6 ways, i.e., 11760 ways. Answer C #### C QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)18.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 36 Paise is given as tax => Total tax incurred = 36 Paise = Rs.36/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−36/100−x)6/100 = 36/100 ⇒ 6(25 −0.36 −x) = 36 ⇒ (25 − 0.36 − x) = 6 ⇒ x = 25 − 0.36 − 6 = 18.7 B) #### B QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/24=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number? options: A)74 B)76 C)70 D)68 E)65 SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) Their sum = 8x - 4 = 292 => x = 37 Smallest number is: 2(x - 2) = 70. ANSWER:C #### C QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:Among the members of the Malmo family, there are three times as many members who do not wear glasses as members who do. Half of the Malmo family members have blue eyes, and 4/5 of the family members who have blue eyes do not wear glasses. What percent of the Malmo family members wear glasses and do not have blue eyes? options: A)10 B)15 C)20 D)25 E)35 SOLUTION:Number in black are given and in red are calculated. Now, since x+3x=100, then x=25 and therefore =25−10=15 Answer: B. #### B QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None SOLUTION:Solution Perimeter of the rhombus = 56 m Each side of the rhombus = 56 / 4 m = 14 m. Height of the rhombus = 5 m Area = (14 x 5) m² = 70 m² Answer B #### B QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? options: A)2 B)4 C)6 D)8 E)12 SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less. Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter ANSWER:D #### D QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ? options: A)7 B)2 C)9 D)2 E)8 SOLUTION:B 2 Relative speed = 2 + 3 = 5 rounds per hour. So, they cross each other 5 times in an hour and 2 times in half an hour. Hence, they cross each other 2 times before 8.30 a.m. #### B QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age. options: A)60 years B)80 years C)70 years D)76 years E)86 years SOLUTION:Let Kumar’s present age be x years and Sailesh’s present age be y years. Then, according to the first condition, x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1) Now. Kumar’s age after 10 years = (x + 10) years Sailesh’s age after 10 years = (y + 10) (x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2) Solving (1) and (2), we get x = 70 and y = 30 Kumar’s age = 70 years and Sailesh’s age = 30 years. ANSWER:C #### C QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)A)1000 B)B)3000 C)C)3500 D)D)2500 E)E)2250 SOLUTION:For 20 staffs: 30010020 = 60000 for driver and cleaning staff: 3001002 =6000 From petty Cash : 1000 Answer is 1000 Answer is A #### A QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed. options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec SOLUTION:If length of train is l and speed of train is s, then l/s = 10 (l+180)/s = 20 (l+180)/l = 20/10 =2 l+180 =2l l= 180 l=180 mtrs s= l/10 = 180/8 = 10 m/sec ANSWER:A #### A QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution? options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30 SOLUTION:Water:soap = 3:4 Soap:Salt=15:20 => For 15 soap, salt = 20 => For 4 Soap, salt = (20/15)4 = 80/15=16/3 So, water:soap:salt = 3:4:16/3= 9:12:16 After open container, water:soap:salt =4.5:12:16 So, water:salt = 4.5:16 = 9:32 ANSWER:A #### A QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles? options: A)1:18. B)1:20. C)1:4. D)1:36. E)1:16. SOLUTION:Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3D(b) = 32R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D. #### D QUESTION:Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel. options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160 SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180; Vessel B = 500 gallons --> milk = 375, water = 125; Vessel A + B = 800 gallons --> milk = 495, water 305. The ratio = 495/305 --> reduce by 5 = 99/61. Answer: A. #### A QUESTION:How many different positive integers are factors of 196 ? options: A) 1 B) 2 C) 3 D) 49 E) 36 SOLUTION:15, 14×15, 14=7^2 × 2^2 So total factors = (6+1)(6+1) = 49 Answer: D #### D QUESTION:There are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution. options: A)1 B)2 C)3 D)4 E)9 SOLUTION:145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A. #### A QUESTION:Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the jobs? options: A)2/3 B)3/4 C)1 D)2 E)3 SOLUTION:Work done by Tina in 1 hr=1/12 Work done by Tina in 8 hr=1/128 which is 2/3 Now,the remaining work is 1/3 which is completed by Ann in 1/39 which is 3hr ANSWER:E #### E QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:If you add all the numbers on your mobile phone , what is the answer? options: A)45 B)50 C)55 D)100 E)60 SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone. Therefore 0+1+2+3+4+5+6+7+8+9=45 Answer is A #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)25 B)29 C)48 D)26 E)54 SOLUTION:A 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. #### A QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)9 B)12 C)18 D)24 E)27 SOLUTION:Total Students = 36 One third of the students are boys = 1/336 = 12 Three fourths of the boys are under six feet tall = 3/412 = 9 ... Therefore Number of boys in the class under six feet tall = 9 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/41/336 = 9... Answer A #### A QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)0 SOLUTION:K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^24^25^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . E #### E QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race? options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters SOLUTION:Answer A runs 25% as fast as B. i.e., if B runs 100 m in a given time, A will run 125 m in the same time. In other words, if A runs 5 m in a given time, then B will run 4 m in the same time. Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat. Ratio of length of start given : length of race :: 1 : 5 In this question, we know that the start given is 7 m. Hence, the length of the race will be 7 * 5 = 35 m. Choice E #### E QUESTION:If x and y are different integers, both divisible by 11, then which is not necessarily true? options: A)x^2 + y^2 is divisible by 11 B)x - y is divisible by 11 C)xy is divisible by 11 D)x + y is divisible by 11 E)x + y is divisible by 22 SOLUTION:Let x = 11k and let y = 11j. Then x+y = 11(k+j) and k+j could be even or odd. Thus 11(k+j) is not necessarily divisible by 22. The answer is E. #### E QUESTION:A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets? options: A)420 B)550 C)490 D)450 E)520 SOLUTION:10 * 157 = 1570 3 * 100 + 5 * 150 = 1050 1570 – 1050 = 520 Answer:E #### E QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15 SOLUTION:Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15 Answer is A. #### A QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil. options: A)12 B)10 C)15 D)19 E)20 SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively. Then, 2x + 3y = 86 ….(i) and 4x + y =112. Solving (i) and (ii), we get: x = 25 and y = 12. Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12. Answer is A. #### A QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen? options: A)1/30 B)1/25 C)1/20 D)1/28 E)1/30 SOLUTION:Probability that John and David will both be chosen out of 8 workers = (2/8)(1/7) = 1/28 Answer D #### D QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/- SOLUTION:Loss = 50010/100 = 50 S.P = C.P - Loss = 500- 50 =Rs.450/- Answer : A #### A QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+9)=4/5 20x=4(3x+9) 8x=36 x=4.5 Quantity of alcohol = (4 x 4.5) litres = 18 litres. Answer is E #### E QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is options: A)3 10 B)2 10 – 1 C)3 10 – 1 D)2 10 E)None of these SOLUTION:Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions. Hence, the number of all possible selections is 3 10 – 1. Answer C #### C QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? options: A)66 B)83.5 C)84 D)95 E)76 SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4 = 84 ANSWER:C #### C QUESTION:Find the odd man out. 14,35,49,60,70 options: A)14 B)35 C)49 D)60 E)70 SOLUTION:All except 60 are multiples of 7 Answer is D #### D QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60? options: A)426 B)430 C)443 D)470 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D #### D QUESTION:A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin? options: A)15/2 B)9/4 C)5/9 D)7/5 E)9/7 SOLUTION:Blue tin or red tin: 2/3 (N) Red tin: (1/3)N Blue tin: (1/4)N What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin) # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12 # of cookies in red and green tin = N/3 + 5N/12 = 9N/12 Fraction T= 5N/12 * 12/9N = 5/9 (C) #### C QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(66)/2 = 18 Answer:A #### A QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:If 4a^4 − 41a^2 + 100 = 0, then what is the sum of the two greatest possible values of a ? options: A)4 B)9/2 C)7 D)41/4 E)25 SOLUTION:just forget about the value of a^4 for the moment and let a^2= X. (its better to work with power of 2 than 4) now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4. so a^2 = 4 and 25/4 so a= +2 and minus 2 and +5/2 and minus 5/2 The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B #### B QUESTION:A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 5 students hold membership in both organizations, how many different committee are possible? options: A)215 B)275 C)325 D)385 E)495 SOLUTION:student government + the student advisory board consists of 9 + 8 = 17 members. 5 students hold membership in both, so they were counted twice. The total number of people to choose from is 17 - 5 = 12 The number of ways to choose 8 members from 12 is 12C8 = 495 The answer is E. #### E QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = prt/100 = 100000043/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:Which one of the following numbers is exactly divisible by 12? options: A)A)12 B)B)13 C)C)14 D)D)15 E)E)16 SOLUTION:12/12=1 answer is A #### A QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell? options: A)111 B)75 C)29 D)128 E)96 SOLUTION:E 96 Joshua sold 90 phones. Rob sold 30 % more phones than Joshua Rob = 90 + 90 × 30% = 90 + 90 × 0.30 = 90 + 27 = 117 Prerna sold 11 more phones than Rob Prerna = 117 + 11 = 128 Declan sold 3/4 of what Prerna sold. Declan= 128 x 3/4 =96 Declan sold 96 phones. The correct answer is E. #### E QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)7 C)9 D)11 E)15 SOLUTION:223 + 43 = 266/17 = 11 (Remainder) D #### D QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen? options: A)1.34 B)2.84 C)3.84 D)4.34 E)5 SOLUTION:40(40/100) = 16 --- 50 ? --- 12 => Rs.3.84 Answer: C #### C QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? options: A)22 B)77 C)28 D)18 E)19 SOLUTION:93 + 123 + 153 = a3 => a = 18 Answer: D #### D QUESTION:If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b = options: A) −5 B) −2 C) 2 D) 46 E) 48 SOLUTION:a(a + 5) = 6 and b(b + 5) = 6 => a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively => a+b = -5 Ans: A #### A QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:In 16 minutes, the minute hand gains over the hour hand by options: A)16° B)80° C)88° D)96° E)None of these SOLUTION:In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand. ∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88° Answer C #### C QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now? options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9 SOLUTION:G is Gunther's current age. Let Mason's current age be M. given M = 2(G-5). four years from now Mason's age will be = 2(G-5) + 10 = 2G four years from now Gunther's age will be = G+10 Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10 Ans : D #### D QUESTION:A train 100 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)68.4 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [100/5] m/sec = [20 * 18/5] km/hr = 72 km/hr. Answer C #### C QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:The following sets each have a mean of 8 and the standard deviations are given in variable form. Set I = {8, 8, 8, 8, 8, 8}, standard deviation = A Set II = {2, 2, 2, 14, 14, 14}, standard deviation = B Set III = {5, 6, 7, 9, 10, 11}, standard deviation = C Rank these three standard deviations from least to greatest. options: A)A, B, C B)B, C, A C)C, A, B D)C, B, A E)A, C, B SOLUTION:The answer should be E as the mean is least deviated in Set I followed by Set III and then Set II. #### E QUESTION:Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1800 options: A)30 B)70 C)210 D)300 E)180 SOLUTION:27 = 333, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3. 100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10. Then we want to know what is the largest possible GCF of x and 2100. Well 1800 = 3 * 6 * 10 * 10 We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible. We know x has one factor of 3, but not two factors --- that takes the 3. We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking. 3610 = 180 If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 1800. E #### E QUESTION:((-1.9)(0.6) – (2.6)(1.2))/2.0 = ? options: A)-0.71 B)1.0 C)1.07 D)1.71 E)-2.13 SOLUTION:Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option. -2.13 Answer E #### E QUESTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y 1997- x1---- y1-- x1+y1 x1= ax .....(P) y1= 1.07y...(Q) x1+y1/x+y = 1.01 solve using P and Q and find x/y #### A QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set? I. 1 II. -4 III. 5 options: A)I only B)II only C)I and III only D)II and III only E)I, II, and III SOLUTION:The question is which of the following must be in the set, not could be in the set. If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set. Answer: C. #### C QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 6 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15 So, T=15-5 = 10.C #### C QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph Total distance to be covered = 333 miles. Time taken would be: 333 miles/111 mph = 3 hours C is the answer. #### C QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ? options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49 SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49 SD: Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7. So, answer will be D. #### D QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2Total igneous rocks = 260 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days? options: A)12 days B)12.5 days C)13 days D)13.5 days E)15.5 days SOLUTION:Both together worked for 3 days. In 3 days , P can do = 3 x 1 18 = 1 6 th work In 3 days, Q can do = 3 x 1 15 = 1 5 th work In 3 days , work finished = 1 6 + 1 5 = 11 30 Balance work = 19 30 Balance work finished by Q => Time taken by Q to finish the balance work = 19 30 x 15 = 9.5 days The whole work was completed in 9.5 + 3 = 12.5 days B #### B QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5x/6 = 5x/16 + 200 25x/48 = 200 x = 384 ANSWER: A #### A QUESTION:The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : options: A)22.75 B)33.25 C)22.25 D)11.75 E)18.75 SOLUTION:Explanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48=18.75 Answer:E #### E QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:A salesman travels a distance of 100 km in 5hours. How much faster in kilometer per hour, on an average, must he travel to make such trip in 1 hour less time? options: A)2km/hr B)3km/hr C)5km/hr D)7km/hr E)10km/hr SOLUTION:Time required = 5 hrs- 1hr = 4hr Required speed = 100/4 = 25km/hr Original speed = 100/5 = 20 km/hr Difference = 25-20 = 5 km/hr Answer is C #### C QUESTION:There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be? options: A)6693 B)6793 C)6893 D)6993 E)7093 SOLUTION:There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is: 9(111+222+444)=9(777)=6993. The answer is D. #### D QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ? options: A)10 hours B)12 hours C)16 hours D)18 hours E)20 hours SOLUTION:Explanation: Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)–(1/2) = 1/12 => B alone can complete the work in 12 hour Option B #### B QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad? options: A)814 B)266 C)287 D)999 E)661 SOLUTION:Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = Required number of tiles = = 814 Answer: A) 814 #### A QUESTION:A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? options: A)240 B)250 C)260 D)270 E)300 SOLUTION:Let total capacity be x we know 200 = 0.50x x = 200/0.50 = 400 Prior to storm, we had 160 bn gallons 400-160 = 240 Answer : A #### A QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)9 B)4 C)8 D)5 E)3 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 41(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1SD=13 and 2 SD below the mean ismean-2SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:60, 67, 63, 15, 61, 10, 15 Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list? options: A)25 B)36 C)53 D)60 E)62 SOLUTION:Yes, it can be solved with observation even without approximation in 30 sec. Just observe given numbers: 10, 15 ,15, 60, 61, 63, 67 Median is very easy to tell - its 60. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 60 DE are already out. Now, we have 25, 36 and 53 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 53. (Notice, if 25 is more than mean then 53 is also. If 36 is more than mean, 53 is also. ) Hence C it is! #### C QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E <<<Examples ends QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If x = 4 and y = −2, what is the value of (x − 2y)^y? options: A)−100 B)0.015 C)0.25 D)4 E)8 SOLUTION:Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE by inversing and squaring 0.015 Answer: B #### B QUESTION:A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand. options: A)11a.m B)12a.m C)10a.m D)10.30p.m E)11.30p.m SOLUTION:bus started after 30min ie .5hrs Now, Time=distance/speed ie Time=27/18 during going ie 1.5 hrs now during the return journey speed increasd by 50% so new speed 27mph Time=27/27 ie 1(RETURN journey) so total time=1+.5+1.5=3hrs so the bus will reach at 11am ANSWER:A #### A QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000? options: A)15 B)16 C)18 D)20 E)24 SOLUTION:5,000(1 + x)^10 = 20,000 (1+x)^10 = 4 = 2^2 (1+x)^10 = ((1+x)^5)^2 = 2^2 Therefore, (1+x)^5 = 2 5000(1 + x)^n = 40,000 (1+x)^n = 8 (1+x)^n = 2^3 (1+x)^n = ((1+x)^5)^3 = (1+x)^15 Therefore, n = 15. The answer is A. #### A QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in: options: A)14 hrs B)15 hrs C)10 hrs D)8 hrs E)9 hrs SOLUTION:work done by leak in 1 hr = (1/2-3/7)=1/4 =>14 hrs ANSWER A #### A QUESTION:The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? options: A)s.1014 B)s.1332 C)s.999 D)s.1085 E)s.1020 SOLUTION:a2 = 3136 => a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 ANSWER:B #### B QUESTION:A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price options: A)Rs.500/- B)Rs.510/- C)Rs.515/- D)Rs.720/- E)Rs.540/- SOLUTION:Loss = 80010/100 = 80 S.P = C.P - Loss = 800- 80 =Rs.720/- Answer :D #### D QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is? options: A)180 B)882 C)277 D)261 E)281 SOLUTION:5x + 12x + 13x = 360 => x = 12 a = 60, b = 144, c = 156 S = (60 + 144 + 156)/2 = 180 Answer: A #### A QUESTION:Find the average of first 20 natural numbers? options: A)5.5 B)7.2 C)10.5 D)12.3 E)15.5 SOLUTION:Sum of first n natural numbers = n(n+1)/2 sum of first 20 natural numbers = 2021/2 =210 average = 210/20 = 10.5 Answer is C #### C QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3(20/60) = 7 hr Answer is D #### D QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish? options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84 SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.150.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40. Answer: D. #### D QUESTION:A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ? options: A)-280 B)300 C)-350 D)-380 E)None SOLUTION:In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -. Let x = the sum required. Then according to the statement x + 680 - 80 = 250 And x = -350. Answer C #### C QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example options: A)100 B)610 C)729 D)900 E)1000 SOLUTION:The hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus, 9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D QUESTION:The average of eleven ten prime numbers which are odd is? options: A)17.72 B)18.52 C)19.63 D)16.53 E)15.63 SOLUTION:Explanation: Sum of first 11 prime no. which are odd = 195 Average = 195/11 = 17.72 Answer:A #### A QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? options: A)720 B)760 C)680 D)780 E)880 SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is 10 x 9 x 8 = 720 ANSWER:A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails? options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16 SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin. Using the binary formula and defining a head as a success, P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2 t= 6/16 = 3/8 The answer is therefore (C) #### C QUESTION:8^100 is divisible by 17. Find the remainder? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4 SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 3x - 8x = 144000 - 160000 => -5x = -16000 => x = 32000 So 16800/20000 = 21/25 Answer - B #### B QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:The tax on a commodity is diminished by 10% and its consumption increased by 15%. The effect on revenue is? options: A)2% decrease B)3.5% increase C)9% decrease D)3% decrease E)2% increase SOLUTION:100 * 100 = 10000 90 * 115 = 10350 ----------- 10000-----------350 100-----------? => 3.5% decrease Answer: B #### B QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:The radius of a semi circle is 6.3 cm then its perimeter is? options: A)35.4 cm B)32.4 cm C)32 cm D)30 cm E)35 cm SOLUTION:Explanation: 36/7 r = 6.3 = 32.4 ANSWER IS B #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible? options: A)1200 B)7200 C)2880 D)5760 E)11520 SOLUTION:SSSSS* 5 short presentations can be arranged in 5!=120 ways. As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways. Total = 120106 = 7,200 Ans:B #### B QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet. The number of revolutions = distance/circumference = 5,280x/t. Answer: A. #### A QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:If the positive integer x is a multiple of 1 and the positive integer y is a multiple of 7, then xy must be a multiple of which of the following? I. 7 II. 2 III. 3 options: A)II only B)I and II only C)I only D)II and III only E)I, II, and III SOLUTION:x=1a y=7b xy=7ab where a,b are integers Hence , xy will always be divisible by 7 . C is the answer. #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5 SOLUTION:Note that we have 5positivetemperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits. Answer: B. #### B QUESTION:Find the simple interest on Rs.300 for 9 months at 6 paisa per month? options: A)142 B)152 C)162 D)172 E)182 SOLUTION:I = (30096)/100 = 162 ANSWER:C #### C QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr? options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 160 * 5/18 = 44 m/sec Time taken = 120/44 = 2.7 sec. Answer: C #### C QUESTION:If x+\|x\|+y=4 and x+\|y\|-y=6 what is x+y=? options: A)11 B)-1 C)3 D)5 E)13 SOLUTION:If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0. If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases). Answer: C. Adding both eqn we get 2x +IxI+IyI = 13 Now considering X <0 and y>0 2x-x +y = 13 we get x+y =11 Hence answer should be A #### A QUESTION:E = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33 SOLUTION:The total number of pairs E,B possible is 45=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2. Answer: B. #### B QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 3 * 2 = 24. Answer: D #### D QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Number of ways to form 6-letter code: 10!/4! = 1098765 Number of ways to form 5-letter code: 10!/5! = 109876 Ratio: 5 to 1 Answer : D #### D QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 15 * 15 = 1350 Answer: A #### A QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)2200 B)1897 C)8799 D)2000 E)2782 SOLUTION:P(11/10)4 - P(6/5)2 = 482 P = 2000 Answer: D #### D QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago? options: A)152460 B)214560 C)138214 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5 Answer is C #### C QUESTION:A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black? options: A)4/7 B)3/5 C)5/8 D)2/3 E)3/4 SOLUTION:Each ball has an equal chance (1/9) of being selected fourth. The probability that a black ball is selected fourth is 6/9 = 2/3. The answer is D. #### D QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!2! or 43/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:How many terminating zeroes T does 200! have? options: A) 40 B) 48 C) 49 D) 55 E) 64 SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C QUESTION:A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)287 B)298 C)350 D)726 E)267 SOLUTION:D = 72 5/18 = 25 = 500 – 150 = 350 Answer: C #### C QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 999998 = 472392 Hence option (A). #### A QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:If x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Use answer options to solve this problem - Put x = 2 So, 5x+2y=4 Or, 5(2)+2y=4 Or, 10+2y=4 Or, 2y=4-10;2y=-6 Or, y=-3(y is negative integer) Answer will be (C) #### C QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:200002+8x=1566510 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow. options: A)32 B)36 C)40 D)44 E)50 SOLUTION:Explanation : Explation: Let length of bridge is X then middle of bridge is X/2. and Cow is standing at X/2-5 from the end so After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side. So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10 so remaining distance is 10m the cow is hit before 2m i.e cow covers 8m and train will cover 32 m. Answer : A #### A QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? options: A)3 B)8 C)9 D)6 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 12 = 8 Answer: B #### B QUESTION:The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ? options: A)6 B)8 C)9 D)10 E)12 SOLUTION:Let the number be xy. Given xy – yx = 36. This means the number is greater is than the number got on reversing the digits. This shows that the ten’s digit x > unit digit y. Also given ratio between digits is 1 : 2 => x = 2y (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4. Hence, (x + y) – (x – y) = 3y – y = 2y = 8 B #### B QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:P makes x sprockets per hour. Then Q makes 1.1x sprockets per hour. 880/x = 880/1.1x + 10 1.1(880) = 880 + 11x 11x = 88 x = 8 The answer is D. #### D QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 300 E)None of these SOLUTION:Explanation : T = 2 years R = 10% TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120 TD = (PW × TR)/100 ⇒ 120 = (PW × 2 × 10)/100 ⇒ 1200 = PW × 2 PW =1200/2 = Rs. 600 Answer : Option A #### A QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)% SOLUTION:100 – 12 = 88 88------12 100------? => 11 3/22% ANSWER:A #### A QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60? options: A)200 B)220 C)240 D)322 E)342 SOLUTION:Required Number = (LCM of 15, 30, 45 and 60) + 20 = 180 + 20 = 200 Option A #### A QUESTION:If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Let length of rectangle = L 8^2 = L4 => L = 64/4 = 16 Answer D #### D QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2PD or m - 2PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:In how many ways can the letters of word INTELLIGENT be arranged such that all the vowels as well as all the Consonants always appear together? options: A)9! B)5!4! C)5!5! D)5!4!2! E)4!7!2! SOLUTION:Since all the vowels and consonants have to be together there can only be there are 4! way to order the vowels and 7! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2. So 4!7!2! (E) #### E QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 10 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? options: A)$506.00 B)$726.24 C)$900.00 D)$920.24 E)$926.24 SOLUTION:If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away. Interest earned after the first time interval: $10,0002%=$200; Interest earned after the second time interval: ($10,000+$200)3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$726.24. Answer: B. #### B QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)298 m B)888 m C)120 m D)217 m E)166 m SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? options: A)03 B)4 C)5 D)1 E)7 SOLUTION:You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines. AB , AC BA , BC CA , CB There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB. The lines are: AB, BC and AC ; 3 lines only. So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important. Answer:A #### A QUESTION:If x and y are integers and x + y = 7, which of the following must be true? options: A)x and y are consecutive integers. B)Both x and y are less than 5. C)If x > 0, then y < 0. D)Both x and y are even. E)If x < 0, then y > 0. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option E is right could you explain #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? options: A)356 B)250 C)127 D)279 E)150 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 15 = 250 m Answer: B #### B QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)2777 B)2999 C)2799 D)2781 E)10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? options: A)$ 4 B)$ 8 C)$ 12 D)$ 16 E)$ 432 SOLUTION:Solution Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408 Amount (SI) = P+PTR/100 = 5000+(500018/100)=5400 Difference = 5408-5400=8 $ ANSWER:B #### B QUESTION:If you have 4 New Year greeting cards and you want to send them to 2 of your friends, in how many ways can this be done? options: A)360 B)12 C)16 D)24 E)None SOLUTION:Solution We have to find number of permutations of 2 objects out of 4 objects. This number is 4P2=4(4-1)=43=12 Answer B #### B QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:The average mark of the students of a class in a particular exam is 90. If 2 students whose average mark in that exam is 45 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam? options: A)10 B)40 C)20 D)30 E)25 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 90 x. Total marks of (x - 2) students = 95(x - 2) 90x - (2 * 45) = 95(x - 2) 100 = 5x => x = 20 Answer: C #### C QUESTION:If SAGE is coded as 4657 and COT is coded as 333. How is GATE coded? options: A)5637 B)5367 C)5763 D)6573 E)6753 SOLUTION:g-5 a-6 e-7 from the code gate t - 3 from bat ANSWER:A #### A QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation : Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer : Option C #### C QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? options: A)months B)months C)months D)months E)months SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 ANSWER:D #### D QUESTION:A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? options: A)29% B)17% C)44% D)46% E)21% SOLUTION:g% = 10 + 10 + (1010)/100 = 21% Answer: E #### E QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:If the speed of a man is 54 km per hour, then what is the distance traveled by him in 25 seconds ? options: A)275m B)360m C)375m D)420 m E)440 m SOLUTION:The distance traveled in 25 sec = 54(5/18) 25 =375m ANSWER:C #### C QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice. options: A)25 B)34 C)50 D)67 E)100 SOLUTION:A =25 1 oz concentrate + 3 oz ofwater = 4 oz jucie 300 oz concentrate +900 oz of waer = 1200 oz juice no of cans==300/12=25 Ratio of juice to water ===> 1:3 total 2006 ounces 12 ounce juice cans ==> 1200/12 == 1001/4 (ratio of jiuce to total) == 25 #### A QUESTION:The speeds of 3 trains in the ratio 10:15:20. The ratio between time taken by them to travel the same distance is? options: A)6:4:3 B)1:2:3 C)4:8:9 D)6:5:2 E)4:8:7 SOLUTION:Ratio of time taken is = 1/10 : 1/15 : 1/20 = 6:4:3 Answer is A #### A QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100? options: A)1345 B)1576 C)2475 D)2578 E)1895 SOLUTION:numbers are 11,13,15-------,97,99 Average of the set: (largest+smallest)/2=(99+11)/2=55; # of terms: (largest-smallest)/2+1=(99-11)/2+1=45 The sum = 4555= 2475 Answer: C #### C QUESTION:Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)s.10 B)s.2 C)s.5 D)s.3 E)s.4 SOLUTION:2500 = D(100/4)2 D = 4 ANSWER:E #### E QUESTION:8k8 + k88 -------- 1,6t6 If k and t represent non-zero digits within the integers above, what is t? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16t6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8+7=16* or 8+8=16 (k can not be less than 7 or 9, as the result won't be 16). After that it's easy to get that k=7 and t=6. Answer: A. #### A QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint T, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Answer:D #### D QUESTION:The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number? options: A)40 B)45 C)55 D)45 E)50 SOLUTION:a1 = 120/3 = 40 a2 = a1 -5 = 35 sum of second list = 353 = 105 therefore the number = 105 -60 = 45 D #### D QUESTION:Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:How many integers between 263,205and 658,805 have tens digit 1 and units digit 3? options: A)3,955 B)3,925 C)3,956 D)3,926 E)3,915 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ... The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956 Answer:C. #### C QUESTION:There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)3/4 E)2/3 SOLUTION:total 8 from take one. 8c1=8 red 6 from one 6c1=6 6/8=3/4 ANSWER:D #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers. NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations. The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 560/60 = 51/1 = 5 New time in minutes to cross 5 miles stretch = 560/40 = 53/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be options: A)21 B)5193 C)77 D)9275 E)19 SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!. So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!. So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320) So remainder is 5193. Answer:B #### B QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7][8] = ? options: A)[22] B)[44] C)[75] D)[88] E)[90] SOLUTION:[7][8]=(72+1)(8/2+1) =[75]. Ans -C #### C QUESTION:A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)500m C)C)650m D)D)750m E)E)1200m SOLUTION:Relative speed of the policeman = 20-16 = 4 km/hr time taken by policeman to cover 300m = (300/1000)(1/4) = 3/40 hr In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m Answer is E #### E QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. options: A)180 B)181 C)182 D)178 E)168 SOLUTION:add the max weights 52+50+78=180 ANSWER:A #### A QUESTION:A day-trader plans to invest a total of $23,600 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$4,000 C)$3,500 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,600 So, the HUNDREDS DIGITS of the 15th investment must be 0 Answer: B #### B QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:If x-y=8, which of the following must be true? I. Both x and y are positive II. If x is positive, y must be positive III. If x is negative, y must be negative options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:The best way to approach such questions is to plug in values for x and y Given: x-y=8 I. Both x and y are positive: Let x=10 and y=2 x-y=8 But, Let x=6 and y=-2 x-y=8 Therefore, NOT TRUE II. If x is positive, y must be positive Let x=10 and y=2 x-y=8 But, Let x = 6 and y=-2 x-y=8 Therefore, NOT TRUE III. If x is negative, y must be negative If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number! Therefore, TRUE Ans: 'C' #### C QUESTION:Convert the 8/36 m/s into kilometers per hour? options: A)0.8 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:8/36 m/s = 8/36 * 18/5 = 8/10 = 0.8 kmph. Answer: A #### A QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: options: A)173 m B)200 m C)273 m D)300 m E)None of these SOLUTION:xplanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, <ACB = 30º and <ADB = 45º. AB/AC=tan30 Answer: C #### C QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:G 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11 5811 =440 So the remainder will be the remainder of 440/14 which is 6 Ans A #### A QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26Ã—72Ã—5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E QUESTION:If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p? options: A)(p+1)/p B)(p - 1)/p C)p/(p + 1) D)p/(1-p) E)(1 - p)/p SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: D #### D QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 16 boys and 44 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic. Table method is shown above; here is how you will use logic: There are 6 happy boys. There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys. We have 6 happy boys and 6 sad boys. Total we have 16 boys. So 16 - 6 - 6 = 4 boys must be neither happy nor sad. Answer (B) #### B QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:A student completes a 3 part exam as follows. The student completes sections A in 6 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour? options: A)7:1 B)9:2 C)8:3 D)5:2 E)6:1 SOLUTION:The time spent on section B and section C is 27 minutes each. The ratio of C to A is 27:6 = 9:2 The answer is B. #### B QUESTION:Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of the interest. If she paid Rs. 432 as interest at the end of the period,what was the rate of interest ? options: A)3.6 B)6 C)18 D)Cannot be determined E)None SOLUTION:Solution Let rate = R% and time = R years.Then, (1200xRxR/100)= 432 = 12R2= 432 = R2=36 =R = 6 Answer B #### B <<<Examples ends QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? options: A)7 B)7.5 C)8 D)8.5 E)9 SOLUTION:The sum of the numbers is 69 = 54 K+M = 54 - 13 - 8 - 8 - 7 = 18 Since K ≠ M, K and M do not equal 9. Thus one of the two numbers is 8 or less and one is 10 or more. Then middle two numbers in the set are 8 and 8. The median is 8. The answer is C. #### C QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) â€“ 24009 ] = Rs. (27000 â€“ 24009) = Rs. 2991. Answer B #### B QUESTION:If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? options: A)s.575 B)s.595 C)s.590 D)s.580 E)s.585 SOLUTION:80 = (4504R)/100 R = 5% I = (45065)/100 = 135 450 + 135 = 585 ANSWER:E #### E QUESTION:If 1535/1038 = a +1/[b+1/{c+(d+1/e)}]. Find abcde? options: A)165/2 B)175/2 C)178/3 D)187 by 2 E)197/2 SOLUTION:by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)} =1+(497/1038) now a=1 =1+{1/(1038/497)} =1+{1/(2+42/497)} =1+{1/ (2+1/(497/42)} now b= 2 similarly expand c=11 d= 1 e=34/8 finally ab bcde 1211134/8 187/2 ANSWER:D #### D QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares. What is the smallest element of S which is divisible by 17? options: A)255 B)355 C)522 D)355 E)664 SOLUTION:Each element of S can be written in the form (x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8 = 5x2 + 10 = 5(x2 + 2) where x is some positive integer with x 3. By iterating over values of x, we observe that when x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement. Hence, the solution is 5(x2 + 2) = 5 51 = 255 correct answer A #### A QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica? options: A)48 B)47 C)46 D)49 E)52 SOLUTION:let their ages are 9x,15x and 25x respectively. difference between the ages of Patrick and Monica = 25x-9x=16x where 49x=147 or x=3 so diff in ages = 16x=163=48 yrs ANSWER:A #### A QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? options: A)28 B)10 C)28 D)27 E)13 SOLUTION:4/12 + x/15 = 1 x = 10 Answer:B #### B QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:How many integers less than 100 have exactly 4 odd factors but no even factors? options: A)11 B)13 C)15 D)17 E)19 SOLUTION:Two cases are possible: x1y1=xy=odd<100x1y1=xy=odd<100, where xx and yy are odd prime numbers, then # of factors will be (1+1)(1+1)=4(1+1)(1+1)=4; If x=3, then y can be: 5, 7, 11, 13, 17, 19, 23, 29, 31 - 9 numbers. If x=5, then y can be: 7, 11, 13, 17, 19 - 5 numbers. If x=7, then y can be: 11, 13 - 2 numbers. OR: x3=odd<100x3=odd<100, where xx is odd prime number, then # of factors will be (3+1)=4(3+1)=4. x can be only 3 - 1 number. Total 9+5+2+1=179+5+2+1=17 . Answer: D. #### D QUESTION:If f(x)= 5x^2- 2x+6 and g(y)= 3y-8, then g(f(x)) options: A)82x^2-9x+38 B)15x^2-6x+10 C)58x^2-4x+58 D)87x^2-5x+96 E)98x^2-7x+94 SOLUTION:g(f(x))=3(5x^2-2x+6)-8 =15x^2-6x+18-8 =15x^2-6x+10 the answer is B #### B QUESTION:I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? options: A)280 B)670 C)230 D)67 E)120 SOLUTION:A x(85/100) = (480 - x)119/100 x = 280 #### A QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669 SOLUTION:they invested in the ratio 1:2 a's share =1/35000=1666 b's share=2/35000=3333 ANSWER:C #### C QUESTION:What is the maximum number of points that 10 circles of different radii intersect? options: A)24 B)26 C)33 D)90 E)100 SOLUTION:the maximum number of points that two circles intersect is two. therefore, each of these 10 circles intersect two point with each of the other 9 circles. as a consequence, the number of these points is equal to two times the number of combination of the 10 circles. 2∗(10!)/(2!∗10!)=90 Answer: D #### D QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)1/10=80.5+7.51/10 80.5+0.75=81.25 E #### E QUESTION:If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be options: A)2 B)4 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 411025 = 44, 100, which is a square of 210 B #### B QUESTION:How much is 90% of 40 is greater than 4/5 of 25? options: A)29 B)776 C)66 D)16 E)99 SOLUTION:(90/100) * 40 – (4/5) * 25 36 - 20 = 16 Answer: D #### D QUESTION:Johnop went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ? options: A)3 km B)6 km C)4.5 km D)km E)none of the above SOLUTION:Assume the distance to the top of the hill (1 way) as: x Now, speed=distance/time => time=distance/speed So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5. For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5 Now, the total time for the trip is given as 4 hrs. Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km So, the distance one side is = 4.5 km. The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km Can someone assist me in understanding where am I wrong here? #### C QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (22) + (11) + (1/31/3) = 46/9 Proportion of work done by B = (11) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4332211 = 144 ways E #### E QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail? options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27 SOLUTION:Probability of getting least one tail at the coin tossed five times. = There is not even a single tail. = 1/32 ; P(T) = 1 - 1/32 = 31/32 ANSWER B #### B QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State? options: A)7000 B)7200 C)7400 D)7600 E)8000 SOLUTION:State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 E) #### E QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5760 lr B)6000 lr C)6500 lr D)4000 lr E)4500 lr SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 4 = 5760 ANSWER A #### A QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:A batsman had a certain average of runs for 16 innings. In the 17th innings, he made a score of 87 runs thereby increasing his average by 3. What is his average after 17 innings? options: A)39 B)88 C)266 D)278 E)221 SOLUTION:Explanation: Assume his initial average = xx His total runs after 16 innings = 16xx After scoring 87 runs his average got increased by 3 to xx + 3 So his total runs after 17 innings = 17 × (xx+3) But it was given that the difference in the total scores after 16 innings and 17 innings = 87 Therefore 17×(x+3)−16x=87⇒x=3617×(x+3)−16x=87⇒x=36 His new average = 36 + 3 = 39 Answer:A #### A QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end? options: A)1,790 B)52 C)2,880 D)98 E)2,560 SOLUTION:Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 46! = 2,880. Answer: C. #### C QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)6 E)5 SOLUTION:2x x = 128 => x= 8 Answer: A #### A QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10987) ==> 5040 ANSWER A #### A QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of the couple and a child, who was born during the interval, is 22Yrs now. How old is the child now ? options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these SOLUTION:(a+b-6-6)/2=26; a+b=64; a+b+c/3=22; solving both c=2 ANSWER:A #### A QUESTION:The side of a cube is 8 m, Find the voiume? options: A)515 B)509 C)502 D)508 E)512 SOLUTION:Cube Volume = a(power)3 a(power)3 = 8(power)3 = 512 m(power)3. Answer is E. #### E QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 45678=6720. ANS:A #### A QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!2!)= 15 ways 4815=720 ANSWER:E #### E QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(5044)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/360/55 = 40 min D #### D QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder? options: A)11 B)13 C)15 D)Data inadequate E)None of these SOLUTION:Number= (31 * Q)+ 29. Given data is inadequate. Answer: D #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)17.6% E)None of these SOLUTION:Explanation: cost price = (225 + 30) = 255 sell price = 300 gain = (45/255)100 = 17.6%. Answer: D #### D QUESTION:If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is options: A)48 km B)50 km C)40 km D)22 km E)70 km SOLUTION:B 50 km. Let the actual distance travelled be x km. Then x/10=(x+20)/14 --> 14x = 10x + 200 --> 4x = 200 --> x = 50 km. #### B QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)12 B)15 C)20 D)24 E)30 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 60 / (60+x) = 4/5 x = 15 The answer is B. #### B QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day? options: A)68 B)69 C)70 D)67 E)76 SOLUTION:let total no of hrs = x they have done 24+17=41 40% of x is 40/100=2/5 x=41+2x/5 x=68.3 ANSWER:A #### A QUESTION:Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 7.5 km apart, if they walk in the same direction? options: A)12 hrs B)14 hrs C)15 hrs D)17 hrs E)None SOLUTION:Sol. to be 0.5 km apart, they take 1 hour. To be 7.5 km apart, they take [1/0.5 7.5] hrs = 15 hrs. Answer C #### C QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. options: A)Rs. 610 B)Rs. 612 C)Rs. 614 D)Rs. 616 E)None of these SOLUTION:Explanation: Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112 So compound interest = (8112 - 7500) = 612 Answer: B #### B QUESTION:The largest 4 digit number exactly divisible by 88 is? options: A)9930 B)9936 C)9944 D)9952 E)9960 SOLUTION:Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944. C) #### C QUESTION:15 + sqrt(- 6 + 8Ã—5Ã·4) =? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:According to order of operations, inner brackets first where 8x5Ã·4 is first calculated since it has a multiplication and a division. 8x5Ã·4 = 40Ã·4 = 10 Hence 15 + sqrt(- 6 + 8Ã—5Ã·4) = 15+ sqrt(- 6 + 10) = 15 + sqrt(4) = 15 + 16 = 31 correct answer A)31 #### A QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.? options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454 SOLUTION:it is given that last 3 digits are randomly dialed Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability = 1/(10)3 = 1/1000 C #### C QUESTION:How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)12 sec B)30 sec C)36 sec D)16 sec E)18 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 600 * 3/50 = 36 sec. Answer: C #### C QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water? options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11 SOLUTION:First mixture: milk and water in the ratio of 3x:4x. Second mixture: milk and water in the ratio 5y:2y. We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3. Answer: A. #### A QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? options: A)26 B)30 C)34 D)38 E)42 SOLUTION:The first number is 22 = 16+6(1). We can continue adding 6 to make a list: 22, 28, 34,... The last number is 196 = 16+6(30) There are 30 numbers in the list. The answer is B. #### B QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(490+x)/5=92 x=(592)-(490) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element? options: A)27 grams B)28 grams C)29 grams D)42 grams E)32 grams SOLUTION:Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 25 grams 25/7 = 3.571... C. 29 grams 29/7 = 4.142....... D. 42 grams 42/7 = 6 E. 32 grams 32/7 = 4.571.... Hence our answer will be (D) #### D QUESTION:A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)2 hours B)5 hours C)6 hours D)8 hours E)3 hours SOLUTION:Number of pages typed by A in one hour=32/6=16/3 Number of pages typed by B in one hour=40/5=8 Number of pages typed by both in one hour=((16/3)+8)=40/3 Time taken by both to type 110 pages=1103/40=8 hours. Answer : D. #### D QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C55C3 = 42 5 = 210 ANS:C #### C QUESTION:If 8 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:8M + 2B = 4(1M + 1B) 8M + 2B = 4M + 4B 4M = 2B The required ratio of work done by a man and a boy = 2:4=1:2 D #### D QUESTION:Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is? options: A)100% B)50% C)180% D)200% E)150% SOLUTION:Let the total original sale be $1000 Then original number of visitors = 100 New number of visitors = 1400/5 = 280 Increase % = 180% Answer is C #### C QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 8 as quotient and the 15 as remainder options: A)1235 B)1557.9 C)1378 D)1635 E)1489 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 8x + 15 7x = 1350 x = 192.9 Large number = 192.9+1365 = 1557.9 B #### B QUESTION:Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn drive? options: A)26 miles B)16 miles C)20 miles D)18 miles E)17 miles SOLUTION:1/2 x 128 = 64 miles Mark drove 1/4 x 128 = 32 miles Justin drove 64 + 32 = 96 miles driven 128 - 96 = 32 miles left 32 ÷ 2 = 16 miles driven by Kaitlyn correct answer B #### B QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)20, 35, 48 E)None of these SOLUTION:Let the present ages are 4x, 7x, 9x. => (4x-8) + (7x-8) + (9x-8) = 56 => 20x = 80 => x = 4 So their present ages are: 16,28,36 ANSWER:B #### B QUESTION:courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose? options: A)22 B)77 C)877 D)99 E)88 SOLUTION:3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters=525 cm = 5 × 5 × 3 × 7 Hence common factors are 3 and 7 Hence LCM = 3 × 7 = 21 Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm. Answer:B #### B QUESTION:A man buys an article and sells it at a profit of 10%. If he had bought it at 10% less and sold it for Rs.55 less, he could have gained 15%. What is the cost price? options: A)197 B)375 C)846 D)278 E)268 SOLUTION:CP1 = 100 SP1 = 110 CP2 = 90 SP2 = 90 * (115/100) = 103.5 6.5 ----- 100 55 ----- ? => 846 Answer:C #### C QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present? options: A)63 B)64.5 C)62.5 D)60.5 E)60 SOLUTION:Let required number of buckets =x If capacity of buckets are reduced, more number of buckets are required (indirect proportion). Therefore, 25:x=(2/5):1 ⇒25=2x/5 ⇒x=62.5 Answer: C #### C QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:(x —1)(x + 3) > 0 (x +5)(x—4) < 0 Which of the following values of x satisfy both inequalities shown? I. -6 II. -4 III. 2 IV. 3 options: A)I and II only B)I and III only C)II and III only D)II and IV only E)II, III, and IV SOLUTION:(x - 1)(x + 3) > 0 --> x<-3 or x>1. (x + 5)(x - 4) < 0 --> -5<x<4. Among choices only -4 and 2 satisfy both inequalities. Answer: E. #### E QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was? options: A)10 years B)12 years C)14 years D)16 years E)17 years SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. E #### E QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9.33% B)9.44% C)9.45% D)9.56% E)9.67% SOLUTION:69(90/100)((100-x)/100) = 56.16 x = 9.56% ANSWER:D #### D QUESTION:In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is : options: A)23 B)37 C)28 D)40 E)50 SOLUTION:Explanation: Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b) Fail in Hindi or English = 25 + 50 â€“ 25 = 50 Therefore students who passed = 100 â€“ 50 = 50. Answer: E #### E QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this?? options: A)360 B)430 C)510 D)540 E)630 SOLUTION:we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives. then we have to arrange 3 different sets in 3! ways. so, 5c14c13c13!=360 ANSWER:A #### A QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 1304=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours * 1 choices = 1C11C1 = 11=1=D #### D QUESTION:If (x - 1)(x - 2) = x^2 + x, what is a possible value of x? options: A) 1/2 B) 2 C) -1 D) 1 E) -2 SOLUTION:Rearranging the given expression: (x - 1)(x - 2) = x^2 + x i.e. x^2 - 3x + 2 = x^2 + x i.e. -4x = -2 i.e. x = -4/-2 = 2 Answer: Option B Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible #### B QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 * 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is? options: A)10 B)12 C)19 D)18 E)20 SOLUTION:SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19 C #### C QUESTION:A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? options: A)299m B)287m C)279m D)100m E)277m SOLUTION:A can give B (5 min - 4 1/2 min) = 30 sec start. The distance covered by B in 5 min = 1000 m. Distance covered in 30 sec = (1000 * 30)/300 = 100 m. A can give B 100m start. Answer:D #### D QUESTION:If 15648 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box? Options: 8 options: A)12 books B)6 books C)24 books D)18 books E)5 books SOLUTION:The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 15648. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 15648 =24 and 18 is divisible by 9. Hence, we need to remove 6 to this number for it to be divisible by 9 Correct Option:B #### B QUESTION:If \|4x+6\| = 50, what is the sum of all the possible values of x? options: A)2 B)-2 C)4 D)-3 E)6 SOLUTION:There will be two cases 4x+6= 50 or 4x+6 = -50 => x =11 or x= -14 sum of both the values will be -14 +11 = -3 Answer is D #### D QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1? options: A)$0.75 B)$1.00 C)$1.25 D)$1.50 E)$1.75 SOLUTION:Salary grade of 4 is p(4)=9.50+0.25(4–1)=9.50+0.253; Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50; p(4)-p(1)=9.50+0.254-9.50=0.75. Answer: A. #### A QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.61.2^3 = 1.0368 The answer is E. #### E QUESTION:At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? options: A)7 B)7/15 C)5/8 D)9/2 E)4/6 SOLUTION:Yellow: Blue = 3:2 Let Yellow = 3x and Blue = 2x 1/3 of Yellow are left handed => 1/3 3x = 3x/3 Yellow left handed 2/3 of Blue are left handed => 2/3 2x = 4x/3 blue left handed fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15 Answer : B #### B QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)13 8/3 days B)13 1/3 days C)13 6/3 days D)63 1/3 days E)13 5/3 days SOLUTION:5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B #### B QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7 SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively. Then, (4.5x - 4)/(3x + 4) = 1/1 1.5x = 8 => x = 5.33 Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D QUESTION:A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ? options: A)7 B)2 C)9 D)2 E)8 SOLUTION:B 2 Relative speed = 2 + 3 = 5 rounds per hour. So, they cross each other 5 times in an hour and 2 times in half an hour. Hence, they cross each other 2 times before 8.30 a.m. #### B QUESTION:Which of the following equations has a root in common with x^2−4x+3=0 ? options: A)x^2-4x-4=0 B)x^2-2x+1=0 C)x^2-x-1=0 D)x^2-10x-1=0 E)x^2+1=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-3) = 0 so the two roots are 1 and 3. Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get -7; Putting 3 we get -7. Reject this option. (B) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. B is the answer. #### B QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N? options: A)107 B)331 C)511 D)691 E)871 SOLUTION:N/P=10 7/P= 20P+7 N/(P+2)=15 2/(P+2)=15P+30+2 solving these two equations we get P=5 N= 107 answer is A. #### A QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:What should come in place of the question mark (?) in the following equation? 45789+ 34567 = 610+ ? options: A)96543 B)13678 C)23456 D)56789 E)79746 SOLUTION:45789+ 34567 = 610+ ? 45789+ 34567 – 610 = 79746 Answer E #### E QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(Ã¢â‚¬â€œ4) 5 (Ã¢â‚¬â€œ4)1 #### A QUESTION:The fourth proportional to 5, 8, 15 is: options: A)15 B)5 C)24 D)8 E)28 SOLUTION:Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x = 5x = (8 x 15) x = (8 x 15)/5= 24. Answer is C. #### C QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:The number of arrangements that can be made with the letters of the word MEADOWSS so that the vowels occupy the even places? options: A)14 B)144 C)720 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways. Hence the total ways are 120 * 6 = 720. Answer:C #### C QUESTION:Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's? options: A)96% B)51.1% C)90% D)52.1% E)None of these SOLUTION:Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125. Then Vicky's salary = 175. Vicky's salary after rise of 40% = 245. [As 10% of Vicky's salary is 17.5 then 40% = 17.54 = 70] . Difference between Vicky's salary and Ashu's salary = 245-125 = 120; . % more Vicky's salary than Ashu's = 120100/125 = 96%. Answer: Option A #### A QUESTION:A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge? options: A)$40,000 B)$45,000 C)$50,000 D)$55,000 E)$60,000 SOLUTION:The customer receives $75 for the first $5000. The customer receives $125 for the next $5000. Let x be the total amount of the customer's annual charge. $200 + 0.03(x-10,000)=0.028x 0.002x=100 x=50,000 The answer is C. #### C QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D QUESTION:Hiralal gave a loan of Rs. 20 to Ramlal and recovered it at the rate of Rs 3.50 for eight months, commencing from the end of 1st month. What is the effective rate of simple interest? options: A)60% B)80% C)20% D)90% E)none SOLUTION:Explanation: Principal = Rs 20 Amount = Rs 3.50 x 8 = Rs 28 Interest = Rs 28 - Rs 20 = Rs 8 Time = 8 months = 8/12 years 8 = 20×8×r/12×100 r = 12×100/20 = 60% p.a. Answer A #### A QUESTION:Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)- 10% B)- 16 2/3 % C)- 52.38% D)- 25% E)- 183 1/3% SOLUTION:Assume 100 enrollments present in 1990 210 % of 1990 = enrollments on 1980 enrollments on 1980 = 210 % change = (enrollment in 1990 - enrollment in 1980)100/(enrollment in 1980) =(100 - 210) 100 / 210 = -11000 / 210 = - 52.38 % Ans - C #### C QUESTION:20 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)200 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 19 people 2nd person will shake hand with 18 people 3rd person will shake hand with 17 people ...... total no. of handshakes = 19+18+17+...+3+2+1 = 19(19+1)/2 = 190 or, if there are n persons then no. of shakehands = nC2 = 20C2 = 190 ANSWER:A #### A QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:850 - (1500 ÷ ?) × 8/15 = 770 options: A)A)31 B)B)10 C)C)15 D)D)26 E)E)17 SOLUTION:Explanation: => 850 - (1500 ÷ ?) × 8/15 = 770 => 850 - 770 = (1500 ÷ ?) × 8/15 => 80 = (1500 ÷ ?) × 8/15 => 80 × 15/8 = (1500 ÷ ?) = 150 => 1/? = 150/1500 = 1/10 => ? = 10 Answer: Option B #### B QUESTION:If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? options: A)20 % B)10 % C)15 % D)22 1/2% E)21% SOLUTION:Explanation: 9 = (140R)/100 R = 22 1/2 % ANSWER IS D #### D QUESTION:An inspector rejects 0.06% of the meters as defective. How many will he examine to reject 2? options: A)A)1500 B)B)2000 C)C)2500 D)D)3000 E)E)3333 SOLUTION:Let the number of meters to be examined be x Then, 0.06% of x = 2 (6/100)((1/100)*x = 2 x = 3333 Answer is E #### E QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x? options: A)(1-x)/x B)(x - 1)/x C)x/(x + 1) D)(x + 1)/x E)x/(1-x) SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: E #### E QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A <<<Examples ends QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty? options: A)36 B)39 C)42 D)48 E)24 SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS. We're told 3 facts about the relative ages of 3 people: 1) Carol's age is 4 times Alice's age 2) Carol's age is 2 times Betty's age 3) Carol is 36 years older than Alice We're asked for BETTY'S age. Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first. IF.... Betty = 24 Then Carol = 2(24) = 48 Then Alice = 48 - 36 = 12 AND 48/4 =12 All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24 E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)x = 240 => x = (240 100)/60 = 400 Answer B #### B QUESTION:Solve 8x – 4 = 4x + 11 options: A)5(1/3) B)6(1/3) C)7(1/3) D)3(3/4) E)9(1/3) SOLUTION:Sol. 8x – 4 = 4x + 11 => 8x – 4x = 11 + 4 => 4x = 15 => x = 15/3 = 3(3/4). Answer D #### D QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches? options: A) 40 B) 60 C) 80 D) 100 E) 120 SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other. And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E. so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A. Now we are left with is B #### B QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ? options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550 SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040 Which is 100 - 20 = 80% of his monthly salary ∴ His salary = 10040x100/80 = 12550 Answer : E #### E QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ? options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 19 x 13 ) / (19 +13 ) km/hr. = 15 km/hr. Correct Option: A #### A QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)1110! B)98! C)87! D)76! E)65! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=1110! Ans:A #### A QUESTION:39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)9 B)12 C)10 D)13 E)15 SOLUTION:Explanation: Let the required number of days be x More persons, less days (indirect proportion) More hours, less days (indirect proportion) Hence we can write as (persons)39:30 (hours) 5:6}:: x:12 ⇒39×5×12=30 × 6 × x ⇒39×5×2=30 × x ⇒39=3×x ⇒x=13 Answer: Option D #### D QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase? options: A)$32 B)$50 C)$320 D)$400 E)$500 SOLUTION:Property tax as a percentage of its assessed value = 8% Increase in assessed value of the property = 24000 - 20000 = 4,000 $ Increase in property tax = (8/100)* 4000 = 320 $ Answer C #### C QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? options: A)x B)(85/12)x C)(85/24)x D)(85/36)x E)(85/48)x SOLUTION:Let Q be the number of homework questions. Q = 4Q/5 + (5/17)(Q/5) + x Q = 68Q/85 + 5Q/85 + x 12Q/85 = x Q = (85/12)x The answer is B. #### B QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10 SOLUTION:The total possible choices are 12C3 = 220 The ways to choose 3 apples: 6C3 = 20 The ways to choose 2 apples: 6C2 6C1 = 90 P(at least 2 apples) = 110/220 = 1/2 The answer is A. #### A QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes SOLUTION:A method has been discussed here to nullify the calculations though. All I can input here is, speed of a crew in still water = 1/2 ( speed upstream + speed downstream) approximating this for time, t = 1/2(84+ (t-7)) giving t = 77 C #### C QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? options: A)126 B)120 C)101 D)112 E)115 SOLUTION:8 shirts 9 pants we can combine 2 shirts with (12-3) pants 29=18 we can combine the other shirts (6) with any pants (9) 912=54 Thus total :108+18=126 ANS:A #### A QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|C\| = -c \|b - 4\| + \|ab - b\| = ? options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab - b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab - b =ab - 2b + 4 Answer: Option B #### B QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10987) ==> 5040 ANSWER A #### A QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is? options: A)0.8% B)8.3% C)0.3% D)2.3% E)0.4% SOLUTION:(1500 R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350 R1 - R2 = 0.3% Answer:C #### C QUESTION:The girl child birth in a town is 40% of boy child birth. What is the number of boy child as a percentage of girl child birth? options: A)150% B)250% C)125% D)35% E)65% SOLUTION:The number of girl child birth in a town is 40% of boy child birth If the boy child birth=10 Girl child birth=4 We are asked to find the number of boy child birth as a percentage of girl child birth B/G=10/4=2.50=250% Answer is B #### B QUESTION:Sum of 42 odd numbers is? options: A)1764 B)1774 C)1784 D)1794 E)1754 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 42 odd numbers = 42^2 = 1764 ANSWER:A #### A QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock? options: A)20029 B)22500 C)20289 D)20027 E)20026 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 450 => x = 22500 Answer: B #### B QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long? options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec SOLUTION:D = 25 * 60 + 1200 = 2700 m T = 2700/60 * 18/5 = 162 sec ANSWER:C #### C QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents SOLUTION:Solution: 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. Answer: A #### A QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:If the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)7 E)18 SOLUTION:Let length of rectangle = L 5^2 = L4 => L = 25/4 = 7 Answer D #### D QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 5x Hence, a1+a2+..+a20+n = 25x So, the fraction asked = 5x/25x = 1/5 Answer C #### C QUESTION:There are 3 people and 3 chairs. In how many different ways people can occupy the chairs? options: A)6 B)15 C)24 D)36 E)120 SOLUTION:number of ways =3! = 6 Answer is A #### A QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? options: A)600 B)2877 C)208 D)1882 E)191 SOLUTION:Explanation: Cost price = Rs.500 profit = 20% of 500 = Rs.100 Selling price = Cost price + Profit = 500 + 100 = 600 Answer:A #### A QUESTION:If P = Q/R, -1 < R < 0 and 4 < Q, which of the following is correct? options: A)P > 4. B)0 < P <4. C)-4 < P < 0. D)P < -4. E)P < -20. SOLUTION:Q is +veR is -ve Eliminate AB For min. value max. numerator and minimize dinominator take Q=4.1P=-0.9 P=4.1/-0.9 P<-4 Ans D #### D QUESTION:The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 300 E)None of these SOLUTION:Explanation : T = 2 years R = 10% TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120 TD = (PW × TR)/100 ⇒ 120 = (PW × 2 × 10)/100 ⇒ 1200 = PW × 2 PW =1200/2 = Rs. 600 Answer : Option A #### A QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? options: A)404 B)452 C)444 D)468 E)422 SOLUTION:312 + 222 - 112 (since 112 is counted twice )= 422 E is the answer #### E QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.) options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08{weight of grapes}=0.8{weight of raisins} --> 0.08x = 0.810 --> x = 100. Answer: D. #### D QUESTION:Machine W can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: W makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Explanation: Let the son's present age be x years. Then, woman's present age = (x + 18) years => (x + 18) + 4 = 2(x + 4) => x + 22 = 2x +8 So, x = 14 Answer: B #### B QUESTION:If xy > 0, which of the following must be negative? options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y SOLUTION:- / + = - Answer : C #### C QUESTION:If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent? options: A)11.2% B)10.2% C)12.2% D)13.2% E)18.2% SOLUTION:$632.40 = (31002R)/100 R = 10.2% Answer: B #### B QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? options: A)30 min B)35 min C)45 min D)50 min E)55 min SOLUTION:there are 9 hours in between 9 a.m. to 6 p.m. 95=45 minutes. ANSWER:C #### C QUESTION:A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? options: A)3 B)4 C)2 D)9 E)12 SOLUTION:Rate of machine R =1/8 Rate of machine S =1/4 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/8 +x/4 =1/2 3x/8=1/2 x=8/6=1.3=2 So no of machine R is 2 Answer C #### C QUESTION:The smallest 2 digit prime number is? options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None SOLUTION:The smallest 3-digit number is 10, which is divisible by 2. 10 is not a prime number. 11 is a prime number. Hence 11 is the smallest 2-digit prime number. A) #### A QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr? options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 160 * 5/18 = 44 m/sec Time taken = 120/44 = 2.7 sec. Answer: C #### C QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions. = 1500 * 2 * 22/7 * 22.4 = 211200 cm = 2112 m Answer: A #### A QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? options: A)2200 B)2550 C)5050 D)6275 E)11325 SOLUTION:Set A contains 8, 10, 12... 50 Set B contains 108 , 110 , 112 ... 150 Number of terms in each set = 22 Difference between corresponding terms in set A and B = 100 Difference between Sum of set B and set A = 10022 = 2200 Answer A #### A QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? options: A)64 B)128 C)151 D)216 E)256 SOLUTION:65 small cube will make a large cube with 4 cubes in each line i.e. Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line. Total number of small cubes in new cube = 6^3 = 216 Extra cube required = 216 - 65 = 151 Hence, C is the answer. #### C QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word â€˜POWERâ€™ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 54321 = 120 ANSWER:E #### E QUESTION:A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? options: A)70 B)52 C)62 D)59 E)50 SOLUTION:total number of players= 16+12+18+13= 59 Answer is D #### D QUESTION:Two cars cover the same distance at the speed of 50 and 61 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)273 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 61x X = 4.55 60 * 4.55 = 273 km ANSWER:B #### B QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h? options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these SOLUTION:Explanation: Let the length of the train be L. Then, => (450 + L)/42 = (650+L)/50. => L= 600 m. Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25(18/5) = 90 Km /hr. ANSWER IS A #### A QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 7 women? options: A)A)84 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C37C2 = 421 = 84 Answer is A #### A QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work? options: A)10 B)12 C)22 D)28 E)20 SOLUTION:A can do the work in 60/4 i.e., 15 days. A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12 So A and B together can do the work in 12 days. Answer: B #### B QUESTION:In case O is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)P and Q E)T and U SOLUTION:P and Q should serve on A ANSWER:D #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year? options: A)10% B)16% C)70% D)80% E)20% SOLUTION:Let the rate of interest during the second year be R%. Given, 4500 {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A #### A QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it? options: A)(y+1)/2 B)(y-1)/2 C)y/(2+1) D)y/(2-1) E)y/2 SOLUTION:Lets put values for y, say y=8 since it's even and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms so putting y=8 in the options, option E = y/2 => 8/2 = 4 , the number of negative integers So, E is the answer #### E QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:What percent of 200 is 55? options: A)0.25% B)4% C)25% D)27.5% E)250% SOLUTION:200x /100 = 55 x = 27.5 Ans: D #### D QUESTION:575.104 x 15.98 Ã· 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 Ã· 9.001 + 21.25 â‰ˆ (575.104 x 16/9) + 21.25 â‰ˆ 1022.40 + 21.25 â‰ˆ 1043.65 Answer: Option B #### B QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)200 B)300 C)400 D)500 E)600 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 5C2) = 200 ANSWER A #### A QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is: options: A)600 B)450 C)350 D)500 E)620 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 40 Ã— 30) Cm(power)2 = 40 Ã— 15 = 600 Cm(power)2 Answer is A. #### A QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam? options: A)2. B)4. C)X=5. D)X=6. E)8. SOLUTION:C. 5 hrs If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C QUESTION:A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows? options: A)24 B)72 C)720 D)336 E)420 SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is permutations = 5! = (5)(4)(3)(2)(1) = 120 The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is permutations = 3! = (3)(2)(1) = 6 Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 1206 = 720 Answer: C. #### C QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)24/78 B)24/709 C)24/76 D)24/71 E)24/72 SOLUTION:Explanation: Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random. Therefore, n(S) = 13C2 = 78 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 24/78 ANSWER:A #### A QUESTION:An athlete runs 200 metres race in 24 seconds. His speed is : options: A)20 km/hr B)24 km/hr C)28.5 km/hr D)30 km/hr E)None of these SOLUTION:Speed = 200/24 m/sec=25/3 m/sec=(25/318/5)km/hr=30 km/hr. Correct Option: D #### D QUESTION:A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? options: A)Rs. 375 B)Rs. 400 C)Rs. 600 D)Rs. 800 E)Rs. 850 SOLUTION:C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24 A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1 C's share (for 3 days) = Rs. (3 1/24 * 3200) =Rs.400 Answer = B #### B QUESTION:Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (660y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:If x is a positive integer, which of the following must be odd? options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3 SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD] C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD Hence C. #### C QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(Ã¢â‚¬â€œ4) 5 (Ã¢â‚¬â€œ4)1 #### A QUESTION:The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)15 kmph B)40 kmph C)18 kmph D)19 kmph E)10 kmph SOLUTION:Speed downstream = 60 + 20 = 80 kmph Speed upstream = 60 - 20 = 40 kmph Answer:B #### B QUESTION:In 1 hour, a boat goes 5 km along the stream and 9 km against the stream. The speed of the boat in still water (in km/hr) is : options: A)3 km/hr. B)2 km/hr. C)7 km/hr. D)8 km/hr. E)5 km/hr. SOLUTION:Speed in still water = 1/2(9 + 5) km/hr = 7 km/hr. ANSWER :C #### C QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.2514) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25x) = 11 0.25x = 8.5 x = 34 miles The answer is D. #### D QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2 SOLUTION:(y^2 − xy)/x=y-x => y^2 − xy = xy -x^2 => x^2 - 2xy + y^2 = 0 => (x-y)^2 = 0 Answer E #### E QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 79 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used. The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost? options: A)981 B)1000 C)1011 D)1101 E)1110 SOLUTION:The number of codes possible if leading zero is allowed = 10101010=10^4 The number of codes possible if leading zero is NOT allowed = 9101010=910^3 The difference = 10^4 - 910^3 = 10^3(10-9) = 10^3.=1000 Answer: B. #### B QUESTION:If cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)7.5 B)9.2 C)10.7 D)15.3 E)18.6 SOLUTION:100 112 ----- 112 ----- 12 100 ------ ? => 10.7% Answer:C #### C QUESTION:Smitty Farm picks 9866 cherries a day. If Smitty distributes their apples evenly across 9 different retail shops, how many cherries would remain with him. options: A)1 cherry B)7 cherry C)2 cherry D)4 cherry E)5 cherry SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs before 9,866. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 9+8+6+6 = 29. If we add 7, then it is divisible by 9. Hence, we need to add 7 to this number for it to be divisible by 9 Correct Option : B #### B QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 Ã— 9 Ã— 9 Ã— 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts. options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22 SOLUTION:Solution : Given SI1 = SI 2 P1 : P2 = 1/R1T1 : 1/R2T2 = 1/(105) : 1/(9:6) 27:25 B #### B QUESTION:Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){11,26} B){18,19} C){16,18} D){16,16} E){14,16} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others. Hence Answer : E #### E QUESTION:The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)80 kg B)85 kg C)90 kg D)100 kg E)110 kg SOLUTION:Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. B) #### B QUESTION:How many numbers from 10 to 10000 are exactly divisible by 9? options: A)900 B)1000 C)1110 D)1200 E)1400 SOLUTION:10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110 Answer : C #### C QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees. options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3 SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7 Answer is A #### A QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P105)/100 P = 6200 Answer: A #### A QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? options: A)20 ounces B)80 ounces C)100 ounces D)120 ounces E)180 ounces SOLUTION:20% sugar in 60 oz solution; Sugar = 6020/100 = 12 oz Water = 60-12 = 48 oz Now; let's add "x" oz of water in the solution; Total solution = 60+x oz Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar) 12 = (60+x) * 5/100 60+x = 240 x = 240 - 60 = 180 oz Answer: "E" #### E QUESTION:A train 200 m long passed a pole in 20 sec. How long will it take to pass a platform 610 m long? options: A)46 B)54 C)92 D)76 E)81 SOLUTION:Speed = 200/20 = 10 m/sec. Required time = (200 + 610)/10 = 81 sec. Answer: E #### E QUESTION:A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)18 B)36 C)59 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36. Answer: B. Hope this helps. #### B QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 45678=6720. ANS:A #### A <<<Examples ends QUESTION:What is the greatest positive integer x such that 7^x is a factor of 343^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:343^10 = (7^3)^10 = 7^30 ANSWER:E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N. options: A)797 B)254 C)597 D)997 E)297 SOLUTION:According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient divisor + remainder = 18 14 + 2 = 254 correc answer B #### B QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 45!. Answer: C. #### C QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 100 = 33 1/3% Answer: A #### A QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? options: A)26 B)30 C)34 D)38 E)42 SOLUTION:The first number is 22 = 16+6(1). We can continue adding 6 to make a list: 22, 28, 34,... The last number is 196 = 16+6(30) There are 30 numbers in the list. The answer is B. #### B QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together? options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2 SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min (1/30)+(1/20)-(1/90)=(1/x) 13/180=1/x => x=180/13 => x=13.85 minutes Answer: D #### D QUESTION:What approximate value should come in place of question mark (?) in the following equation 287.532 + 1894.029 – 657.48 = 743.095 + ? options: A)870 B)790 C)780 D)770 E)890 SOLUTION:? = 285 + 1895 – 655 – 745 or, ? = 780 Answer C #### C QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E QUESTION:The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)91.8 cm D)92.5 cm E)152.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 35) + 2(35) = 49.5 + 70 = 152.5 cm Answer:E #### E QUESTION:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert? options: A) 20% B) 25% C) 40% D) 60% E) 75% SOLUTION:could you use a venn diagram and just go with the number 100. 60 people order dessert and coffee... which is the union of D and C. T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither. B 25% #### B QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. Answer:B #### B QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon? options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x SOLUTION:Amount of gas you added to your car: 19-x Price per gallon: (19-x)/20 Answer: C #### C QUESTION:In the x-y plane, the area of the region bounded by the graph of \|x+y\| + \|x-y\| = 10 is options: A)8 B)625 C)16 D)20 E)24 SOLUTION:I've never seen such kind of question in GMAT before. OK there can be 4 cases: \|x+y\| + \|x-y\| = 10 A. x+y+x-y = 10 --> x=5 B. x+y-x+y = 10 --> y=5 C. -x-y +x-y= 10 --> y=-5 D. -x-y-x+y=10 --> x=-5 The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be2525=625 Answer: B #### B QUESTION:Convert the 9/36 m/s into kilometers per hour? options: A)0.9 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:9/36 m/s = 9/36 18/5 = 9/10 = 0.9 kmph. Answer: A #### A QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit? options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5% SOLUTION:55% is 25%-points above 30% and 5%-points below 60%. So the ratio of Sue's mix to Jane's mix is 1:5. 1/670% = 11.7% The answer is B. #### B QUESTION:A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago? options: A) 8 B) 10 C) 12 D) 14 E) 7 SOLUTION:Let's say Age of Richard isR Age of David isD Age of Scott isS Now Richard is 6 years older than David, i.e. R = D +6 David is 8 years older than Scott i.e. D = S +8 If in 8 years, Richard will be twice as old as Scott i.e. R+8 = 2x(S+8) i.e. R+8 = 2S + 16 i.e. R = 2S+8 But R = D+6 = (S+8)+6 = S+14 therefore, 2S + 8 = S +14 i.e. S = 6 i.e. R = 20 i.e. D = 14 Now, how old was David 7 years ago? i.e. D-7 = 14-7 = 7 years Answer: Option E #### E QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.20. The probability that neither A nor B occur is _________ options: A)0.45 B)0.4 C)0.55 D)0.05 E)0.6 SOLUTION:we are apply that formula.............. P(AorB)=P(A)+P(B)-P(A AND B) =.25+.40-.20 =.45 but the probability of neither A nor B=1-.45 =0.55 ANSWER:C #### C QUESTION:44Ã—98Ã—101=? options: A)435512 B)434431 C)548654 D)543286 E)546543 SOLUTION:44Ã—(100-2)Ã—(100+1) (4400-88)Ã—(100+1) 4312Ã—(100+1) 431200+4312=435512 answer A #### A QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)64% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5(4/5) of the original price, which nets to 0.64 of the original price, or 64%. E #### E QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream? options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7 SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 B #### B QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)2 months B)7 months C)8 months D)10 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 months ANSWER:B #### B QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)12 B)3 C)5 D)8 E)10 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER A 12 #### A QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages? options: A)(12/x)y B)(5/x)y C)(10/x)y D)(10x)y E)(13/x)y SOLUTION:x page in 10 mins i.e. 1 page in 10/x mins i.e. y pages in (10/x)y Answer: option C #### C QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is: options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %. SOLUTION:Explanation : Let sum = x. Then, S.I. = x/3 Let N =3R [x * 3R * R / 100] = x/3? R^2 = 100/9 R = 10/3 = 3 1/3%. Hence, Rate = 3 1/3 %. Answer : C #### C QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)(9C2) =736= 252 Answer : B #### B QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files? options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr SOLUTION:Server J processes 480/4 files per hour = 120 per hour Server Y processes 180/8 files per hour = 60 per hour Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour 480/180 = 2 2/3 hours=C #### C QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C14C3)+(4C24C2)+(4C34C1)+4C4 = (44)+(66)+(44)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after? options: A)7 min B)9 min C)4 min D)9 min E)1 min SOLUTION:Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1. x(2/75 + 1/45) + (30- x) 2/75 = 1 11x + 180 - 6x = 225 => x = 9 Answer:B #### B QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is : options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5 SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 495 99c - 99a = 99(c - a) = 495 495 = 995 = 99(c - a) So c - a = 5 Answer (E) #### E QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B QUESTION:What is the area of a square field whose diagonal of length 20 m? options: A)228 B)271 C)200 D)277 E)181 SOLUTION:d2/2 = (20 20)/2 = 200 Answer:C #### C QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? options: A)124 B)150 C)212 D)243 E)316 SOLUTION:3^5 = 243 The answer is D. #### D QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3700 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700. Answer: A) 3700 #### A QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”? options: A)5 B)10 C)16 D)20 E)9 SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum). E #### E QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is: options: A)276 B)299 C)230 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 9) and (23 x 10). Larger number = (23 x 10) = 230. Answer: Option C #### C QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2 options: A)I only B)I,II only C)II only D)I,III only E)III only SOLUTION:12=223 16=2222 GCF =22=4 Answer : C #### C QUESTION:In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A? options: A)2 B)3 C)5 D)6 E)8 SOLUTION:I like to put the numbers in prime factors so it is easier and faster to visualize. 14n/60 If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have (27n)/(2^235) Simplifying 7n/(235) The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7. The number could be 235, or 2352, or 235..... However to be less than 200 we can not add any prime number. 235 = 120 If we added the next prime factor 7, we would have A=2357 = 840 Thus, answer B #### B QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees. options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3 SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7 Answer is A #### A QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/5 B)2/5 C)3/10 D)3/7 E)1/7 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface? options: A)27 B)16 C)12 D)18 E)11 SOLUTION:2 π * 2r * 3r = 12 πr2 Answer:C #### C QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed? options: A)1180 B)1320 C)1540 D)1760 E)1920 SOLUTION:22C3 = 222120 / 6 = 1540 The answer is C. #### C QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 15 = 45 => x = 60 km/hr. Answer:A #### A QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year? options: A)200 B)600 C)900 D)1600 E)2000 SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x. Let y be the number of female students this year. x/400 = 2(2x/y) y = 1600 The answer is D. #### D QUESTION:A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 4) II. (2, 3) III. (4, 1) options: A)I only B)II only C)III only D)I and II E)I, II, and III SOLUTION:Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive. When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis. When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis. When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis. The answer is B. #### B QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is options: A)131 B)176 C)274 D)405 E)495 SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}. 6 times 40 something is approx north of 240 Hence the answer is (C) 274 #### C QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 61/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal. If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these SOLUTION:Explanation: Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 34 => 300+L = 15×34 = 510 => L = 510-300 = 210 meter Answer: Option C #### C QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? options: A)50 % B)60 % C)70 % D)80 % E)40 % SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:B #### B QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} options: A)20 B)40 C)80 D)140 E)60 SOLUTION:Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60. Answer:E #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25100)/20=125 ANSWER:D #### D QUESTION:How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is: options: A)4 B)5 C)6 D)7 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 15 : 9 :: 12 : x => 12 x 15 x x = 10 x 8 x 12 => x = 10 x 9 x 12 / (12 x 15) => x = 7 Answer : D #### D QUESTION:A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work? options: A)4 days B)2 days C)6 days D)8 days E)9 days SOLUTION:C 6 days 4/10 + 9/x = 1 => x = 15 1/10 + 1/15 = 1/6 => 6 days #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 9/3 m = 150 m. ANSWER : OPTION D #### D QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen? options: A)1.34 B)2.84 C)3.84 D)4.34 E)5 SOLUTION:40(40/100) = 16 --- 50 ? --- 12 => Rs.3.84 Answer: C #### C QUESTION:Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $880.What was original rent of friend whose rent is increased? options: A)800 B)900 C)1600 D)1100 E)1200 SOLUTION:0.2X = 4(880-800) 0.2X = 320 X = 1600 Answer C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:Because of weight limits, a lorry can carry a maximum of 20 crates of apples. The weight of a crate of oranges is 3434 the weight of a crate of apples. If 10 crates of apples were loaded into the lorry, what is the maximum number of crates of oranges that the lorry can still accommodate? options: A)8 B)9 C)12 D)13 E)14 SOLUTION:There's still room for 10 crates of apples. The weight of 10 crates of apples is the same as the weight of 10∗(4/3)=13 1/3 crates of oranges. Because the number of crates has to be an integer, the lorry can accommodate a maximum of 13 crates of oranges. Answer: D #### D QUESTION:The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is: options: A)1439 B)1440 C)1459 D)1449 E)1549 SOLUTION:LCM = 1440 1440 - 1 = 1439 ANSWER:A #### A QUESTION:(8^16)+(16^10)+(4^24) = ? options: A)(4)(2^29+1) B)(6)(2^48) C)(9)(2^49) D)(28)(2^53) E)2^148 SOLUTION:I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ) So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents. Here's how my brain works with this one, Step 1: Recognize a common base. (8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48) Step 2: Recognize the factor and pull out of the equation. = (2^48)(1 + (2^4) + 1) = (2^48)(1 + 16 + 1) = (2^48)(18) Step 3: Recognize this is not an answer and adapt. (2^48)(18) = (2^48)(2)(9) = 2^148 Answer is E. #### E QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was? options: A)1.42liters B)2.5liters C)3liters D)5.6liters E)7liters SOLUTION:Let the original quantity be x liters alcohol solution in x liters = 30/100 x = 3x/10 kg (3x/10)/(x+20) = 20/100 3x = x/5 + 4 14x = 20 x = 1.42liters Answer is A #### A QUESTION:In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A? options: A)0 B)5 C)10 D)15 E)25 SOLUTION:You should notice that 552=110 so 11,000 is divisible by 55: 55200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> BA=00=0. Next number divisible by 55 is 11,000+55=11,055: BA=55=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. D #### D QUESTION:Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? options: A) 5.5% B) 3.6% C) 4.4% D) 5.2% E) 6.0% SOLUTION:Let amount spent by Jill = 100 Clothing=50, Food=20, others=30 Tax on clothing= 2.5 Tax on others=3 Percentage= 5.5/100=5.5% Answer: A #### A QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions. = 1500 * 2 * 22/7 * 22.4 = 211200 cm = 2112 m Answer: A #### A QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 663373, so we need one 7 and one 3 to make it a square of a number. so 73= 21 Ans: B #### B QUESTION:E = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33 SOLUTION:The total number of pairs E,B possible is 45=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2. Answer: B. #### B QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? options: A)2400 B)2880 C)2787 D)3087 E)0728 SOLUTION:1200 12: x * 9 = 2:3 x = 2400 Answer: A #### A QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 1110^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 11 = 495 Answer A #### A QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20 options: A)15 ÷ 3 x 3 - 5 = 20 B)15 + 3 ÷ 3 + 5 = 20 C)15 x 3 + 3 + 5 = 20 D)15 x 3 ÷ 3 + 6 = 20 E)15 x 3 ÷ 3 + 5 = 20 SOLUTION:Answer : E #### E QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is? options: A)75 B)78 C)80 D)82 E)86 SOLUTION:Divisor = (6 * 3) + 2 = 20 5 * Quotient = 20 Quotient = 4. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 4) + 6 = 86 E) #### E QUESTION:Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)18 sec B)70 sec C)21 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 120 + 280 = 400 m. The time required = d/s = 400/20 = 20 sec. Answer: D #### D QUESTION:If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is: options: A)3:4:5 B)12:15:20 C)20:15:12 D)6:8:10 E)8:4:12 SOLUTION:Explanation: 6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12 ANSWER IS C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.052400+x+0.08x = 2400+x+0.08(2400+x) 0.052400+0.08x = 0.06x+0.082400 0.02x = 2400(0.08-0.05) x = 24000.03/0.02 = 3600 Ans:D #### D QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 years B)9 years C)4 years D)6 years E)2 years SOLUTION:Explanation: 100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer: Option D #### D QUESTION:A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together? options: A)2 8/11 B)2 8/198 C)2 8/7 D)2 8/18 E)2 8/112 SOLUTION:Sol. A’s 1 day’s work = 1 th 5 part of whole work and B’s 1 day’s work = 1 th 6 part of whole work ? (A + B)’s one day’s work = 1 1 11 5 6 30 th part of whole work. So, both together will finish the work in 30 days 2 8/ 11 days. Answer:A #### A QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ? options: A)5 B)4 C)3 D)2 E)-2 SOLUTION:Since x is an integer, (-12x)^(4x) is always positive. So, 12x^4x = 12x^(15 - x) 4x = 15 - x 5x = 15 x = 3 Answer: C #### C QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)(1000-9) = (1009)(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2 SOLUTION:Ans: Very interesting question. As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls Probability of choosing any box is 1/ 2. So probability of taking one red ball = 12×(1)+12(3864)≃0.8 Answer:B #### B QUESTION:The 7th grade French and Spanish classes each have 26 students in them, and there are nine students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes? options: A)26 B)28 C)30 D)32 E)34 SOLUTION:French class + Spanish class = 52 students. Nine students are in both classes so they were counted twice. The number of students taking just one class is 52 - 2(9) = 34. The answer is E. #### E QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Asha=25 Nisha =n Usha =3n Asha=2a Nisha =a Usha =34 The difference of all ages must be same 25-2a=n-a=3n-34 We will get two equation 2n+a=34 n+a=25 From the equation we will get n=9 and a=16 The ages are Asha=2a=32 Nisha =16 and Usha =34 Sum of the ages =100 (32+x)+(16+x)+(34+x)=100 82+3x=100 3x=18 x=6 Age of Usha =34+6=40 ANSWER:D #### D QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability. options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53 SOLUTION:Explanation : There are total 4 letters. The probability that P gets the first position is 1/4. The probability that O is in the second position is 1/3. Likewise, probability for C and Y are 1/2 and 1/1. Hence, the required probability is:- => (1/4) x (1/3) x (1/2) x 1. => 1/24. Answer : C #### C QUESTION:If x and y are integers and x=50y + 49, which of the following must be odd? options: A)xy B)x + y C)x + 4y D)3x-1 E)3x+1 SOLUTION:x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd you don't know whether Y is even or odd, so you need to try. A: odd * even = even ; oddodd= odd ->not true B: odd + odd = even ; odd+even = odd -> not true C: odd + 4odd = odd ; odd + 2even = odd -> TRUE, stop here. D&E -- EVEN Answer C #### C QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:16 people can write 52 book in 12 days working 8 hour a day.then in how many day 206 can be written by 64 people? options: A)309/26 B)309/28 C)309/22 D)319/26 E)339/26 SOLUTION:work per day epr hour per person= 52/(12816) // eq-1 people= 64; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 206/(p864) // eq-2 eq-1==eq-2; p= 309/26 ANSWER:A #### A QUESTION:In how many Q ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6666= 1296 ------(1) Total number of passwords in which no letter repeats = 6C44!= 1524=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item? options: A)256 B)260 C)316 D)320 E)350 SOLUTION:Fill the diagram step by step: coconut, almonds, and peanuts.PNGAlso given that there are total of 435 bags and 210 bags contain almonds. From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320. Answer: D. #### D QUESTION:A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? options: A)109 ways B)908 ways C)128 ways D)108 ways E)104 ways SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 12 = 108 ways. Answer:D #### D QUESTION:A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate? options: A)480 B)580 C)680 D)280 E)380 SOLUTION:Let the total no of mangoes in the crate be x Then the no of bruised mango = 1/30 x Let the no of unsalable mangoes =3/4 (1/30 x) 1/40 x =12 x=480 Answer is A. #### A QUESTION:If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe? options: A)15 B)60 C)75 D)90 E)105 SOLUTION:This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one. Teena covers 55 miles in 60 mins. Yoe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +15 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 15 miles in 60 mins So answer 30+60= 90 mins.D #### D QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B <<<Examples ends QUESTION:A train 440 meters long is running with a speed of 65 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)40.338 sec B)41.338 sec C)42.338 sec D)40 sec E)34.338 sec SOLUTION:D = 440 + 180 =620 S = 65 * 5/18 = 18.05556 mps T = 620/18.05556 =34.33846 E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax? Choices options: A)$22.68 B)$23.94 C)$24 D)$25.20 E)$30 SOLUTION:A. #### A QUESTION:How much is 80% of 60 is greater than 4/5 of 25? options: A)15 B)28 C)16 D)12 E)73 SOLUTION:(80/100) * 60 â€“ (4/5) * 25 48 - 20 = 28 Answer: B #### B QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’? options: A)25% B)50% C)23% D)28% E)None of these SOLUTION:Cost price = 240×100/120= 200 S.P. at no discount = 240×100/80 = 300 ∴ % profit = 100×100/200 = 50 % Answer B #### B QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? options: A)5 A B)10 A C)15 A D)18 A E)25 A SOLUTION:Movies: 75 % comedies. 25 % remaining genre. Now in this 25 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 2x/3. Total 5x/3. 5x/3 = 25; x = 15 Action movies: 15 % Drama movies: 10 % we can say that out of 100 z,: comedies: 75 z action: 15 z drama: 10 z Now action movies were A This means: A = 15 z. z = A/ 15 Comedies: 75 z = 75 * (A/15) 5 A A is the answer. #### A QUESTION:What percent is 2 gm of 1 kg? options: A)0.5 % B)0.2% C)1.5% D)2% E)3% SOLUTION:1 kg = 1000 gm 2/1000 × 100 = 200/1000 =1/5 = 0.2 % B) #### B QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:If xy not equal 0 and x^2y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x 2/100 * 2/3 = 200 B capital = 150001/6 = 2500.Answer: C #### C QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs? options: A)1640 B)1650 C)1660 D)1670 E)1680 SOLUTION:number of ways = 8765 = 1680 Answer is E #### E QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L4 => L = 36/4 = 9 Answer D #### D QUESTION:The salary of a person was reduced by 20%. By what percent should his reduced salary be raised so as to bring it at par with his original salary? options: A)50% B)32% C)25% D)43% E)29% SOLUTION:Let the original salary be $100 New salary = $80 Increase on 80 = 20 increase on 100 = 20/80 100 = 25% Answer is C #### C QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2 SOLUTION:Given: length = 17 cm, breadth = 13 cm Perimeter of rectangle = 2 (length + breadth) = 2 (17 + 13) cm = 2 × 30 cm = 60 cm We know that the area of rectangle = length × breadth = (17 × 13) cm22 = 221 cm2 ANSWER :A #### A QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is? options: A)675 B)680 C)685 D)690 E)695 SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec. Length of the train = 75 * 9 = 675 m. Answer: Option A #### A QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person? options: A)400 B)410 C)420 D)430 E)440 SOLUTION:Largest 3 digit number divisible by 24= 984 So their shares are (9843/12=246) , (9844/12=328) , (9845/12=410) ANSWER:B #### B QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 17 E)e) 12 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 850 = 17 Answer: D #### D QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z? options: A)1:8 B)1:4 C)2:1 D)4:1 E)10:1 SOLUTION:x= 5y, y= 2z X : Y , Y : Z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 So, X : Z = 10 : 1 (E) #### E QUESTION:On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3. In this case: the x-intercept is the value(s) of x for s = 0. 0 = x^2 - x^3; 0 = x^2(1 - x); x = 0 or x = 1. Answer: C. #### C QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)6 B)5 C)8 D)9 E)4 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8.Answer: C #### C QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)31% E)12% SOLUTION:Let the price be 100. The price becomes 140 after a 40% markup. Now a discount of 20% on 140. Profit=112-100 12% answer E #### E QUESTION:If x^2+(1/x^2)=7, x^4+(1/x^4)=? options: A)10 B)11 C)12 D)14 E)47 SOLUTION:-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47. Thus, the answer is E. #### E QUESTION:Which of the following is a pair of co–primes? options: A)(16, 62) B)(18, 25) C)(21, 35) D)(23, 92) E)none SOLUTION:Solution H.C.F. of 18 and 25 is 1. So, they are co-primes. Answer B #### B QUESTION:What inequality represents the condition 1<x<13? options: A)\|x\|<3 B)\|x+5\|<4 C)\|x-7\|<6 D)\|-5+x\|<4 E)\|3+x\|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any \|x-a\|<b a is a center and b is a half of length. So, \|x-7\|<12/2 represents our inequality (answer C) #### C QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price? options: A)$2000 B)$2500 C)$2400 D)$3120 E)$1540 SOLUTION:115% of cost - 110% of cost = $120 5% of cost = $120 cost = 120100/5 = $2400 Answer is C #### C QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 235711131719 to some power of 10. # of different approximations are possible. Approach #1: 25=10; 37=~20 (actually more than 20); 1119=~200 (actually more than 200); 1317=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 25=10 317=~50 (actually more than 50); 713=~100 (actually less than 100); 1119=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} options: A)20 B)40 C)80 D)140 E)60 SOLUTION:Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60. Answer:E #### E QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:Given f(x) = 3x – 5, for what value of x does 2[f(x)] – 4 = f(3x – 6) options: A)3 B)4 C)6 D)7 E)13 SOLUTION:Answer = A = 3 f(x) = 3x – 5 2[f(x)] – 4 = f(3x – 6) 2(3x-5) -4 = 3 (3x-6) - 5 6x - 14 = 9x - 23 x = 3 #### A QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income? options: A)Rs.900 B)Rs.800 C)Rs.500 D)Rs.1000 E)Rs.1200 SOLUTION:X * 4/5 * 80/100 = 576 X = 14400/16 X = 900 ANSWER:A #### A QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: A #### A QUESTION:For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive? options: A)None B)One C)Two D)Three E)Four SOLUTION:$ is basically a factorial of a number. So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive. From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range. For example: 7!+2=2(34567+1) --> a multiple of 2, thus not a prime; 7!+3=3(24567+1) --> a multiple of 3, thus not a prime; ... 7!+10=10(3467+1) --> a multiple of 10, thus not a prime. Answer: A. #### A QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.) options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08{weight of grapes}=0.8{weight of raisins} --> 0.08x = 0.815 --> x = 150. Answer: C. #### C QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 34t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is? options: A)621 B)276 C)236 D)600 E)211 SOLUTION:Explanation: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6 And also given that, profit share of B is Rs. 1500 => 5 parts out of 15 parts is Rs. 1500 Now, required difference is 6 - 4 = 2 parts Required difference = 2/5 (1500) = Rs. 600 Answer: D #### D QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:What is the area of a square with perimeter 8P ? options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16 SOLUTION:Each side is 2p A = (2p)^2 = 4(p^2) Answer B #### B QUESTION:In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first? options: A)2 people B)6 C)14 D)16 E)24 SOLUTION:FIRST OFFUnderstand what you are trying to find - In this case, you are trying to find how many people rank Vanilla first. For someone to rank Vanilla first, they have to rank them before Chocolate or Strawberry. This should be the very first hint that the correct answer cannot be bigger than 1/10 * 60 = 6. So if you are time pressured on the real test, at least you narrowed down the selections to two choices - not bad. But what now? Solve the easier problem. From 60 people, we are already told that 3/5 of them rank Vanilla last, leaving us with 2/5 of the people not ranking vanilla last - 24 people. So what are those combinations that vanilla are not last? A) C, V, S B) S, V, C C) C, S, V (vanilla first) D) S, C, V (vanilla first) What are we ultimately hunting for here? The number of people that rank vanilla first:C+D Now let's represent the given info into three equations 1) A+B+C+D = 24(2/5 of the people do not rank vanilla last) 2) A+C+D = 6(1/10 rank vanilla before chocolate) 3) B+C+D = 20(1/3 rank vanilla before strawberry) Subtract equation 1 from 2, leaving us with B = 24 - 6 = 18 Sub in B into equation 3 and solve for C+D 18 + C + D = 20 C+D = 20 - 18 = 2 There you go! 2 people out of the 60 ranked Vanilla as first A #### A QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was? options: A)Rs. 692.80 B)Rs. 820 C)Rs. 990 D)Rs. 1385 E)None SOLUTION:Answer Income of the deceased = Total income of 4 members - total income of remaining 3 members. = 735 x 4 - 550 x 3 Rs. = 1290 Rs. Correct Option: E #### E QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses? options: A)1/8 B)1/3 C)1/4 D)1/2 E)1 SOLUTION:P(THH) = 1/21/21/2=1/8 The answer is A. #### A QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years? options: A)100 B)120 C)200 D)220 E)264 SOLUTION:P = 240 R = 10% Required population of town = P(1 + R/100)^T = 240(1 + 10/100) = 240(11/10) = 264 Answer is E #### E QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal. If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 33=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen? options: A)119 B)1,200 C)3,240 D)3,600 E)14,400 SOLUTION:To meet the conditions we can have only 2 cases: 2 officers and 3 civilians: C25∗C39=840 3 officers and 2 civilians: C35∗C29=360 Total: 840+360=1,200. Answer: B. #### B QUESTION:The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? options: A)16 B)3/√2 C)8 D)2√2 E)(√2)/3 SOLUTION:800score Official Solution: The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2. The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B). #### B QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? options: A)20 coins B)30 coins C)50 coins D)100 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 175 ⇒ 1.75x = 175 ⇒ x = 100 coins Answer D #### D QUESTION:Average of first five multiples of 3 is options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation: Average=3(1+2+3+4+5) / 5=45 / 5=9 Option A #### A QUESTION:a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12 options: A)7 B)8 C)9 D)10 E)11 SOLUTION:add 44+12=56 now 56divided by 12 so we get 8 as reaminder ANSWER:B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:There are different 15 circles. What is the number of the greatest possible points with which the circles intersect? options: A)390 B)100 C)110 D)180 E)210 SOLUTION:Maximum points of intersection between n different circles = n(n - 1) = 1514 = 210 Answer: E #### E QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream? options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these SOLUTION:Explanation : Speed downstream = 96⁄8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12-4 = 8 kmph Speed upstream = 8-4 = 4 kmph Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B QUESTION:The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.) options: A) 1 B) 4 C) 7 D) 11 E) 10 SOLUTION:We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients... 3 ingredient blends: ABC ABD ACD BCD Total blends = 4 B #### B QUESTION:From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys? options: A)120 B)140 C)185 D)190 E)210 SOLUTION:The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are: (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a '''' (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185 C #### C QUESTION:Which of the following MUST yield an integer when divided by 11? options: A)The sum of eleven consecutive positive integers. B)The square of a prime number. C)The sum of two odd integers. D)The product of three consecutive odd numbers. E)The difference between a multiple of 8 and a multiple of 3. SOLUTION:For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, Ans(A). #### A QUESTION:If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? options: A)4% B)10% C)14% D)15% E)18% SOLUTION:Let Cost of PROD for 1 ticket = 1 So COP for n tickets = n So for selling n tickets, SP = 1.2 * n = 1.2n So SP of 1 ticket = 1.2 SP of 95% tickets = 1.2 * 0.95n So profit % = (1.2 * 0.95n - n)/n * 100 = 0.14 * 100 = 14% Answer - C #### C QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60100)/36) %=285% Answer E #### E QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:Because of weight limits, a lorry can carry a maximum of 20 crates of apples. The weight of a crate of oranges is 3434 the weight of a crate of apples. If 10 crates of apples were loaded into the lorry, what is the maximum number of crates of oranges that the lorry can still accommodate? options: A)8 B)9 C)12 D)13 E)14 SOLUTION:There's still room for 10 crates of apples. The weight of 10 crates of apples is the same as the weight of 10∗(4/3)=13 1/3 crates of oranges. Because the number of crates has to be an integer, the lorry can accommodate a maximum of 13 crates of oranges. Answer: D #### D QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:how many 1x1x1 cubes can you fit in a 15x16x13 box? options: A)3,200 B)3,150 C)3,448 D)3,120 E)2,980 SOLUTION:The answer is D) 3,120. A 1x1x1 cube has an area of 1. The 15x16x13 box has an area of 3,120. If you divide 3,120 by 1, you get 3,120. Therefore the answer is D. #### D QUESTION:The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following? options: A)1 B)10 C)10^2 D)10^3 E)10^4 SOLUTION:Because the question asks for what value isclosestthe question invites approximation. Let's look at the numerator: 10^9 - 10^2 10^9 is HUGE compared to 10^2. So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself). Likewise, 10^7 is HUGE compared to 10^3. So 10^7 - 10^3 is very close to 10^7. So we have: 10^9/10^7 or 10^(9-7) = 10^2. Choose C. #### C QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52(15/60) =13m sum of length and breadth = 68(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2120 = 60 sq meter Answer: B) 60 #### B QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N * 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now? options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9 SOLUTION:G is Gunther's current age. Let Mason's current age be M. given M = 2(G-5). four years from now Mason's age will be = 2(G-5) + 10 = 2G four years from now Gunther's age will be = G+10 Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10 Ans : D #### D QUESTION:Two friends want to buy a snack. They combine their money and find they have $3.80, consisting of quarters, dimes, and nickels. If they have 34 coins and the number of quarters is half the number of nickels, how many quarters do they have? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Let x be the number of quarters. Then 2x is the number of nickels. (1) 25x + 10x + 10D = 380. Then 7x + 2D = 76 (2) 3x + D = 34. Then 6x + 2D = 68 Let's subtract equation (2) from equation (1). x = 8 The answer is B. #### B QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=5015/85=8.82 ANSWER:E #### E QUESTION:In what time will a train 95 m long cross an electric pole, it its speed be 214 km/hr? options: A)1.6 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 214 5/18 = 59 m/sec Time taken = 95/59 = 1.6 sec. Answer: A #### A QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x1/10 + Nx1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)8.7 days B)2.0 days C)6.6 days D)7.7 days E)4.8 days SOLUTION:C = 1/2 - 1/8 - 1/8 = 5/24 => 4.8 days Answer: E #### E QUESTION:Two trains are moving in opposite directions with speed of 210 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds options: A)56 B)48 C)47 D)26 E)24 SOLUTION:Explanation: Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds Answer: Option E #### E QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 9 inches long, how wide is Jordan's rectangle, in inches? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 9x=180x x=20 answer is D #### D QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)172 SOLUTION:Explanation: Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. Therefore, 160 x 2.40 + x x 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER IS B #### B QUESTION:A can do a piece of work 20 days. B can do work in 35 days. In how many days they will complete the work together? options: A)15 days B)16.32 days C)12.72 days D)17 days E)18 days SOLUTION:LCM = 140, Ratio= 20:35=4:7 No of days= 140/(4+7) = 90/5 = 12.72 days ANSWER:C #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 â€“ 4xy (x- y)2 = 625 â€“ 576 => (x â€“ y) = 7 ANSWER: A #### A QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is: options: A)2/9 B)1/9 C)8/9 D)7/9 E)1/4 SOLUTION:let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house there will be 1 case when x,y,z will buy house a another when they buy house b and another when they buy house c so the prob that they buy same house is 31/27=1/9 ANSWER:B #### B QUESTION:A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72 SOLUTION:Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A #### A QUESTION:Robert's salary was decreased by 60% and subsequently increased by 60%. how much percentage does he lose? options: A)10% B)20% C)25% D)36% E)50% SOLUTION:let original salary be $100 Salary after decreasing 60% = 100 - 100 x 60/100 = $40 Salary after increasing 60% on $40 = 40 + 40 x 60/100 = $64 Percentage of loss = 100 - 64 = 36% Answer : D #### D QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:On a certain farm the ratio of horses to cows is 3:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 5:3. After the transaction, how many more horses than cows would the farm own? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Originally, there were 3k horses and k cows. 3(3k-15) = 5(k+15) 9k-5k = 75+45 4k = 120 k = 30 The difference between horses and cows is (3k-15)-(k+15) = 2k-30 = 30 The answer is B. #### B QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches? options: A)25 B)23 C)22 D)15 E)18 SOLUTION:Area of Carol's rectangle = 245 = 120 Let width of Jordan's rectangle= w Since , the areas are equal 8w = 120 =>w = 15 Answer D #### D QUESTION:An exam consists of 2 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes? options: A)1/16 B)37/256 C)1/2 D)219/256 E)15/16 SOLUTION:If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct. If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails. So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct. Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37. The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 1/16. A #### A QUESTION:What distance will be covered by a bus moving at 72 kmph in 30 seconds? options: A)287 B)600 C)289 D)276 E)207 SOLUTION:72 kmph = 72 5/18 = 20 mps D = Speed * time = 20 * 30 = 600 m. Answer:B #### B QUESTION:Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The total number in the three clubs is 17+24+22=63. All 50 students signed up for at least one club. 3 of those students signed up for exactly one more club. 63 - 53 = 10 so 5 students must have signed up for exactly three clubs. The answer is A. #### A QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment? options: A)360 B)420 C)230 D)540 E)610 SOLUTION:Let the value of each installment be Rs.x [x/(1+(20/100))]+[x/(1+(20/100))2]=550 (100x/120)+(10000x/14400)=550 (5x/6)+(25x/36)=550 x=360 Option A #### A QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer? I. w + t + 2 II. w^2 + 2wt + t^2 III. w^2 + t^2 options: A)None B)I only C)II only D)III only E)I, II, and III SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even. Check all options: I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard; II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard; III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard. Answer: A. #### A QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!3! = 51840 - 4320 = 47520 ways A #### A QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B QUESTION:The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination options: A)14 years B)14 years 5 month C)14 years 8 month D)15 years E)15 years 5 month SOLUTION:(d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100 2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years 3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month C #### C QUESTION:In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons? options: A)200 B)210 C)230 D)250 E)270 SOLUTION:7p3 = 7 × 6 × 5 = 210 B) #### B QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:A driver goes on a trip of 50 kilometers, the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? options: A)35 B)36 C)40 D)42 E)45 SOLUTION:The time for the first part of the trip was 25/60 = 5/12 hours. The time for the second part of the trip was 25/30 = 5/6 hours. The total time for the trip was 5/12 + 5/6 = 15/12 = 5/4 hours. The average speed for the trip was 50 / (5/4) = 40 kph The answer is C. #### C QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? options: A) 1000 B) 625 C) 1,250 D) 2,500 E) 10,000 SOLUTION:total fish = x percentage of second catch = (2/40)100 = 5% so, x 5% = 50 x = 1000 ans.A #### A <<<Examples ends QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15 SOLUTION:Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15 Answer is A. #### A QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C QUESTION:If one cat eats 1.5 rats in 1.5 days, then in howmany days 3 cats will eat 3 rats?? options: A)1 Day B)2 Days C)3 Days D)4 Days E)5 Days SOLUTION:1Cat ------ 3/2 Rat --------- 3/2 Days 1 Cat ------(3/2)2 Rat -----(3/2)2 Days (Rat doubled, days doubled) 13 Cat----- 3 Rat -----------3/3=1 Day (Cat3 , Same rat , Days/3 ) ANSWER:A #### A QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:If p and q are prime numbers, how many divisors does the product p^3 q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall? options: A)5/7 B)1 C)10/7 D)12/7 E)24/7 SOLUTION:Solution:Let work done by man, women and girl per hour be m,w,g respectively. Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3). No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6. So, n = 1/(7/24) = 24/7 Option, E #### E QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 5050 = 2500m = 2.5km Speed = 602.5=150km/hr Answer is D #### D QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)128 C)276 D)297 E)236 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2pir. The perimeter of a semicircle is 2pir/2 + 2r = pir + 2r The perimeter is pi9 + 29 which is about 46. The answer is D. #### D QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4 SOLUTION:5C3 (1/2)^3(1/2)^2 = (5 4 * 3!)/2!3! * 1/32 W= 5/16 Answer - C #### C QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 34t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams T? options: A)T=16 B)T=32 C)T=64 D)128 E)512 SOLUTION:Weight directly proportional to 4 pi r^2 Now, 4pi is constant, so, weight is directly proportional to r^2. When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8; (0.15)^2 4 proportional to 84, solving further (0.15)^2 2 ^2 = (0.152)^2 = 0.3 ^ 2; so answer = 32 (B) #### B QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store? options: A)36 B)54 C)72 D)90 E)101 SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18: (A) 36 = 182 (B) 54 = 183 (C) 72 = 184 (D) 90 = 185 (E) 101 = not a multiple of 18 ans is E #### E QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ? options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-2)= 0 so the two roots are 1 and 2. Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. A is the answer. #### A QUESTION:The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: options: A)678 B)944 C)456 D)323 E)899 SOLUTION:: Explanation: Clearly, the numbers are (59 x 13) and (59 x 16). {\color{Blue} \therefore } Larger number = (59 x 16) = 944. Answer: B)944 #### B QUESTION:A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)30 D)88 E)35 SOLUTION:US = 25 DS = 45 M = (45 + 25)/2 = 35 Answer:E #### E QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 320000/5=12000 ANSWER:E #### E QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? options: A)2% B)17% C)25% D)65% E)83% SOLUTION:New Value – Old Value)/Old Value x 100 We are given: February sales this year = 400 million February sales last year = 320 million We need to determine the percent increase between sales from last year to sales this year. Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula. (New Value – Old Value)/Old Value x 100 [(400 – 320)/320] x 100 = 25%. The answer is C. #### C QUESTION:A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members? options: A)182 B)208 C)224 D)229 E)302 SOLUTION:If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x but we are given .85x = 195 x = 229 So the original number of faculty members is 229 Correct Answer - D #### D QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and â€“4; #### B QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it? options: A)(y+1)/2 B)(y-1)/2 C)y/(2+1) D)y/(2-1) E)y/2 SOLUTION:Lets put values for y, say y=8 since it's even and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms so putting y=8 in the options, option E = y/2 => 8/2 = 4 , the number of negative integers So, E is the answer #### E QUESTION:A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ? options: A)22 B)23 C)25 D)35 E)30 SOLUTION:Explanation: Clearly, we have : B-3 = E ...(i) B + 3 = D ...(ii) A+B = D + E+10 ...(iii) B = C + 2 ...(iv) A+B + C + D + E= 133 ...(v) From (i) and (ii), we have : 2 B = D + E ...(vi) From (iii) and (vi), we have : A = B + 10 ...(vii) Using (iv), (vi) and (vii) in (v), we get: (B + 10) + B + (B - 2) + 2B = 133 => 5B = 125=> B = 25. ANSWER IS C #### C QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:What is the different between the place value and face value of 6 in the numeral 5468? options: A)45 B)54 C)60 D)36 E)44 SOLUTION:place value of 6 = 6 * 10 = 60 face value of 6 = 6 60 - 6 = 54 Answer is B #### B QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:The mean of (54,825)^2 and (54,827)^2 = options: A)(54,821)^2 B)(54,821.5)^2 C)(54,820.5)^2 D)(54,826)^2 + 1 E)(54,821)^2 – 1 SOLUTION:54825^2 = (54826-1)^2 = 54826^2 + 1^2 - 2548261 54827^2 = (54826+1)^2 = 54826^2 +1^2 + 2548261 Taking the average of above 2 , we get (54826)^2 +1 hence the answer is D #### D QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:Find the middle one when The sum of three consecutive even numbers is 36? options: A)10 B)12 C)15 D)16 E)20 SOLUTION:3 consecutive numbers can be a - 1, a, a + 1 So sum of numbers = 3a = 36. Hence a = 12. B #### B QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by: options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800 SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6) = 147 : 189 : 126 = 7 : 9 : 6. Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22 = Rs.3600 ANSWER:C #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 34 = 12 Answer: C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5 6 = 30 Answer is B #### B QUESTION:number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9 options: A)1290 B)1296 C)1380 D)1480 E)1580 SOLUTION:we have to make 4 digit number in which the format is d> c > b > a __ __ __ __ 1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4) 2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3) 3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2) 4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1) hence every place can be filled by 6 digits, 6* 6* 6* 6 = 1296 ANSWER:B #### B QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)120 E)200 SOLUTION:6C34C2 =120=D #### D QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10100/((100-10 )5) = Rs. 2(2/9) B #### B QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with two children, what is the probability that all the children are of the same gender? options: A)1/2 B)1/16 C)1/9 D)1/4 E)1/25 SOLUTION:There are two cases. All boys and all girls. case 1. all boys. 1/21/2= 1/4 case 2 .all girls. 1/21/2=1/4 We will add the cases to get 1/2 #### A QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected? options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14 SOLUTION:1- (4c3/8c3) = 13/14 Answer : C #### C QUESTION:The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7) options: A)80 m2 B)84 m2 C)88 m2 D)86 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 4 = 88 m2 Answer C #### C QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:A can give B 70 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)139.78 B)139.13 C)139.22 D)111.0 E)111.12 SOLUTION:A runs 1000 m while B runs 930 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 800)/930 = 860.21 m. B can give C = 1000 - 860.21 =139.78m. Answer:A #### A QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles? options: A)4329 B)2799 C)4312 D)2799 E)2712 SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: C #### C QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be? options: A)1 B)2 C)3 D)5 E)7 SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number. If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum. Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3. The correct answer is choice (C). Note:1 is not a prime number. #### C QUESTION:The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)52 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 4 hours 20 minutes = 260 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (260 – 20)/5 = 48 minutes ANSWER D #### D QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? options: A)1500 B)1600 C)1750 D)1900 E)2000 SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. #### C QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work? options: A)10 B)12 C)22 D)28 E)20 SOLUTION:A can do the work in 60/4 i.e., 15 days. A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12 So A and B together can do the work in 12 days. Answer: B #### B QUESTION:Two numbers N and 16 have LCM = 48 and GCF = 8. Find N. options: A)11 B)32 C)24 D)48 E)50 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 16 N = 48 * 8 N = 48 * 8 / 16 = 24 correct answer C #### C QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg options: A)2:0 B)2:3 C)2:1 D)2:2 E)2:8 SOLUTION:By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B #### B QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 560/60 = 51/1 = 5 New time in minutes to cross 5 miles stretch = 560/40 = 53/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:How many different values of positive integer x, for which \|x+7\|<x, are there? options: A)0 B)2 C)3 D)8 E)16 SOLUTION:Answer A I opted to put the random value option. i used 0 , 7 , -7 and the the extreme of 30 and -30.. i was able to solve it in 1:09 B #### B QUESTION:The product of all the prime numbers less than 30 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^9 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19 ,23, 29 = 110^7 2.32.910^9 =6.6710^9 E #### E QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:We have 8 people and 5 chairs. In how many ways chairs can be occupy? options: A)1200 B)1450 C)1680 D)1912 E)900 SOLUTION:no. of ways they can be occupy = 8765 = 1680 Answer is C #### C QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:rom the beginning; Initially milk to water is 12l : 8l remove half 6 - 4 add 10l milk 16 - 4 remove half 8 - 2 add 10l milk 18 - 2 18:2 = 9:1 ANSWER:B #### B QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500(1+(4/100)2] = Rs (7500 (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 * 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ? options: A)500 B)1000 C)1500 D)2000 E)3000 SOLUTION:Explanation: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively. Then, 2x + 3y = 3500 ...(i) and 3x + 2y = 4000 .....(ii) solving (i) and (ii) we get x = 1000, y = 500 ANSWER IS B #### B QUESTION:A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? options: A)40 B)33 C)50 D)51 E)52 SOLUTION:Yes, ensure that you understand the relation thoroughly! Cost per liter = K * Fraction of Spirit 40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2. 20 = K * (1/2) K = 40 Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water) Cost for 3 liters = 40 * (1/3) * 3 = 40 cents A. 40 cents #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:60 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)8 days B)6 days C)7 days D)9 days E)12 days SOLUTION:1 women's 1 day work = 1/420 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/420 + 10/140) = 1/12 5 women and 10 children will complete the work in 12 days. Answer: E #### E QUESTION:A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards? options: A)450 B)600 C)700 D)2400 E)3200 SOLUTION:Answer C) 9600 yards need 1200 lbs 1 Yard will need 1200/9600 = 1/8 lbs 3600 Yards will need 1/8* 5600 Yards = 700lbs #### C QUESTION:The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class? options: A)218 B)226 C)234 D)242 E)250 SOLUTION:1/22/5 + 3/43/5 = 4/20 + 9/20 = 13/20 The number of degrees is 13/20 * 360 = 234 degrees The answer is C. #### C QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (10080)/(8001) = 10% Answer: E #### E QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week? options: A)25% B)30% C)35% D)40% E)45% SOLUTION:E for me. Let managers comminsion rate be M. m5000+ 20.055000=2750 5000m=2250 m=45/100=45% #### E QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is: options: A)91 B)910 C)1001 D)1911 E)None of these SOLUTION:Explanation: Required number of students = H.C.F of 1001 and 910 = 91. Answer: A #### A QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food. options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400 SOLUTION:Part of salary left =1-(2/5+3/10+1/8) =7/40 Let the monthly salary be $x Then (7/40) of x=1400 X=8000 Expenditure on food=$2400 Option D #### D QUESTION:A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share. options: A)Rs. 3240 B)Rs. 2520 C)Rs. 2880 D)Rs. 3360 E)None of these SOLUTION:Explanation: Let C's investment = Rs. x B's investment = Rs. (x - 3000) A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000) Now, (A + B + C)'s investment = Rs. 72000 => x + (x - 3000) + (x + 3000) = 72000 => 3x = 72000 => x = 24000 Hence, A's investment = Rs. 27000 B's investment = Rs. 21000 C's investment = Rs. 24000 Ratio of the capitals of A, B and C = 27000 : 21000 : 24000 = 9 : 7 : 8 A's share = Rs. [(8/24) Ã— 8640] = Rs. 2880 Answer: Option C #### C QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x2+y4=140 heads: x1+y1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)1110! B)98! C)87! D)76! E)65! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=1110! Ans:A #### A QUESTION:A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display? options: A)15/56 B)3/28 C)1/28 D)1/56 E)3/55 SOLUTION:Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator. Total no of ways we can choose 3 from 11 is 11c3, which is the denominator. So, the probability: 9c1/11c3= 3/28 ans is E. #### E QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 3 = Rs.2025 Answer:C #### C QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)34 D)12 E)13 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(10081/4504.5) years =4 years Answer B #### B QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:If $600 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 7 years? options: A)$750.00 B)$823.50 C)$973.25 D)$100.25 E)$793.49 SOLUTION:Using CI Formula: A=P(1+r/n)^nt A=600(1+4/7)^47 A=793.49 Option: E #### E QUESTION:There are 10 orators A, B, C, D, E, F, G, H, I and J. In how many ways can the arrangements be made so that A always comes before B and B always comes before C. options: A)10! / 3! B)8! / 6! C)5! x 3! D)8! / (5! x 3!) E)8! / (5! x 4!) SOLUTION:Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C. The remaining 7 people have to be arranged in 7 places. Thus, 10C3 x 7! =10! / 3! ANSWER:A #### A QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price? options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these SOLUTION:Explanation : CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140 100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12 Answer : Option A #### A QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)5/18 = 45 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder? options: A)11 B)13 C)15 D)Data inadequate E)None of these SOLUTION:Number= (31 * Q)+ 29. Given data is inadequate. Answer: D #### D QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)38.89 B)39.18 C)38.78 D)38.0 E)38.18 SOLUTION:Explanation : After 10 days : 300 women had food for 35 days. Suppose 275 women had food for x days. Now, Less women, More days (Indirect Proportion) 275 : 300 :: 35 : x => 275 x x = 300 x 35 => x = 300 x 35 / 275 => x = 38.18 Answer : E #### E QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends? options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65 SOLUTION:Praveen spent and gave to his two friends a total of 12.25 + 2x= $4.65, x is the amount spent to one friend. Money left 50.50 -2x = $31.85. Then 2x=$18.65. correct answer is B) $ 18.65 #### B QUESTION:18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place? options: A)144 B)131 C)279 D)90 E)45 SOLUTION:there are 18 business exec and in each handshake 2 business execs are involved. hence 18C2=153 Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake. total=153+126=279 ANS: C #### C QUESTION:Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)14 E)16 SOLUTION:The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: D. #### D QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Option B #### B QUESTION:Find the distance covered by a man walking for 42 min at a speed of 10km/hr? options: A)7km B)3km C)4km D)5km E)6km SOLUTION:Distance = 1042/60 = 7 km Answer is A #### A QUESTION:One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? options: A)120 % B)140 % C)162/3 % D)20 % E)None SOLUTION:Sol. CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain. Answer D #### D QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:A man can do a piece of work in 5 days, but with the help of his son he can do it in 2 days. In what time can the son do it alone ? options: A)7 1/2 days B)6 1/2 days C)5 1/3 days D)3 1/3 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/2−1/5)=(5−2)/10=3/10 So son will do whole work in 10/3 = 3 1/3 days Answer: D #### D QUESTION:A train running at 1/3 of its own speed reached a place in 9 hours. How much time could be saved if the train would have run at its own speed? options: A)8hrs B)10hrs C)12hrs D)15hrs E)6hrs SOLUTION:time taken if run its own speed = 1/39 =3 hrs Time saved = 9 - 3 = 6 hrs Answer : E #### E QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 * 18/5 = 8 sec ANSWER:C #### C QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 Ã— 110/100 Ã— 110/100 = 12100 C #### C QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:If y = \|\|x – 3\| – 2\|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = \|\|x – 3\| – 2\| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits? options: A)53978 B)53916 C)53961 D)56781 E)None of these SOLUTION:Explanation: The greatest 5 digit number that can be formed using the given digits = 74320 The smallest 5 digit number that can be formed using the given digits = 20342 .: The required difference = 74320 - 20342 = 53978 Answer: Option A #### A QUESTION:A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y 1997- x1---- y1-- x1+y1 x1= ax .....(P) y1= 1.07y...(Q) x1+y1/x+y = 1.01 solve using P and Q and find x/y #### A <<<Examples ends QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length? options: A)87 B)69 C)40 D)72 E)24 SOLUTION:Speed = 75 Km/hr = 75(5/18) m/sec = 125/6 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 (6/125) = 24 seconds Answer: E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1200 employees, then the no. of female employees who are computer literate ? options: A)504 B)674 C)672 D)960 E)None SOLUTION:Solution: Total employees, = 1200 Female employees, 60% of 1200. = (60 1200) /100 = 720. Then male employees, = 480 50 % of male are computer literate, = 240 male computer literate. 62 % of total employees are computer literate, = (62 1200) /100 = 744 computer literate. Thus, Female computer literate = 744 - 240 = 504. Answer: Option A #### A QUESTION:In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)48% C)57% D)59% E)61% SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400 So, Required percentage = 11628/24400 * 100 = 48% B #### B QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = \| (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 3 = Rs.2025 Answer:C #### C QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)285 m B)240 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x = 285 m. Answer: A #### A QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:How many 5-digit positive integers exist the sum of whose digits are odd? options: A)36000 B)38000 C)45000 D)90000 E)None SOLUTION:Solution: There are 9�104 = 90000, 5-digit positive integers. Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number. Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number. Answer: Option C #### C QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are? options: A)60, 120, and 30 B)60, 30, and 120 C)30, 60, and 120 D)30, 120, and 60 E)120, 30, and 60 SOLUTION:Let the numbers be 2x, x and 4x (2x + x + 4x)/3 = 70 7x/3 = 70 x = 30 The numbers in order are 60, 30, and 120 The answer is B. #### B QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)? options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above. SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively. Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4; Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11. Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours. Answer: C. #### C QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468? options: A)1000 B)1100 C)1200 D)1300 E)1600 SOLUTION:Local value of 4 = 4 x 100 = 400 Place value of 4 = 4 There fore = 4 x 400 = 1600 E #### E QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c11c11c1)/5c3 =3/10 ANSWER:A #### A QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(34)+x/(35)=84/60 x=6 km ANSWER:C #### C QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken? options: A)6 B)8 C)2 D)5 E)4 SOLUTION:Explanation: Mary and her sister complete half work in 2.5 days => they can complete whole work in 5 days Answer: Option D #### D QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate? options: A)69 B)70 C)71 D)72 E)73 SOLUTION:number of ways = 23!3! = 72 Answer is D #### D QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+224=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-254 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25 SOLUTION:Explanation : Face value of each share = Rs.20 Dividend per share = 9% of 20 = 9×20/100=9/5 He needs to have an interest of 12% on his money ie, Money Paid for a share 9×12/100=9/5 Money Paid for a share=9/5×100/12=15 ie, Market Value of the share = Rs.15 Answer : Option C #### C QUESTION:The prices of tea and coffee per kg were the same in june. In August the price of coffee shot up by 20% and that of tea dropped by 20%. if in August , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ? options: A)45 B)50 C)40 D)35 E)30 SOLUTION:Let the price of tea and coffee be x per kg in June. Price of tea in August = 1.2x Price of coffee in August = 0.8x . In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50 1.2x(1/2) + 0.8x(1/2) = 50 => x =50 B #### B QUESTION:If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x? options: A)a) 100a B)b) 1/100a C)c) 1/a D)d) 10/a E)e) 10,000/a SOLUTION:x= a/100 * y So y= 100/a * x So y= (10000/a)/100 * x E #### E QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase? options: A) $320 B) $800 C) $320 D) $600 E) $850 SOLUTION:Increase in house value = $28,000 - $18,000 =$10000 So, tax increase = 8% of$10000=$800 Answer: B #### B QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:Jackson invested $500,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P? options: A)$115,384 B)$120,000 C)$121,072 D)$124,129 E)$130,000 SOLUTION:x be the amount invested in account P 0.12x +(500000-x)0.25=60,000 15000/.13=x x=1500000/13=11...=$121,072 hence answer is C #### C QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M): m------M---------------W w In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 315/60 =15/20 miles and the man walks the distance mM, which is 39/60 = 9/20 mile. The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes. Answer B. #### B QUESTION:12 times a number gives 156. The number is options: A)11 B)12 C)13 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 12×N=156⇒N=13 Correct Option: C #### C QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months. options: A)7500 B)6500 C)8125 D)9125 E)None of them SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years. Simple Interest = (PRT)/100 = Rs.(73,000(50/3)(3/4)(1/100))= Rs.9125 Answer is D. #### D QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:There are 9 people in the room. There are two pairs of siblings within that group. If we choose two people, what is the probability that they will not be siblings? options: A)12/18 B)17/18 C)2/9 D)1/18 E)4/18 SOLUTION:we have XXXXXBBCC We have to take into the account when we have XX, XB, XC So 5/94/8 5/92/8 and 5/92/8 note we need to multiply these by 2 (except the first) b/c we can have BX and CX. 20+20+20 --> 60/72 --> 30/36 --> 15/18 then next is BC 2/92/8 --> 4/72 2/36 1/18 --> multiply this by 2 b/c of CB so 2/18+15/18 --> 17/18 ANSWER:B #### B QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour. options: A)2 B)1.5 C)2.25 D)3 E)1.75 SOLUTION:The distance between the man's home and the store is 500 meters. 3 times means that the man made the 500 meter trip 6 times in total. 6 * 500 = 3000 meters or 3 km. Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075. Correct answer is 2.25 km per hour #### C QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All two 2. One symmetry and other two non 4. All the two letters can be arranged in 2 ways ( 11c2+ 11c1 * 15c2) 2 ( 1110/ 2 + 11 * 15 * 14 / 2 ) * 2 2420 IMO option D is the correct answer.. OA please...will correct if I missed anything..D #### D QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 54321 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 321 = 6ways Now, arrange all with the boys together 1206 = 720ways ANSWER:D #### D QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:If a is a positive integer, which of the following could NOT be the square of a? options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752 SOLUTION:A number ending with 2 can never be a perfect square. Units digit of a perfect square must be: 1,4,9,6,5 Answer E) #### E QUESTION:A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup? options: A)1.5 B)1.75 C)2.14 D)2.34 E)2.64 SOLUTION:Let the total solution is 150 L with 80 L water70 L syrup. To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup. Therefore we are taking 55 L of syrup from initial solution and replacing with water. using urinary method: 70 L syrup in 150 L solution 55 L syrup in 117.9 L solution We started by multiplying 10 Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14. Correct option : C #### C QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.2 Probability of Tail, P(T) = 0.8 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2(0.2)^3(0.8)^2 1 Tail and 4 Heads, Probability = 5C1(0.2)^4(0.8)^2 0 Tail and 5 Heads, Probability = (0.2)^5 Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 Answer: option A #### A QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c? options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3 SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}). But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms. Answer: C. #### C QUESTION:A ship sails 4 degrees north, then 14 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ? options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:Let x = the latitude sought. Then marking the northings +, and the southings -; By the statement x + 4 - 14 + 17 - 19 = -11 And x = 1. Answer B #### B QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer? options: A)2 B)4 C)8 D)10 E)7 SOLUTION:Given 108x is a perfect cube so we will take 216 = 666 108x = 216 x = 216/108 = 2 correct option is A #### A QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:In how many ways can the letters of the word REPORT be arranged? options: A)1206 B)360 C)2520 D)3000 E)3478 SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways B #### B QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1996 has to be the ring finger Answer is (D) #### D QUESTION:At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.) options: A)96 B)240 C)E=256 D)E=384 E)E=480 SOLUTION:Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers.... We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E #### E QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 1060 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:The ratio 25:50 expressed as percent equals to options: A)50 % B)85 % C)25 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 25 is what percent of 50, which can be calculated as, (25/50)100 = 25 * 2 = 50 Answer: Option A #### A QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)23 days B)16 days C)11 days D)24 days E)35 days SOLUTION:D 24 days 2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days #### D QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2SDtomean + 2SD, thus from 50-250.5=51 to 50+250.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is options: A)u B)v C)w D)y E)z SOLUTION:a is one time, b,2 times so on... so 323=n(n+1)/2.. 0r n(n+1)= 646... now 2526=650...2425<646 so n= 25. and 25th alphabet is Y. ans D #### D QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)300 B)368 C)375 D)337 E)639 SOLUTION:A+B+C = 1200 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1200 => 300 Answer:A #### A QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:In how many years will a sum of money double itself at 10% per annum? options: A)2 years 4 months B)4 years 2 months C)8 years 4 months D)10 years 8 months E)None SOLUTION:Sol. Let sum = x. Then, S.I. = x ∴ Time = [100 * S.I. / PR] = [100 x / x * 12] years = 8 1/3 years = 8 years 4 months. Answer C #### C QUESTION:A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ? options: A)1/3 kmph B)2/3 kmph C)1/4 kmph D)1/2 kmph E)1/6 kmph SOLUTION:Explanation: Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr. Speed in downstream = 3 x 60/18 = 10 km/hr Rate of current = (10-9)/2 = 1/2 km/hr. ANSWER IS D #### D QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? options: A)3:16. B)2:3. C)4:9 D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C #### C QUESTION:Suppose there is a number 235 such that sum of first two digits is equal to the third digit. How many such 3 digits numbers are possible? options: A)42 B)43 C)44 D)45 E)46 SOLUTION:As we know that total digits are 0 ,1, 2, 3,4,5,6,7,8,9 if three digit no is xyz this means x+y=z must hold so we have to select two no out of 10 ans is 10 c 2=45 ANSWER:D #### D QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:The average of 11 numbers is 11. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is options: A)10.4 B)11.5 C)81.5 D)11.5 E)21.5 SOLUTION:Explanation: Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4. Answer: A #### A QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x â€“ 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:If the quotient a/b positive, which of the following must be true? options: A)a > 0 B)b > 0 C)ab > 0 D)a-b > 0 E)a+b > 0 SOLUTION:a/b>0 means aa and bb have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0. Answer: C. #### C QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230m B)240m C)250m D)260m E)270m SOLUTION:speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s time= 9sec let the lenght of second train is x total distance covered= 260 + x therefore, D= speedtime thus 260 + x = 500/9 * 9 x= 500-260=240 m ANSWER:B #### B QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? options: A)1/12 B)0 C)12/212 D)11/12 E)11/13 SOLUTION:0 If one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope. ANSWER:B #### B QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? options: A)32 : 48 B)32 : 42 C)32 : 45 D)32 : 41 E)42 : 45 SOLUTION:Explanation: A : B (80004)+(40008) : (90006)+(60006) 64000 : 90000 32 : 45 Answer:C #### C QUESTION:A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years. options: A)Rs. 376000 B)Rs. 204000 C)Rs. 36000 D)Rs. 18000 E)Rs. 260000 SOLUTION:Investments-- A=14000x4+16000x20=376000 B=12000x2+10000x18=204000 C=20000x18=360000 So C's Share = 94000xC/(A+B+C)=36000 ANSWER:C #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/91 B)33/18 C)33/29 D)33/18 E)33/12 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 12C4/15C4 = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:A #### A QUESTION:The perimeter of one square is 48 cm and that of another is 36 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined? options: A)13√4 B)13√2 C)23√2 D)12√4 E)15√2 SOLUTION:4a = 48 4a = 36 a = 12 a = 9 a2 = 144 a2 = 81 Combined area = a2 = 225 => a = 15 d = 15√2 Answer: E #### E QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 800018 : (80004) + (400014) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)235 m B)245 m C)247 m D)249 m E)252 m SOLUTION:length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = (130+x)/30 m/s = 45 × (10/36) = (130+x)/30 = 45 × 10 × 30 /36 = 130+x = 45 × 10 × 10 / 12 = 130+x = 15 × 10 × 10 / 4 = 130+x = 15 × 25 = 130+x = 375 = x = 375-130 =245 #### B QUESTION:Find the middle one when The sum of three consecutive even numbers is 36? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:3 consecutive numbers can be a - 1, a, a + 1 So sum of numbers = 3a = 36. Hence a = 12. B #### B QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot? options: A)1 B)17 C)88 D)12 E)15 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B QUESTION:A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle? options: A)13π B)26π C)262√π D)52π E)4π SOLUTION:The distance between the two points is sqrt(8) radius = sqrt(8)/2 Area= pi(sqrt(8)/2)^2 E.4π #### E QUESTION:On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers? options: A)1 : 3 B)2 : 3 C)2 : 1 D)3 : 1 E)4 : 5 SOLUTION:Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10 Required ratio = 20 : 10 = 2 : 1 C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800 100 = 75% ANSWER:B #### B QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:If n = 3^6 – 2^6 which of the following is NOT a factor of n? options: A)97 B)7 C)35 D)5 E)19 SOLUTION:3^6 - 2^6 = (3^3)^2 - (2^3)^2 =(3^3 + 2^3)(3^3 - 2^3) =(27+8)(27-8) =3519 =7519 Therefore, 97 is Not a factor of n. A #### A QUESTION:A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? options: A)25/42 B)25/46 C)25/41 D)25/49 E)25/23 SOLUTION:Total fruits = 9 Since there must be at least two apples, (⁵C₂ ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer:A #### A QUESTION:A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? options: A)3.75 days B)3.99 days C)2.67 days D)2.98 days E)2.44 days SOLUTION:1/4 + 1/8 = 3/8 8/3 = 2.67 days Answer: C #### C QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B QUESTION:In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ? options: A)35 B)39 C)48 D)50 E)52 SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 C #### C QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:A ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)28.97 B)28.0 C)28.47 D)27.47 E)29.47 SOLUTION:Explanation : After 10 days : 200 women had food for 25 days. Suppose 175 women had food for x days. Now, Less women, More days (Indirect Proportion) 175 : 200 :: 25 : x => 175 x x = 200 x 25 => x = 200 x 25 / 175 => x =28.47 Answer : C #### C QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(5044)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/360/55 = 40 min D #### D QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:Among the answers given below, which is nearly equal to √7? options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0 SOLUTION:2.6 is nearly equal to the square root of 7 2.62.6=6.76 2.52.5=6.25 difference 7 - 6.76=0.24 7 - 6.25=0.75 Since 0.24 is lesser of both, 2.6 is closer. Answer is C #### C QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)52% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16 so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52% ANSWER:D #### D QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 72/247 7410 = 2160 Answer: A #### A QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)1.6 B)1 C)0.4 D)0.16 E)0.016 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi1610 = pih100100 (h is distance that the oil level dropped) h = 160/10,000 = 16/1000 = 0.016 ft The answer is E. #### E QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:If n is a positive integer, then n(n+1)(n+2) is +ve and options: A)divisible by 4 whenever n is even B)divisible by 3 only when n is odd C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n(n+1)(n+2)= +ve even integer divisible by 4 ( e.g 3,4,&5) A #### A QUESTION:A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction? options: A)8% B)10% C)2% D)5% E)6% SOLUTION:Actual price = 100+10 = $110 Saving = 10/110 100 = 100/11 =10% approximately Answer is B #### B QUESTION:A man took loan from a bank at the rate of 10% p.a. simple interest. After 3 years he had to pay Rs. 3000 interest only for the period. The principal amount borrowed by him was: options: A)8000 B)10000 C)11000 D)12000 E)13000 SOLUTION:Principal = (100X3000)/(10X3)= Rs. 10000 answer : B #### B QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 Ã— 16 = 368 m2 Area of the inner rectangle = 19 Ã— 12 = 228 m2 Required area = (368 â€“ 228) = 140 m2 Answer B #### B QUESTION:For all positive integers n and m, the function A(n) equals the following product: (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8 SOLUTION:For all positive integers n and m, A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2) B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive. A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...} A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2) The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ... missing numbers are 1/8, 1/13, 1/16, .... B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25) here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values The largest reciprocal that present in B(25) but not in A(5) is 1/3 Answer A #### A QUESTION:60 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)8 days B)6 days C)7 days D)9 days E)12 days SOLUTION:1 women's 1 day work = 1/420 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/420 + 10/140) = 1/12 5 women and 10 children will complete the work in 12 days. Answer: E #### E QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by options: A)64 B)8 C)4 D)64 E)1/64 SOLUTION:Say r=2 => V1 = 1/64 when r=1; V2 = 1/16 V2 = 4V1. Answer=C=4 #### C QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%? options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5% SOLUTION:Let marked price = $100. Then, C.P. = $64, S.P. = $87 Gain % = 23/64 100 = 35.9%. B #### B QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61? options: A)6.5 B)12.5 C)28 D)30.5 E)40 SOLUTION:Some of pyhtagron triplets we need to keep it in mind. Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61). So now we know the triangle is an right angle triangle. The circle circumscribes the triangle. The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 Ans. D #### D QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:The number 0.8 is how much greater than 1/2 ? options: A)½ B)3/10 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .8-1/2=x 8/10-1/2=x x= 3/10 ans B #### B QUESTION:What is the speed required for a car to cover a distance of 600 km in 5 hours? options: A)160 kmh B)140 kmh C)150 kmh D)130 kmh E)120 kmh SOLUTION:Speed= Distance / Time Speed = 600 / 5 = 140 Answer: B #### B <<<Examples ends QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is? options: A)4km/h B)3km/h C)2km/h D)(1/2) km/h E)E)None SOLUTION:100 --- 10 DS = 10 ? ---- 1 80 ---- 20 US = 4 ? ----- 1 S = (10 - 4)/2 = 3 kmph ANSWER:B #### B QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:1/2+[(2/33/8)+4]-7/16= options: A)29/16 B)19/16 C)69/16 D)9/13 E)0 SOLUTION:1/2+[(2/33/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C #### C QUESTION:If log10 2 = 0.3010, the value of log10 80 is: options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252 SOLUTION:= log10 8 + log10 10 = log10 (23 ) + 1 = 3 log10 2 + 1 = (3 x 0.3010) + 1 = 1.9030. ANSWER B #### B QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26 SOLUTION:Explanation: Let the present age of P and Q be 3x and 4x respectively. Eight years ago, P was half of Q in age => 2(3x – 8) = (4x – 8) => 6x – 16 = 4x – 8 => 2x = 8 => x = 4 7x=74=28 Answer: Option B #### B QUESTION:The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted? options: A)8 B)5 C)15 D)22 E)6 SOLUTION:Let the two numbers be 6x and 5x. Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k. (6x - k) / (5x - k) = 5/4 => 24x - 4k = 25x - 5k => k = x. 6x - 5x = 5 => x = 5 k = x = 5. Answer:B #### B QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? options: A)1/3 B)1/30 C)1/42 D)2 E)30 SOLUTION:Pete covered 3.560=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42. Answer: C. #### C QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2 SOLUTION:39/360 22/7 * 12 * 12 = 49m2 Answer:C #### C QUESTION:If w and t are positive integers, wt + w + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let wt + t + w = x Add 1 on both sides: wt + t + w + 1 = x + 1 t(w + 1) + w + 1 = x + 1 (w + 1)(t + 1) = x + 1 Minimum value of (w + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> wt + t + s cannot be 6 Answer: B #### B QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:There are 3 people and 3 chairs. In how many different ways people can occupy the chairs? options: A)6 B)15 C)24 D)36 E)120 SOLUTION:number of ways =3! = 6 Answer is A #### A QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days B will the work get over? options: A)60 B)70 C)B=75 D)B=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 10010=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used. The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost? options: A)7000 B)1000 C)1011 D)1101 E)1110 SOLUTION:The number of codes possible if leading zero is allowed = 10101010=10^4 The number of codes possible if leading zero is NOT allowed = 7101010=910^3 The difference = 10^4 - 710^3 = 10^3(10-7) = 710^3. Answer: A. Similar questions to practice: Hope it helps. #### A QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:If xy not equal 0 and x^2y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)45% C)32% D)40% E)28% SOLUTION:answer b male-employed - 64% female-employed-19% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 19/64 =28 E #### E QUESTION:A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal. options: A)6:7 B)4:5 C)5:8 D)25:64 E)3:5 SOLUTION:The hare takes 3 leaps and the jackal takes 5 leaps. 1 hare leap = 4/3 jackal leaps Thus the hare's 3 leaps = 3(4/3) = 4 jackal leaps. The ratio of their speeds is 4:5. The answer is B. #### B QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 58 = Rs. 2784. Answer:A #### A QUESTION:The C.P of 20 pens is equal to the S.P of 12 pens. Find his gain % or loss%? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:20 CP = 12 SP 20 --- 8 CPgain 100 --- ? => 40% Answer: D #### D QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml SOLUTION:Explanation: Profit (%) = 9.09 % = \inline \frac{1}{11} Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml] Answer: A) 83.33 ml #### A QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers The answer is D. #### D QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 45678=6720. ANS:A #### A QUESTION:How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!? options: A)2 B)3 C)5 D)6 E)9 SOLUTION:7! = 720 1/1000 < 1/720< 1/100 0.001 < 1/720 < 0.01 So 1/720 has 2 leading zeros Answer: A #### A QUESTION:What is the largest integer n such that 2^n is a factor of 20^8 ? options: A)1 B)2 C)4 D)8 E)16 SOLUTION:20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16. Answer: E. #### E QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? options: A)16 km B)87 km C)89 km D)67 km E)20 km SOLUTION:Let the distance between A and B be x km. Total time = x/(9 + 1) + x/(9 - 1) = 3.5 => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x = 16 km. Answer:A #### A QUESTION:A shopkeeper cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 20% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)32% C)23.365% D)22.109% E)2% SOLUTION:Anyways, one can infer that he 'steals' 20% from suppliers and then charges 10% extra to customers So basically 1.2 * 1.1 = 1.32 Given that 1 is start point, we get 32% more Hence answer is B #### B QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (Â³Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:14,24,54,34,44,56,53, ? options: A)44 B)55 C)66 D)77 E)88 SOLUTION:14-24...dif -10 54-34..dif -20 44-56..dif-12 53-77...dif-24 ANSWER:D #### D QUESTION:The product of all the prime numbers less than 25 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^8 E)10^5 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19,23 =2.2 10^8 D #### D QUESTION:The contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots? options: A) 24 B) 26 C) 30 D) 46 E) 50 SOLUTION:carrrots = (carrrots + kiwi + x)0.3 24 = (30 + 24 + x)0.3 x = 26. Answer: B. #### B QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits? options: A)36 B)77 C)88 D)99 E)22 SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1) Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2) Multiplying equation (1) by 2 and subtracting it from equation (2), we get => 2r = 72 => r = 36. Answer: A #### A QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y? options: A)560 B)616 C)672 D)728 E)784 SOLUTION:ans B 616... remainders = .32=32/100=8/25=16/50 and so on.. so two digit remainders are 16+24+32+....+96.. W=8(2+3+4....+12)=616 #### B QUESTION:8^100 is divisible by 17. Find the remainder? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate? options: A)12% B)14% C)15% D)18% E)None of these SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100) ⇒ 122.40 = 160(1−10/100)(1−d2/100) ⇒ 1−d2/100=122.40×100/160×90=0.85 ⇒ d2 = (1 - 0.85) × 100 = 15% Answer C #### C QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4PIR^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ? options: A)21st B)22nd C)23rd D)24th E)None of these SOLUTION:In 2 minutes, he ascends = 1 metre ∴ 10 metres, he ascends in 20 minutes. ∴ He reaches the top in 21st minute. Answer B #### B QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? options: A)124 B)150 C)212 D)243 E)316 SOLUTION:3^5 = 243 The answer is D. #### D QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20. So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40. #### B QUESTION:A jogger running at 9 km/hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)89 B)20 C)36 D)88 E)30 SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 180 + 120 = 300 m. Time taken = 300/10 = 30 sec. Answer: Option E #### E QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50X + 500 (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)14% B)23% C)30% D)50% E)100% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.410 = 14 Wage of Charles = 1.6 10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100% = 2/14 * 100% =14% Answer A #### A QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen? options: A)1/30 B)1/25 C)1/20 D)1/28 E)1/30 SOLUTION:Probability that John and David will both be chosen out of 8 workers = (2/8)(1/7) = 1/28 Answer D #### D QUESTION:Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? options: A)21, 12 B)9, 0 C)15, 6 D)10, 1 E)14, 5 SOLUTION:the larger number: x the smaller number: y twice the larger: 2x three more than five times the smaller: 5y + 3 relationship between ("is"): 2x = 5y + 3 four times the larger: 4x three times the smaller: 3y relationship between ("sum of"): 4x + 3y = 71 Now I have two equations in two variables: 2x = 5y + 3 4x + 3y = 71 I will solve, say, the first equation for x: x = (5/2)y + (3/2) Then I'll plug the right-hand side of this into the second equation in place of the "x": 4[ (5/2)y + (3/2) ] + 3y = 71 10y + 6 + 3y = 71 13y + 6 = 71 13y = 65 y = 65/13 = 5 Now that I have the value for y, I can solve for x: x = (5/2)y + (3/2) x = (5/2)(5) + (3/2) x = (25/2) + (3/2) x = 28/2 = 14 Answer: E #### E QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:If an article is sold at 19% profit instead of 12% profit, then the profit would be $84 more. What is the cost price? options: A)$900 B)$1200 C)$1500 D)$1800 E)$2100 SOLUTION:7% cost price = $84 1% * cost price = $84 / 7 = $12 The cost price is $1200. The answer is B. #### B QUESTION:A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set? options: A)25 B)30 C)35 D)45 E)46 SOLUTION:for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same.. here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5.. remaining 6= 2011-5=215.. therefore each valueof these 6 int =215/6=35 ans C #### C QUESTION:2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes? options: A)2 B)4 C)6 D)500 E)0 SOLUTION:2 men.....there are no other!!!! #### A QUESTION:A fruit seller sells mangoes at the rate of Rs.14 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 15%? options: A)Rs.11.81 B)Rs.12 C)Rs.18.94 D)Rs.12.31 E)None SOLUTION:Solution 85 : 14 = 115 : x x= (14Ã—115/85) = Rs.18.94 Hence, S.p per Kg = Rs.18.94 Answer C #### C QUESTION:In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100? options: A)30 B)20 C)25 D)40 E)50 SOLUTION:X scores 45 while Y score 40 and Z scores 30. The number of points that Z scores when Y scores 100 = (100 30)/25 = 60. In X game of 100 points, Y gives (100 - 60) = 40 points to C. D #### D QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago? options: A)27 B)30 C)33 D)36 E)39 SOLUTION:P = 3Q so Q = P/3 P+10 = 2(Q+10) = 2(P/3+10) P/3 = 10 P = 30 Three years ago, P was 27. The answer is A. #### A QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ? options: A)3990 B)1540 C)1995 D)3672 E)None of these SOLUTION:In order that two books on French are never together, we must place all books as under X E X E X E X E X E .....X E X where E denotes the position of an English book and X that of a French book. Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways Answer B. #### B QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 35y= 15y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:A swimmer can swim in still water at 4 km/h. If the speed of the water current is 1 km/h, how many hours will the swimmer take to swim against the current for 6 km? options: A)1.2 B)1.4 C)1.6 D)1.8 E)2 SOLUTION:The swimmer can swim against the current at a speed of 4-1 = 3 km/h. The time it will take is 6/3 = 2 hours. The answer is E. #### E QUESTION:Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 36/49, what is the probability that the next one she draws will be pink? options: A)1/7 B)4/7 C)3/7 D)16/49 E)40/49 SOLUTION:The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 36/49 = (6/7) * (6/7) Therefore probability that the next one she draws is pink = 1/7 Option (A) #### A QUESTION:At Bala's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009? options: A)700 B)1000 C)1300 D)1600 E)2000 SOLUTION:At Bala's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year: R2008= R2007(1+x) R2009= R2007(1+x)^2=1.44R2007 (1+x)^2 = 1.44 1+x=1.2 x=0.2 aka revenue increases 20% each year and cost increases 10% annually Next solve for R2007and C2007: R2007= C2007- 1000 1.2R2007- 1.1C2007= 0 1.2[C2007- 1000] - 1.1C2007= 0 0.1C2007= 1,200 C2007= 12,000 R2007= 11,000 Finally find 2009 profits: Profit2009= 1.4411,000 - 1.2112,000 Profit2009= 15,840 - 14,520 Profit2009= 1320 Answer: C #### C QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20100/1000 = 2.0% Answer is A #### A QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 33=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work. options: A)27 days B)54 days C)56 days D)68 days E)78 days SOLUTION:Explanation: As per question, A do twice the work as done by B. So A:B = 2:1 Also (A+B) one day work = 1/18 To get days in which B will finish the work, lets calculate work done by B in 1 day = =(1/18∗1/3)=1/54 [Please note we multiplied by 1/3 as per B share and total of ratio is 1/3] So B will finish the work in 54 days Option B #### B QUESTION:Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last? options: A)6 B)7 C)8 D)8 1/9 E)10 SOLUTION:Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job. Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15 3/20 (t) = 7/15 ---> t = 3 1/9 Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days Answer: D #### D QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.2 feet C)3.3 feet D)3.0 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+2=36 36/12=3.0 feet ANSWER:D #### D QUESTION:Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? options: A)13 B)14 C)18 D)11 E)10 SOLUTION:(5 + x)/20 + 5/25 = 1 => x = 11 days Answer:D #### D QUESTION:A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $900 was the net sum to be paid for the entire work, what was the average daily wage of B? options: A)$144 B)$90 C)$60 D)$54 E)$48 SOLUTION:The correct answer is C. #### C QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? options: A)27 B)34 C)50 D)61 E)78 SOLUTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. Machine starts manufacturing Red and ended on Black. This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78 Only 78 is given in the options. So answer = 78 ANSWER:E #### E QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1x X=11.81% Answer D) #### D QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase? options: A)16.66% B)17% C)15.8% D)12% E)None of these SOLUTION:Explanation : Solution: reduction in consumption = [r/(100+r) 100]% = (20/120 * 100) = 16.66% Answer : A #### A QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 851 is 0. The answer is A. #### A QUESTION:A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 120 miles at 60 mph? options: A)15% B)20% C)25% D)27% E)40% SOLUTION:Total time for travelling 120 miles @ 60 mph = 120/60 = 2 hour = 120 minutes. Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 120 minutes it will use = 3 gallons. Thus, full tank = 3+8 = 11 gallons --->3/11= 27% of the fuel used. D is the correct answer. #### D QUESTION:24 machines can do a work in 10days. How many machines are needed to complete the work in 40days? options: A)10 B)6 C)4 D)7 E)5 SOLUTION:Required number of machines = 2410/40 = 6 Answer is B #### B QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be options: A)3:2 B)1:1 C)1:2 D)3:4 E)3:8 SOLUTION:Lots of little places to make a mistake or panic here. =) R = 3G B = R/2 G/R = 1/3 ----> Doubled G/R = 2/3 R/B = 2 ----> Doubled R/B = 4 B/G = (B/R)(R/G) = (1/4)(3/2) = 3/8 ANSWER:E #### E QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:If p/q = 5/4 , then 2p+q= ? options: A)12 B)14 C)13 D)15 E)16 SOLUTION:let p=5, q=4 then 25+4=14 so 2p+q=14. ANSWER:B #### B QUESTION:A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg? options: A)Rs.120 B)Rs.125 C)Rs.130 D)Rs.135 E)Rs.140 SOLUTION:Explanation: 2400(40/100) = 960 ---- 8 ? ---- 1 => Rs.120 Answer: A #### A QUESTION:The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is: options: A)3 months B)4 months C)5 months D)6 months E)7 months SOLUTION:S.I. on Rs. 1600 = T.D. on Rs. 1680. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%. Time = (100x80)/(1600x15)= 1/3 year = 4 months answer : B #### B QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K? options: A)1 B)3 C)4 D)2 E)6 SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b) So k is 2 Option D #### D QUESTION:3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions? options: A)(A + B)2 - 4AB B)(A – B)2 + 4AB C)A2 + B2 - 4AB + 2AB D)A2 – B2 + 2B(B – A) E)None of these SOLUTION:1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB 2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB 3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB 4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB Therefore, (1) = (3) = (4) ≠ (2) Therefore, expression (2) is wrong ANSWER IS B #### B QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by: options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800 SOLUTION:A : B : C = (16000 x 3 + 11000 9) : (12000 * 3 + 17000 * 9) : (21000 * 6) = 147 : 189 : 126 = 7 : 9 : 6. Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22 = Rs.3600 ANSWER:C #### C QUESTION:Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price? options: A)(YP)/100X B)100X/(YP) C)(YP)+100X D)(YP)-100X E)(YP)100X SOLUTION:Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P 100 = 100X/(YP) Answer : B #### B QUESTION:Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 options: A)4/7 B)5/3 C)4/5 D)5/8 E)7/18 SOLUTION:Clearly n(S)=66=36 Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2), (6,6)} n(E)=14. Hence p(e)=n(e)/n(s)=14/36=7/18 ANS: E #### E QUESTION:Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)22 B)66 C)48 D)77 E)21 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 5/18 = 125/6 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 6/125 = 48 sec. Answer:C #### C QUESTION:A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $140 B) $160 C) $220 D) $240 E) $264 SOLUTION:12$ per week! An year has 52 weeks. Annual charges per year = 52* 12 = 624$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 30 = 360$ 624 - 360 = 264 Ans E #### E QUESTION:Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?. options: A)Rs. 10000 B)Rs. 20000 C)Rs. 30000 D)Rs. 40000 E)Rs. 50000 SOLUTION:Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev’s share = Rs.(150000×2/6) = Rs. 50000 Answer E #### E QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:A die is thrown three times. Events X and Y are defined as below: X : 4 on the third throw Y : 6 on the first and 5 on the second throw What is the probability of X given that Y has already occurred. options: A)1/6 B)1/7 C)1/8 D)1/11 E)1/13 SOLUTION:The sample space has 216 outcomes. Now X = (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4) (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4) (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4) Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)} and X n Y = {(6,5,4)}. Now P(Y) = 6/216 and P (X n Y) = 1/216 Then P(X\|Y) = (1/216)/(6/216) = 1/6. A #### A QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 * 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4 SOLUTION:P1 takes 12 hrs Rate for P2P3 together = 1/16 + 1/18 = 17/144 Therefore they take 144/17 Ratio = 144/17 = D #### D QUESTION:Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A? options: A)29491 B)28491 C)39491 D)49491 E)59491 SOLUTION:Compound ratio of A:B:C A:B = 3:4 B:C = 5:6 ---------- A:B:C = 15:20:24 We can divide Rs.116000 in this ratio. Share of A = 15/59 * 116000 = 29491 ANSWER:A #### A QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work? options: A)2 days B)76 days C)8 days D)6 days E)4 days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 day's work = 1/9 * 6 = 2/3 Remaining work = 1 - 2/3 = 1/3 18 men's 1 day work = 1/108 * 18 = 1/6 1/6 work is done by them in 1 day. 1/3 work is done by them in 6 * 1/3 = 2 days. Answer: A #### A <<<Examples ends QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers? options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by x = 2y - 4 We use the sum of the two numbers to write a second equation. x + y = 20 Substitute x by 2y - 4 in x + y = 20 to obtain 2y - 4 + y = 20 Solve for y to find y = 8 and x = 2y - 4 = 12 Answer B #### B QUESTION:In an election contested by two parties, Party ADMK secured 24% of the total votes more than Party DMK. If party DMK got 266,000 votes, by how many votes did it lose the election? options: A)34,000 B)56,000 C)164,000 D)168,000 E)200,000 SOLUTION:ADMK + DMK = 100 ---- (1) ADMK - DMK = 24 ---- (2) Solving (1) and (2) ADMK = 62% and DMK = 38% 38% of Total = 266000 Total = 700000 ADMK = 434000 Difference = 434000 - 266000 = 168000 Answer: D #### D QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 26th September was a Wednesday. The answer is C. #### C QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph? options: A)22 sec B)77 sec C)25 sec D)18 sec E)12.5 sec SOLUTION:D = 100 + 150 = 250 S = 72 * 5/18 = 20 mps T = 250/20 = 12.5 sec Answer:E #### E QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? options: A)126 B)120 C)101 D)112 E)115 SOLUTION:8 shirts 9 pants we can combine 2 shirts with (12-3) pants 29=18 we can combine the other shirts (6) with any pants (9) 912=54 Thus total :108+18=126 ANS:A #### A QUESTION:The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is: options: A)270 B)300 C)299 D)322 E)345 SOLUTION:the numbers are (18 x 11) and (18 x 15). Larger number = (18 x 15) = 270. ANSWER :A #### A QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x50 = 200040 x=1600 2000 ------- 400 Answer: A #### A QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:P makes x sprockets per hour. Then Q makes 1.1x sprockets per hour. 880/x = 880/1.1x + 10 1.1(880) = 880 + 11x 11x = 88 x = 8 The answer is D. #### D QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is? options: A)621 B)276 C)236 D)600 E)211 SOLUTION:Explanation: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6 And also given that, profit share of B is Rs. 1500 => 5 parts out of 15 parts is Rs. 1500 Now, required difference is 6 - 4 = 2 parts Required difference = 2/5 (1500) = Rs. 600 Answer: D #### D QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/25 = 40/2 =20 Answer:B #### B QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 6c+3. The minimum is 3 when c=0. The maximum is 45 when c=7. There are 8 such numbers. The answer is D. #### D QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even) Least number = 2 A #### A QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:Which of the following numbers is divisible by 4? options: A)27767 B)10224 C)26778 D)26679 E)26711 SOLUTION:10224. This is the only option with last two digits divisible by 4 Answer:B #### B QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:In your classes you counted 120 hands. How many students were at the class? options: A)60 B)61 C)85 D)86 E)88 SOLUTION:Total number of hands = 120 We have 2 hands. To find how many students were at the class, divide the total number of hands by the number of hands we have. We get, divide 120 by 2 220 ÷ 2 = 60 Therefore, there were 60 students at the class. ANSWER IS A #### A QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? options: A)2 B)5 C)15 D)20 E)25 SOLUTION:Audery and Ferris collective Work rate: 1/4 + 1/3 = 7/12 Collective work Time = 12/7 = 1.7 Hrs Job Was actually done in = 2 (Includes breaks) Breaks = Actual time taken - Collective work time = 2 - 1.7 = .3 Hrs = 1/2 so ferrais took 6 breaks =.3/6=.06 hrs = 5 m so Answer is B) 10 mins #### B QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.42^10=0.41024=409.6 The answer is C. #### C QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction? options: A) 49 B) 9 C) 28 D) 26 E) 21 SOLUTION:x/y = 2/5 -> 1 (x+4)/2y = 1/3 -> 2 Divide 1 by 2 : => 2x/(x+4) = 6/5 => 5x = 3x + 12 => x = 6 => y = 5/2 * 6 = 15 so x - y = 9 The answer is B #### B QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300 SOLUTION:Let the cost of one toy = X. Then, cost of 18 toys = 18X. Gain = 3X. SP of 18 toys = Rs. 27300. Gain = SP â€“ CP 3X = 27300 â€“ 18X 21X = 27300 X = Rs. 1300. ANSWER : OPTION E #### E QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ? options: A)d B)3d C)15d D)d + 5 E)d + 15 SOLUTION:If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change. If we increase or decrease each term in a set by the same percent (multiply by a constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5. Answer: D. #### D QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. options: A)180 B)181 C)182 D)183 E)184 SOLUTION:52+50+78 = 180 Answer: A #### A QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in? options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec ANSWER: D #### D QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is options: A)360 B)240 C)2520 D)480 E)None of these SOLUTION:Solution Order of vowels of fixed âˆ´ required number of ways are 7!/2!. Answer C #### C QUESTION:The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A ? options: A)12 B)27 C)21 D)18 E)11 SOLUTION:(A+B) - (B+C) = 18 A - C = 18. C is younger than A by 18 years. Answer: D #### D QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)51 23/27% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27% Answer B #### B QUESTION:If log303 = a, log305 = b, then log308 =? options: A)3(1 - a - b) B)(a - b + 1) C)(1 - a - b) D)(a - b + 1) E)none of these SOLUTION:a + b = log3015 = log30(30/2) = 1- log302 => log302 = (1 - a - b) Therefore, log308 = 3(1 - a - b). ANSWER:A #### A QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2 options: A)I only B)I,II only C)II only D)I,III only E)III only SOLUTION:12=223 16=2222 GCF =22=4 Answer : C #### C QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)17 E)72 SOLUTION:Explanation: As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 56 adults = 72 children Hence, the meal can be catered to 72 children. ANSWER: E #### E QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? options: A)330 B)650 C)729 D)800 E)890 SOLUTION:Choose 4 starters from a team of 11 players. Order is not important. \inline {\color{Black} 11C_{4}}= 330 A #### A QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D QUESTION:Which of the following equations represents a line that is perpendicular to y=1/2x+3? options: A)y−2x=8 B)2x+4y=10 C)3y+6x=12 D)4y−8x=16 E)5x−10y=20 SOLUTION:For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2 Answer: E #### E QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 58 = Rs. 2784. Answer:A #### A QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2 SOLUTION:John's speed - 12 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles. Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr. Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours Answer B #### B QUESTION:Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q? options: A)15:8 B)15:5 C)15:9 D)15:2 E)15:3 SOLUTION:Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8 Answer:A #### A QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...) options: A)31 B)42 C)46 D)56 E)68 SOLUTION:Explanation : We have two series here 34, 37, 40, 43, ... (Increase by 3) 7, 14, 28, ... (Multiply by 2) Hence, next term is 28 × 2 = 56 Answer : Option D #### D QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? options: A)$110 B)$152.3 C)$180 D)$220 E)$260 SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition. A-E = 1/10(A+E) ==> 9A = 11E ------------ (1) Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E 1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2) Substituting (1) in (2): 11E/911 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 2209/13 =152.3 B #### B QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (512/5)/100] P= 1500.Answer:A #### A QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B. options: A)16 years B)24 years C)8 years D)12 years E)18 years SOLUTION:let present age of A be A let presennt age of B be B in 6 yrs A+6:B+6=3(B-4):B=6 ie A+6=3(B-4) but given A=B+6 so B+6+6=3(B-4) B=12 ANSWER:D #### D QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C26C2=150 Answer E #### E QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:In 16 minutes, the minute hand gains over the hour hand by options: A)16° B)80° C)88° D)96° E)None of these SOLUTION:In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand. ∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88° Answer C #### C QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench? options: A)700 B)710 C)720 D)800 E)820 SOLUTION:npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) #### C QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part? options: A)17 B)21 C)31 D)45 E)47 SOLUTION:Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation larger number – smaller number = 7 which is equivalent to Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31. C #### C QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 4 senior and 1 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)60 E)200 SOLUTION:6C44C1 =60=D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform? options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m SOLUTION:Speed = 300/24 = 25/2 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 25/2 => x = 187.5 m. Answer:C #### C QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set? I. 1 II. -4 III. 5 options: A)I only B)II only C)I and III only D)II and III only E)I, II, and III SOLUTION:The question is which of the following must be in the set, not could be in the set. If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set. Answer: C. #### C QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:A Cuban cigar would cost 3 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar? options: A)19.7$. B)23$. C)14.7$. D)35$. E)37.4$. SOLUTION:The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each. From the given data we know French cigar < Cuban cigar < Arabic cigar and each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer. Therefore C is the answer. #### C QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x? options: A)Three B)Four C)Five D)Six E)Seven SOLUTION:Since the number is positive and even and contains only 3 and 4 as digits, then its numbers digit is 4 and is fixed. As there are not many possibilities for x, I found the most simple method to just start plug in numbers starting from the first and least value of x, which is answer key A. three If x would have 3 digits, then we have 4 possibilities (since 4 is always the number digit for an even number): 334: is divisible by 4 but not by 3 344: is divisible by 4 but not by 3 434: is not divisible by 4 nor by 3 444: is divisible by 4 AND by 3 - then CORRECT ANSWER A #### A QUESTION:A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.24, find the sum of money? options: A)288 B)262 C)72 D)123 E)267 SOLUTION:A:B:C = 100:65:40 = 20:13:8 8 ---- 24 41 ---- ? => Rs.123 Answer: D #### D QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these SOLUTION:Explanation : Total numbers = 70 Total numbers in 1 to 70 which has 1 in the unit digit = 7 Total numbers in 1 to 70 which has 9 in the unit digit = 7 Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14 Required percentage = (14/70) × 100 = 140/7 = 20% Answer : Option B #### B QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(13651.89+7201.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:If d<0, which of the following represents a positive number? options: A)d\|d\| B)\|d\|d C)\|d\|/d D)-d\|d\| E)d/ \|d\| SOLUTION:Answer : D #### D QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 66 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? options: A)2.5 sec B)4.25 Sec C)5 sec D)12.5 sec E)None SOLUTION:Solution Speed = (144 x 5 /18) m/sec = 40 m / sec Time taken = (100 /40) sec = 2.5 sec. Answer A #### A QUESTION:Income and expenditure of a person are in the ratio 4 : 3. If the income of the person is Rs. 20000, then find his savings? options: A)Rs.3600 B)Rs.3603 C)Rs.3639 D)Rs.3632 E)Rs.5000 SOLUTION:Let the income and the expenditure of the person be Rs. 4x and Rs. 3x respectively. Income, 4x = 20000 => x = 5000 Savings = Income - expenditure = 4x - 3x = x So, savings = Rs.5000 Answer: E #### E QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:At a certain organisation, the number of male members went up by 15% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? options: A)1:2 B)1:3 C)2:3 D)3:2 E)2:1 SOLUTION:men increase by 15% ==> 1.15M = males in 2001 women decrease by 6% ==> 0.94F = women in 2001 total employees increase by 1.2% ==> 1.012(M + F) = total number of employees in 2001 Obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.15M + 0.94F = 1.012(M + F) 1.15M + 0.94F = 1.012M + 1.012F 1.15M - 1.012M = 1.012F - 0.94F 0.138M = 0.072F M/F = (0.072)/(0.138) = 72/138 = 1/2 Answer =(A) #### A QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 960/45 = 94/3 = 12 New time in minutes to cross 9 miles stretch = 960/35 = 912/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr. What is the speed of the boat? options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph SOLUTION:speed upstream = 10/3 speed of boat down stream = 10/6 speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph ANSWER:A #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 18/5 km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Option B #### B QUESTION:In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King. Who am I? options: A)Johny B)Jacky C)Ricky D)David E)Alex SOLUTION:D I am DAVID. At the core I have 5 If we talk in roman numeric system, 5 = V Similarly, 500 stands in the beginning and end 500 = D I also include the first letter i.e. A and the first number i.e. I (in roman numeric system) All of them combine to form DAVID. #### D QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is options: A)74 B)78 C)86 D)92 E)106 SOLUTION:Divisor = (6 * 3) + 7 = 25 5 * Quotient = 25 Quotient = 5. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 5) + 6 = 106. E) #### E QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 25,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000 ANSWER:D #### D QUESTION:P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together. options: A)2 B)3 3⁄7 C)4 ¼ D)5 E)5 ¼ SOLUTION:Explanation : Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 => Working together, they will complete the work in 24/7 days = 3 3⁄7 days Answer : Option B #### B QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:A is followed by B means : A comes first,B comes next A preceded by B means : B comes first, A comes next The sets which satisfy the condition is: 5 3 8 1 3 8 7 3 4 ANSWER:C #### C QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 235^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:w 10!= 10987654321 = 253322272352232 = 2^83^45^27 6= 23 Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D #### D QUESTION:If A lends Rs.4000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? options: A)112.5 B)122.5 C)132.5 D)114.5 E)180 SOLUTION:(40001.53)/100 => 180 ANSWER:E #### E QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph SOLUTION:US = 45 DS = 55 M = (45 + 55)/2 = 50 Answer:D #### D QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ? options: A)5 B)-45 C)45 D)50 E)60 SOLUTION:Explanation: => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)] = 5 - (50) = - 45 Answer: Option B #### B QUESTION:How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)12 sec B)30 sec C)36 sec D)16 sec E)18 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 5/18 = 50/3 m/sec. Time taken to pass the man = 600 * 3/50 = 36 sec. Answer: C #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is S? options: A)50+A/200 B)50+3S/100 C)50+S/40 D)100+S/50 E)100+3S/100 SOLUTION:50+S/40=C #### C QUESTION:If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)? options: A) 1 B) 13 C) 26 D)25 E) 1014 SOLUTION:x = 14 + 16 + ... + 62 = (largest + smallest)/2 (# of terms) = (14 + 62)/225 = 3825. GCD of 25 and 3925 is 25. Answer: D. #### D QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is : options: A)427 B)859 C)860 D)4320 E)None of these SOLUTION:Solution Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390(85/100)(75/100) = 248 Answer: C #### C QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:385, 462, 572, 396, 429, 671, 264 options: A)385 B)429 C)671 D)264 E)None of these SOLUTION:Solution In each number except 429,the middle digit is the sum of the other two. Answer B #### B QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)22 B)45 C)66 D)88 E)12 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? options: A)s.1014 B)s.1332 C)s.999 D)s.1085 E)s.1020 SOLUTION:a2 = 3136 => a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 ANSWER:B #### B QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 6/9% B)42 3/7% C)42 7/7% D)42 6/7% E)22 6/7% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D <<<Examples ends QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above SOLUTION:5510 = 550 665 = 330 880/15 = 58.66 ANSWER:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5 options: A)15 B)20 C)25 D)32.5 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5 Answer: Option D #### D QUESTION:One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)9:4 C)5:6 D)5:0 E)2:4 SOLUTION:Explanation: 45 * 5/18 = 10 25:20 => 5:4 Answer: Option A #### A QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a quarter of its new value. What is the stock's value at the end of Monday? options: A)X. B)3X/8. C)2X/3. D)X/3. E)X/4. SOLUTION:Stock value= X AT sunday end= x+.5X= 1.5 X On monday the value drop to 1/4rd of its value on sunday 1.5x/4= 3X/8 B is the answer #### B QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ? options: A)5 B)-45 C)45 D)50 E)60 SOLUTION:Explanation: => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)] = 5 - (50) = - 45 Answer: Option B #### B QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years? options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150 SOLUTION:P= $2000 R = 20% T = 2 years Machine value before 2 years = P/[(1-R/100)^T] =20005/4 5/4 =$3125 Answer is A #### A QUESTION:A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion? options: A) 81 B) 83 C) 85 D) 86 E) 89 SOLUTION:Overall, there can be 81 minuses. Tus, it is A. #### A QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days? options: A)1/8 B)1/3 C)1/6 D)1/2 E)5/3 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/60 (A + B)'s one day's work = 1/30 + 1/60 = 1/20 The part of the work completed in 10 days = 10 (1/20) = 1/2. Answer:D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 \Answer:C #### C QUESTION:The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period? options: A)$1.18 B)$1.17 C)$1.16 D)$1.15 E)$1.14 SOLUTION:Let x be the number of loaves sold in May. Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June. The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) = (80 + 127 + 144) / (3) = 351/3 = $1.17 The answer is B. #### B QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1â„2 C)17 D)Data inadequate E)None of these SOLUTION:12 M Ã— 18 = 12 W Ã— 18 Ã— 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 Ã— 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12Ã—18/12 2/3=17days Answer C #### C QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40 SOLUTION:SOL: Lets consider h(100): => 2468.........98100 => (21) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50) => (2^50) * (1234........4950) => h(100) = (2^50) (50!) We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100). But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50; ANSWER:E #### E QUESTION:A man buys Rs. 60 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: options: A)s. 12 B)s. 15 C)s. 18 D)s. 21 E)s. 45 SOLUTION:Dividend on Rs. 60 = Rs. 9/100 x 60 =Rs. 5.4 . Rs. 12 is an income on Rs. 100. Rs. 5.4 is an income on Rs.100/12 x 5.4 = Rs. 45. Answer: Option E #### E QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 20 : 8 :: 12 : x => 8 x 20 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (8 x 20) => x = 6 Answer : C #### C QUESTION:Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ? options: A)1/2 B)1/4 C)1/5 D)1/6 E)1/3 SOLUTION:(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened. From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3. Answer: E. #### E QUESTION:Two coins are tossed, find the probability that two Tails are obtained options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3 SOLUTION:The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(T,T)} P(E) = n(E) / n(S) = 1/4 B #### B QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(34)+x/(35)=84/60 x=6 km ANSWER:C #### C QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620 options: A)22 B)12 C)14 D)16 E)None of these SOLUTION:? = 2620−256 /197=12 Answer B #### B QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ? options: A)2013 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2012) = 2013 Ans: A #### A QUESTION:A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)7 km D)5 km E)2 km SOLUTION:Let the total distance be 3x km. Then, x/8 + x/9 + x/10 = 47/60 x/3 = 47/60 => x = 2.33. Total distance = 3 * 2.33 = 6.99 km. Answer:C #### C QUESTION:If c is 14% of a and 40% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 250% SOLUTION:Answer = D 14a/100 = 40b/100 b = 14a/40 = 35a/100 = 35% #### D QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these SOLUTION:Explanation : Total numbers = 70 Total numbers in 1 to 70 which has 1 in the unit digit = 7 Total numbers in 1 to 70 which has 9 in the unit digit = 7 Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14 Required percentage = (14/70) × 100 = 140/7 = 20% Answer : Option B #### B QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k * 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:Can you find next number in tricky mathematical series below? 111 , 113 , 117 , 119 , 123 , 137 ? options: A)151 B)161 C)171 D)131 E)121 SOLUTION:Solution: 151 (131+20) Explanation: 1st 7 prime numbers post 100 are 101 , 103 , 107 , 109 , 113 , 127 , 131 ...Adding 20 to numbers 121 , 123 , 127 , 129 , 133 , 147 , 151 Answer A #### A QUESTION:What least number must be subtracted from 9679 so that the remaining number is divisible by 15? options: A)3 B)1 C)16 D)4 E)15 SOLUTION:On dividing 9679 by 15, we get remainder = 4. Required number be subtracted = 4 ANSWER:D #### D QUESTION:A student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:xC1 * (x-1)C1=42 x^2 -x -42 =0 (X-7 (X+6) = 0 X= 7 , -6 -6 can't possible. Hence 7 should be the answer A #### A QUESTION:A car covers a distance of 1080 km in10 hrs. What is its speed in mps. options: A)40 m/s B)25 m/s C)20 m/s D)15 m/s E)30 m/s SOLUTION:Explanation: Distance = Speed x Time Speed = (1080/10) = 108 kmph Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps. Answer: Option E #### E QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail? options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8 SOLUTION:Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {HHH,HTH,THH,HHT} P(E) = n(E)/n(S) =4/8 = 1/2 Answer is D #### D QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer? options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1 SOLUTION:9x^2-16y^2=3x+4y (3x+4y)(3x-4y)=3x+4y 3x-4y=(3x+4y)/(3x+4y) 3x-4y=1 Answer is option C #### C QUESTION:In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 32 more than twice the number of heads => 2(d + 2c) = 32 + 2(c + d) => d + 2c = 16 + c + d => 2c = 16 + c => c = 16 i.e., total number of cows = 16 Answer is C. #### C QUESTION:If 3^x = 2, then 3^(4x+3) = options: A)429 B)454 C)432 D)438 E)108 SOLUTION:3^x=2 3^4x=2^4 3^4x=16 3^(4x+3) =3^4x3^3 =1627 =432 Answer: C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases Answer: option E #### E QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52(15/60) =13m sum of length and breadth = 68(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2120 = 60 sq meter Answer: B) 60 #### B QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r1^2 . h1/r2^2. h2 => 1/15 = (1)^2h1/(2)^2h2 => h1/h2 = 3/5 i.e. h1 : h2 = 3:5 Answer: A #### A QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls. options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7% SOLUTION:Let the cost price of 1 balls be Rs 1 Cost of 14 balls= Rs 14 Selling price of 14 balls = 9 Gain/loss = 14 - 9 = 5 %=5/14âˆ—100= 35.7 Answer: A #### A QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose? options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0 SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x' The problem boils down to: Rose to Poppy: s+3=x/6 ------- 1 Daisy to Rose: s=(x+18)/10------ 2 so from 1 we can re write x as x=6s+18 substitute the value of x in 2 gives us s=1.8 m/s D #### D QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)5 B)7 C)3 D)1/2 E)4 SOLUTION:Explanation: M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: C #### C QUESTION:A brick measures 20cm10cm7.5cm how many bricks will be required for a wall 25m2m0.75m ? options: A)24000 B)23000 C)22000 D)25000 E)27000 SOLUTION:2520.75=20/10010/1000.75/100X 25=1/100X X=25000 Answer :D #### D QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2(0.1)^3(0.9)^2 1 Tail and 4 Heads, Probability = 5C1(0.1)^4(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. options: A)121km B)242km C)224km D)112km E)115km SOLUTION:Explanation: Average Speed =2Ã—21Ã—24/21+24=22.4 km/hr Total distance =22.4Ã—10=224 km ANSWER IS C #### C QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:.05% of cans of beans that go down a conveyor belt are sealed improperly and must be disposed of. How many cans of beans must pass down a conveyor belt for 5 cans to be sealed improperly? options: A)500 B)5000 C)4000 D)2500 E)10000 SOLUTION:Let the number of total cans of beans be x Then, .05% of x=5 (5/100)(1/100)x=5 x=10000 Answer is E #### E QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor options: A)625 B)1296 C)1540 D)1478 E)360 SOLUTION:Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5555=5^4=625. Answer: A. #### A QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 12 = 84 Answer is A #### A QUESTION:In your classes you counted 120 hands. How many students were at the class? options: A)60 B)61 C)85 D)86 E)88 SOLUTION:Total number of hands = 120 We have 2 hands. To find how many students were at the class, divide the total number of hands by the number of hands we have. We get, divide 120 by 2 220 ÷ 2 = 60 Therefore, there were 60 students at the class. ANSWER IS A #### A QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:Remainder of (6^17+17^6)/7= ? options: A)2 B)1 C)0 D)3 E)4 SOLUTION:6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7 17^6/7 = (27+3)^6/7 = 3^6/7 = 27^2/7 =(47-1)^2/7 =(-1)^2/7 = 1/7 so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0 ANSWER:C #### C QUESTION:A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price? options: A)d+5/1.05 B)d/1.05 +5 C)1.05d-5 D)d-5/1.05 E)1.05(p – 5) SOLUTION:Let x be the price of the item. Final price after discount and sales tax = x (1 - d/100) * 1.05 Let e be the percent discount which would result in the same final price. Then, x * (1 - d/100) * 1.05 = x * (1 - e/100) => 1.05 - 1.05d/100 = 1 - e/100 => e/100 = 1.05d/100 - .05 => e = 1.05d - 5 Hence ,option C is correct. #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4 Median = 4 Difference = 4-4 = 0 Option A #### A QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next? options: A)4.7 B)4.5 C)6.7 D)8.9 E)9.2 SOLUTION:In this simple addition series, each number increases by 0.8. ANSWER A #### A QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final100 =21/121100=8/33100=17% approxiamately. option A is correct. #### A QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D? options: A)55 B)61 C)69 D)90 E)97 SOLUTION:c + d = 11 5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15 D=15 c+d=9=C+15=9=C=9-15=-6 C=-6 5C + 8D=5(-6)+8(15)=-30+120=90 Hence, D is the right answer. #### D QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger? options: A)6 m B)5 m C)4 m D)3 m E)None of the above SOLUTION:Sol. Let the length of the tiger be x metres and its speed be y m/sec. Then, x / y = 1 ⇒ y = x ∴ (x + 20) / 5 = x ⇔ x = 5 m. Answer B #### B QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= lw = 1/2 wd (l=1/2 d or d=2l) top face area= wd side face area= wd = 1.5 dl (w=1.5l) Volume = lwd= 192 l1.5l2l= 192 l=4 Side face area= ld= l2l= 424 =32 E is the answer #### E QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:John bought 9.25m of cloth for $425.50. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)54 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $425.50 Cost per metre = 425.50 ÷ 9.25 The cost of the cloth per metre = $ 46 Answers: A #### A QUESTION:A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal. options: A)6:7 B)4:5 C)5:8 D)25:64 E)3:5 SOLUTION:The hare takes 3 leaps and the jackal takes 5 leaps. 1 hare leap = 4/3 jackal leaps Thus the hare's 3 leaps = 3(4/3) = 4 jackal leaps. The ratio of their speeds is 4:5. The answer is B. #### B QUESTION:A mixture contains alcohol and water in the ratio 2:5. If 10liters of water is added to the mixture, the ratio becomes 2:7. Find the quality of alcohol in the given mixture. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let the quantity of alcohol and water be 2x and 5x 2x/(5x+10) = 2/7 20x = 4(3x+5) x=5 Quantity of alcohol = 25 = 10liters. Answer is B #### B QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=520=100 Total price of 3 packet milk=312=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:A train 330 m long passed a pole in 11 sec. How long will it take to pass a platform 760 m long? options: A)76 sec B)89 sec C)87 sec D)35 sec E)36 sec SOLUTION:Speed = 330/11 = 30 m/sec. Required time = (330 + 760)/30 = 36 sec. Answer:E #### E QUESTION:The product of n consecutive positive integers is always divisible by? options: A)n^2 -1 B)(n+1)! C)2n +1 D)n! E)n^2 + 1 SOLUTION:Plug in some vlues and check - Product of first 2 number is 21 Product of first 3 number is 321 Product of first 4 number is 4321 Product of first 5 number is 54321 So, The product of first n natural numbers is always divisible by n! , answer will be (D) #### D QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white SOLUTION:In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated Answer: A #### A QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 22=2^2=4. Total # of ways: 4C22^2=24. Answer: A #### A QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 918 = 162. Answer: Option A #### A QUESTION:Which of the following is NOT the sum of the squares of two integers? options: A)36 B)37 C)65 D)146 E)147 SOLUTION:List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. (A) 36 - 9+25. NO. (B) 37 - 1+36. NO. (C) 65 - 1+64. NO. (D) 146 - 25+121. NO. (E) - must be the answer. ANSWER:E #### E QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 541=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is options: A)131 B)176 C)274 D)405 E)495 SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}. 6 times 40 something is approx north of 240 Hence the answer is (C) 274 #### C QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element? options: A)a) L(1 + K / 5) B)b) L * (K/100) - 20L C)c) 20L(1+K/100) D)d) 20(1+K/100)-19L E)e) L(K/5)-19 SOLUTION:Let's assume the value of new element to bea. So converting the word problem into equation, (19L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K But according to the answer options, problem writer wanted to conveyk% percent rise in average value. If we consider this case than resulting equation will be, (19L + a) / ( 19+1 ) = L + (K/100)L ==> 19L + a = 20 [ L + KL/100] ==> a= 20L + KL/5 -19L ==> a= L + KL/5 , which is equivalent to option [A] #### A QUESTION:A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: options: A)49 B)4 C)12 D)9 E)27 SOLUTION:Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 14 : 6 :: 21 : x 14 * x = 6 x 21 x = (6 x 21)/14 x = 9. Answer is D. #### D QUESTION:A student is ranked 13th from right and 8th from left.how many are there? options: A)18 B)19 C)20 D)21 E)22 SOLUTION:13th from right means = x + 12 8th from left means = 7 + x Total = 12+7+1 = 20 ANSWER:C #### C QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)6 B)12 C)20 D)24 E)27 SOLUTION:402/3 3/4= 20 Answer: C #### C QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11 inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing may help you with this one.) options: A)100 B)130 C)120 D)110 E)101 SOLUTION:3 x 11 = 33 V = 33 x missing measure V is 330 330 ÷ 33 = 10 which is the missing measure of the side of the box top 10 x 11 = 110 sq. ft. which is area of the top of the box. correct answer D #### D QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 920+7100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,700 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip? options: A)14.0 B)13.0 C)12.0 D)11.0 E)10.0 SOLUTION:Solution:H stopped 700 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs. this means she reached there at 11:00. speed difference between them is 800-500=300 ft/hr so by the time H stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00 means 12:00 is the answer. C #### C QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 71+1 (71+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:Magnabulk Corp sells boxes holding i magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate? options: A)100bi/m B)bi/(100m) C)100bi/m D)m/(bi) E)bi/m SOLUTION:We're given some facts to work with: 1) Magnabulk Corp sells boxes holding I magnets each. 2) The boxes are shipped in crates, each holding B boxes. 3) Magnabulk charges M DOLLARS for each crate We're asked for the price charged per magnet, in CENTS.... IF.... I = 2 B = 3 M = 12 (2 magnets per crate)(3 crates) = 6 magnets $12 for 6 magnets = $2 per magnet = 200 cents per magnet So we're looking for an answer that equals 200 when I=2, B=3 and M=12. There's only one answer that matches... Answer is C #### C QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount. options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500 SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. B #### B QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%? options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5% SOLUTION:Let marked price = $100. Then, C.P. = $64, S.P. = $87 Gain % = 23/64 * 100 = 35.9%. B #### B QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)766 m B)156 m C)245 m D)156 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C #### C QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 â€¦. (i) A + B = (88 x 2) = 176 â€¦. (ii) B + C = (72 x 2) = 144 â€¦.(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 â€¦. (iv) Subtracting (i) from (iv), we get : B = 63. Bâ€™s weight = 63 kg. Answer D #### D QUESTION:1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? options: A)10.5 B)12.5 C)13.5 D)11.5 E)11 SOLUTION:100015 = 1200x x = 12.5 ANSWER B #### B QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ? options: A)60 sec B)70 sec C)80 sec D)50 sec E)90 sec SOLUTION:72 kmph=725/18 mps=20mps. 54 kmph=545/18 mps=15 mps. The train has to travel (200+100)m=300m to overtake the other one. Resultant velocity=(20-15)mps=5 mps time it takes to travel 300m at a velocity of 5 mps is 60 sec.. Ans 60 sec. ANSWER:A #### A QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. â€¹=â€º 61. Answer C #### C QUESTION:Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? options: A)x B)(85/12)x C)(85/24)x D)(85/36)x E)(85/48)x SOLUTION:Let Q be the number of homework questions. Q = 4Q/5 + (5/17)(Q/5) + x Q = 68Q/85 + 5Q/85 + x 12Q/85 = x Q = (85/12)x The answer is B. #### B QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field? options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m ANSWER:A #### A QUESTION:Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. If he now has an equal amount of money in each pocket, then how much money did he originally have in his left pocket? options: A)$120 B)$130 C)$140 D)$150 E)$160 SOLUTION:Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120 in his left pocket (and $80 in his right pocket) before moving $20 from his left to his right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120). correct answer E #### E QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed? options: A)36 B)64 C)72 D)80 E)100 SOLUTION:you count up combinations twice. 498... and let me name 6 with students A,B,C,..,F after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same. I don't think that's the only mistake. 64 is a factor of = 2^24^2 144 is a factor of = 2^43^2. These are very different numbers and you cannot divide 144 with something to get to 64. #### B QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:Which of the following is a prime number options: A)9 B)2 C)4 D)8 E)7 SOLUTION:Explanation: A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself. So from above options 2 is that number Option B #### B QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4 SOLUTION:Method- 1 There are 9 fine pieces of pen and 3 defective in a lot of 16 pens i.e. Probability of first pen NOT being defective = (13/16) i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective] Probability of Both pen being NON-defective = (12/15)(13/16) = 13/20 Answer: option D #### D QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B <<<Examples ends QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book. options: A)23777 B)69667 C)26976 D)2697 E)1079 SOLUTION:Explanation: Number of digits used in 1 digit numbers = 19 = 9 Number of digits used in 2 digit numbers = 290 = 180 Number of digits used in 3 digit numbers = 3900 = 2700 Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320 Hence, number of pages with 4 digit number = 320/4 = 80 Total number of pages = 1079 ANSWER: E #### E QUESTION:N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is options: A)(a) 61250 B)(b) 65525 C)(c) 42455 D)(d) 62525 E)(e) 55425 SOLUTION:The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question. To start, we're given information on the sub-sets of numbers: -The 1st set has 1 number -The 2nd set has 2 numbers -The 3rd set has 3 numbers Etc. So the 50th set will have 50 numbers in it. Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching... The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers Etc. This pattern will continue all the way down to... The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'... So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive... Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)... 25(1226+1275) = 25(2501) = 62525 D #### D QUESTION:14 times a number gives 210. The number is options: A)11 B)12 C)15 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 14×N=210⇒N=15 Correct Option: C #### C QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is options: A)153550 m^2 B)153600 m^2 C)153700 m^2 D)153800 m^2 E)153900 m^2 SOLUTION:Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m^2. Option B #### B QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4332211 = 144 ways E #### E QUESTION:If the cost price of 60 boxes is equal to the selling price of 50 boxes, the gain percent is options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let C.P. of each box be Re. 1. Then, C.P. of 50 boxes = Rs. 50; S.P. of 50 boxes = Rs. 60. Gain % = 10/50 100 = 20% Answer:D #### D QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? options: A)600 B)720 C)10080 D)14320 E)14800 SOLUTION:for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!2=10080 ans C #### C QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used? options: A)180 grams B)220 grams C)250 grams D)350 grams E)1400 grams SOLUTION:I too think 1400 grams should be the answer. My reasoning is The h20 content in 700 gms of water is 1 h20 content in 24% solution is 0.76 Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84 Let amount of solution be X Then the equation can be set up 7001 + 0.76X = 0.84 (X+700) 0.08X = 112 8X = 11200 X = 1400 (ANS E) #### E QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 220500 + 18000 = 59000 Answer: D #### D QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle. options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110° SOLUTION:Solution If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence x + 3x + 8x = 180 Solve for x 12x = 180 x = 15 The measures of the three angles are x = 15° 3x = 3 × 15 = 45° 8x = 8 × 15 = 120° ANSWER IS C #### C QUESTION:A rocket soars for 12 seconds at 150 meters per second. It then plummets 600 meters in 3 seconds. What is the average speed of the rocket in meters per second? options: A)140 B)150 C)155 D)160 E)175 SOLUTION:When soaring, the rocket travels a total distance of 1800m(150m/s for 12s) While plummeting the rockets travel distance of 600m in 3s The total distance traveled is 2400m(1800 + 600) The time taken to travel this distance is 15s(12 + 3) Average speed = 2400/15 = 160 ANS: (Option D) #### D QUESTION:10^(600) Ã· 10^(580) = ? options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24 SOLUTION:10^(600) Ã· 10^(580) = 10^ (600-580) = 10^20 Answer : B #### B QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5 SOLUTION:Rate(1)=1/5 Rate(2)=1/8 Combined = 13/40 Work done in 2 days=13/20 Work left = 7/20 Rate Time = Work left 1/8 * Time = 7/20 Time=14/5 C #### C QUESTION:If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m? options: A)2m −1 B)4m C)6m D)7m E)6m/5 SOLUTION:20m - n = p Add n to both sides: 20m = n + p Add m to both sides: 21m = n + p + m Now, divide both sides by 3 7m = (n + p + m)/3 = the average of n, p, and m D #### D QUESTION:Mr. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:If 75 percent of 600 is 50 percent of x, then x=? options: A)800 B)900 C)1000 D)1100 E)1200 SOLUTION:0.75 * 600 = 0.5 * x x = 7.5/5 * 600 = 900 #### B QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball? options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these SOLUTION:similar triangle properties.. 2/r+6 = 6/r-6 giving r = 12. Answer: A #### A QUESTION:At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have? options: A) 160 B) 120 C) 190 D) 200 E) 400 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 60% % of of employees other than secretaries and salespeople = 100 - 75 = 25% But this number is given as 30 so 25% of x = 30 x = 120 Therefore there a total of 120 employees in the company K Correct answer - B #### B QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? options: A)109 ways B)908 ways C)128 ways D)108 ways E)104 ways SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways. Answer:D #### D QUESTION:When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ? options: A)2 B)7 C)5 D)3 E)6 SOLUTION:Let n=3 (leaves a remainder of 3 when divided by 24) 9n = 9(3) =27, which leaves a remainder of 6 when divided by 7. difference = 6 - 3 = 3. Answer D #### D QUESTION:A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h? options: A)25% B)50% C)69% D)80% E)100% SOLUTION:Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder. This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5. Original cylinder 7/8 New cylinder 3/5 So 3/5/7/8 = 3/58/7 = 0.69 or 69%. Answer C #### C QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2 SOLUTION:John's speed - 12 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles. Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr. Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours Answer B #### B QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26 SOLUTION:Explanation: Let the present age of P and Q be 3x and 4x respectively. Eight years ago, P was half of Q in age => 2(3x – 8) = (4x – 8) => 6x – 16 = 4x – 8 => 2x = 8 => x = 4 7x=74=28 Answer: Option B #### B QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? options: A)49 B)55 C)59 D)71 E)92 SOLUTION:Total = 55 Thrower = 37 Rest = 55 - 37 = 18 Left Handed = 18/3 = 6 Right handed = 12 If all Thrower are right handed then total right handed is 37 + 12 = 49 so A. 49 is the right answer #### A QUESTION:The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is: options: A)870 B)600 C)287 D)771 E)191 SOLUTION:Explanation: Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870 Now total salary of 8 workers = 3870 âˆ’ 870 = 3000 Total salary of 9 workers including the new supervisor = 9 Ã— 430 = 3870 Salary of the new supervisor = 3870 âˆ’ 3000 = 870 Answer: A #### A QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3% SOLUTION:675 ---- 225 100 ---- ? => =33 1/3% Answer:C #### C QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction? options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40 SOLUTION:x / (1/18) = (2/5) / (7/9) x = 291 / 1857 = 1/35 The answer is D. #### D QUESTION:Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: T makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:The fourth proportional to 14, 22 and 28 is? options: A)21 B)66 C)88 D)99 E)44 SOLUTION:(2228)/14 = 44 Answer: E #### E QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $5760. What is the average monthly balance maintained by John in his account during the year? options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400 SOLUTION:bank balance is doubled with accumulation of interest tp 5760.. this means INTEREST is 5760/2=2880 for entire year.. although since interest is 10% of avg MONthly balance, it becomes 28800.. B #### B QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 312=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat? options: A)3! B)8! C)11! D)12! E)14! SOLUTION:Ans.(A) Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:A man divides $8600 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? options: A)A)$200 B)B)$1000 C)C)$800 D)D)$1011.76 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 44X+44X+2X=8600 16X+16X+2X=8600 34X=8600, X=252.94. Daughter receives four times of nephew so 4 * 252.94 = 1011.76. So Each Daughter receives $800. answer is option D) $1011.76. #### D QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)100 = 25% ANSWER:A #### A QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen? options: A)Rs.32 B)Rs.28 C)Rs.36 D)Rs.25 E)None of these SOLUTION:Let the cost of each pen and pencil be 'p' and 'q' respectively. 16p + 8q = 352 --- (1) 4p + 4q = 96 8p + 8q = 192 --- (2) (1) - (2) => 8p = 160 => p = 20 ANSWER:E #### E QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word â€˜POWERâ€™ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 54321 = 120 ANSWER:E #### E QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)x = 240 => x = (240 * 100)/60 = 400 Answer B #### B QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)(3X-4Y) IS ODD TRUE B)II only C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd 3x - is always negative and odd 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always odd I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is A #### A QUESTION:A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price? options: A)197 B)476 C)279 D)278 E)268 SOLUTION:CP1 = 100 SP1 = 105 CP2 = 95 SP2 = 95 * (105/100) = 99.75 5.25 ----- 100 25 ----- ? => 476 Answer:B #### B QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 130 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor. options: A)233 B)877 C)279 D)176 E)291 SOLUTION:Explanation: area of the room = 544 * 374 sq cm size of largest square tile = H.C.F of 544cm and 374cm= 34cm area of 1 tile = 3434 sq cm no. of tiles required = (544374) / (34 * 34) = 176 Answer: D) 176 #### D QUESTION:4,25,49,121,169,289, options: A)361 B)169 C)189 D)209 E)219 SOLUTION:19^2= 361 because follow sequence of square of the prime numbers ANSWER:A #### A QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27 SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30 We can write 30 as product of two numbers in following ways 130 215 310 56 4 cases = 42 i.e. 8 factors (including 1) Factors greater than 1 = 7 Answer: Option D #### D QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 3/ 50 sec = 12sec Answer : C #### C QUESTION:The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)14 years B)17 years C)18 years D)12 years E)11 years SOLUTION:9 2 = 181 Answer:C #### C QUESTION:A certain sum of money at simple interest amounted Rs.780 in 5 years at 4% per annum, find the sum? options: A)337 B)268 C)198 D)650 E)168 SOLUTION:780 = P [1 + (54)/100] P = 650' Answer:D #### D QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)8 B)9 C)7 D)5 E)4 SOLUTION:Explanation: x â€“ y = 5 4x â€“ 6y = 6 x = 12 y = 7 Answer:C #### C QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)x years. ((2/5)x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business? options: A)6 : 13 : 90 B)5 : 12 : 90 C)5 : 11 : 80 D)6 : 11 : 90 E)12 : 6 : 90 SOLUTION:Ratio of their investments = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90 Answer D #### D QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)Rs.7288 B)Rs.2542 C)Rs.2522 D)Rs.2625 E)Rs.6271 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? options: A)76 hrs B)99 hrs C)55 hrs D)90 hrs E)11 hrs SOLUTION:1/9 - 1/x = 1/10 => 90 hrs Answer: D #### D QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z? options: A)decrease of 7.5% B)decrease of 26.5% C)increase of 16.5% D)increase of 24.5% E)increase of 32.5% SOLUTION:After the changes, z = 1.5x(0.7y)^2 = (1.50.49)xy^2 = 0.735z The answer is B. #### B QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand. options: A)11a.m B)12a.m C)10a.m D)10.30p.m E)11.30p.m SOLUTION:bus started after 30min ie .5hrs Now, Time=distance/speed ie Time=27/18 during going ie 1.5 hrs now during the return journey speed increasd by 50% so new speed 27mph Time=27/27 ie 1(RETURN journey) so total time=1+.5+1.5=3hrs so the bus will reach at 11am ANSWER:A #### A QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=280/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:There are two bridges running parallel over river Kauvery, and they are 1 KM apart. A man started rowing the boat upstream under first bridge, his hat fell into river while he was exactly under second bridge. He realized that after 15 mts, and started rowing in opposite direction, he eventually caught his hat under First Bridge. What is the speed of river Kauvery? options: A)5km/h B)4km/h C)3km/h D)1km/h E)2km/h SOLUTION:Let the upstream velocity=xkm/h so he goes first 1 km then 15 min with this velocity so total goes=x15/60+1 km=x+4/4 km and now he in downstream cover this distance in 15 min so his downstream velocity=x+4/415=x+4/60 now speed of river=1/2[downstream speed-upstream speed] =1/2[x+4/60-x/60]km/min =2km/h ANSWER:E #### E QUESTION:A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)22 1/8 B)22 1/2 C)22 1/1 D)22 1/5 E)22 1/9 SOLUTION:1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 ¼ 2 = 22 1/2 days Answer:B #### B QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (204) days let X = number of machines needed to complete the job in 10 days 1/(420) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 1860 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 70 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/8,100 C)7/48,000 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 70/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=70/8001/600=7/48,000. Answer: C. #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and â€“4; #### B QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)51 23/27% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27% Answer B #### B QUESTION:A man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)7.6 % B)7.7 % C)16.21 % D)13.6 % E)7.8 % SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 54 pens = Rs. 46 S.P. of 54 pens = 99% of Rs. 54= Rs. 53.46 Profit % = (Profit /C.P.) x 100 Profit% = (7.46/46) x 100 = 16.21 % ANSWER: C #### C QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution? options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30 SOLUTION:Water:soap = 3:4 Soap:Salt=15:20 => For 15 soap, salt = 20 => For 4 Soap, salt = (20/15)4 = 80/15=16/3 So, water:soap:salt = 3:4:16/3= 9:12:16 After open container, water:soap:salt =4.5:12:16 So, water:salt = 4.5:16 = 9:32 ANSWER:A #### A QUESTION:A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle? options: A)13π B)26π C)262√π D)52π E)4π SOLUTION:The distance between the two points is sqrt(8) radius = sqrt(8)/2 Area= pi(sqrt(8)/2)^2 E.4π #### E QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:If x^2+(1/x^2)=7, x^4+(1/x^4)=? options: A)10 B)11 C)12 D)14 E)47 SOLUTION:-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47. Thus, the answer is E. #### E QUESTION:A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is: options: A)22 B)24 C)77 D)26 E)81 SOLUTION:Explanation: Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. Answer: B #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)1/2 B)1/2 C)8/15 D)9/20 E)9/24 SOLUTION:Explanation : Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20 Answer : D #### D QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/95=250/9=27 7/9m ANSWER:D #### D QUESTION:If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in only mean being modified but not the median. A) A is removed B) A and J are removed C) B and I are removed D) A,B,C,H,I,J are removed E) A and E are removed options: A)1) A and B B)2) A and E C)3) A,C,E D)4) All of them E)5) None of them SOLUTION:There are 10 equidistant numbers on the number line. Mean and median will be the average of middle two numbers. If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where mean will change and median will not change. Answer: E #### E QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300 SOLUTION:Let the cost of one toy = X. Then, cost of 18 toys = 18X. Gain = 3X. SP of 18 toys = Rs. 27300. Gain = SP â€“ CP 3X = 27300 â€“ 18X 21X = 27300 X = Rs. 1300. ANSWER : OPTION E #### E QUESTION:2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes? options: A)2 B)4 C)6 D)500 E)0 SOLUTION:2 men.....there are no other!!!! #### A QUESTION:If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 5 * 7 * 11 So j= 2, k= 5, l= 7, m= 11 j+ m= 2 + 11 = 13 Answer - B #### B QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? options: A)8 B)9 C)8.5 D)9.5 E)10.5 SOLUTION:In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work. So 3/5 of the work should have been completed by the two of them together before Jane left. Their combined rate of work is 1/20 + 1/12 = 8/60 Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days. So total number of days taken to complete the work =9/2 + 4 = 8.5 days. C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings? options: A)Rs.3600 B)Rs.3629 C)Rs.3279 D)Rs.3629 E)Rs.3283 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 18000 => x = 3600 Savings = Income - expenditure = 5x - 4x = x So, savings =Rs.3600. Answer: A #### A QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd? options: A)5/18 B)13/36 C)3/8 D)5/8 E)23/36 SOLUTION:player begins with containing tiles 1 to 10 and have equal probability of selecting means Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there. Next , player draws one title , if number is even player stops or otherwise title is odd without replacement player draws second title. If second title is even , player stops or title is odd without replacement player draws third title. in third title , without replacement of first and second title, player draws and stops it. the sum of tilte probability is odd. here two conditions are possible. 1st condition is 1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/105c1. Here are we are not selecting 1st condition as even stops because sum of tile is odd. Here 5 odd numbers are there we can select 1out of 5 odd numbers. without replacement of fist we select second tilte is even. is 5/105c1/9c1. here we are selecting one number out of remaining 9 numbers. so probability is 5/18. we are selecting 1 even number out of 5. 2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title. Then probability is 5/104/93/8=1/12. Finally sum of probability of two conditions is 5/18+1/12 =5/18. so option A is correct. #### A QUESTION:A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone? options: A)6 days B)8 days C)12 days D)10 days E)5 days SOLUTION:Explanation: A and B 1day's work = 1/6 A alone can do 1day's work = 1/12 what time B will take to do the work alone? B = (A+B) - A = (1/6) - (1/12) = 12 Days Answer: Option C #### C QUESTION:The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)15 kmph B)40 kmph C)18 kmph D)19 kmph E)10 kmph SOLUTION:Speed downstream = 60 + 20 = 80 kmph Speed upstream = 60 - 20 = 40 kmph Answer:B #### B QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ? options: A)35 B)15 C)40 D)52 E)14 SOLUTION:C Let the sum of nine member (total) =x and the age of old one=z so its average 4 yrs before=(x+z)/10. after 4 yrs let z be replaced by y. so now avg=(x+410+y)/10 now (x+z)/10=(x+40+y)/10 so after solving it found z=y+40. so old person is 40yrs older than young one. #### C QUESTION:A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes? options: A)36 B)54 C)108 D)270 E)324 SOLUTION:ONE Veggiematik machine can chop 36 carrots in 4 minutes So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ONE Veggiematik machine can chop 54 carrots in5minutes So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes In other words, SIX Veggiematik machines can chop 270 carrots in5minutes Answer D #### D QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Four pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ? options: A) 5 B) 12 C) 24 D) 32 E) 120 SOLUTION:CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!. But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2. The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5. Answer: option A #### A <<<Examples ends QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 100) = > 57% ANSWER C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)9.30 a.m B)10 a.m C)10.40 a.m D)11 a.m E)11.40 am SOLUTION:Suppose they meet x hours after 7 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 10 a.m. answer B #### B QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 6 km/h. The man's rate is? options: A)5 kmph B)6 kmph C)7 kmph D)4 kmph E)9 kmph SOLUTION:Explanation: DS = 16 US = 6 S = ? S = (16 - 6)/2 =5 kmph Answer: A #### A QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:calendar=52097083 november=538=8651 march=2308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&53 E)9525&54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:Combine terms: 15a + 26b -4b – 16a. options: A)4a + 22b B)-28a + 30b C)-a + 22b D)28a + 30b E)5a + 30b SOLUTION:Solution: 15a + 26b -4b – 16a. = 15a – 16a + 26b – 4b. = -a + 22b. Answer: (C) #### C QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both? options: A)975 B)1150 C)1175 D)1243 E)1525 SOLUTION:Failed in 1st subject = 342500/100 = 850 Failed in 2nd subject = 422500/100 = 1050 Failed in both = 152500/100 = 375 Failed in 1st subject only = 850-375 = 475 Failed in 2nd subject only = 1050-375 = 675 Passed in either subject but not in both = 675+475 = 1150 Answer is B #### B QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? options: A)87 B)89 C)90 D)93 E)95 SOLUTION:Total score on 3 tests = 813 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 834 = 332 Score required on the fourth test = 332 - 243 = 89 Option B #### B QUESTION:he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)29 B)1 C)10 D)30 E)8 SOLUTION:Average of 30 numbers = 0. Sum of 30 numbers (0 x 30) = 0. It is quite possible that 29 of these numbers may be positive and if their sum is a the 30th number is (-a). Answer: Option A #### A QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 804 / 60 = 5 hours 33 mins Answer â€“ B #### B QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour? options: A)64,420 B)78,840 C)83,160 D)88,970 E)94,320 SOLUTION:21.9 * 3600 = 78,840 The answer is B. #### B QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken? options: A)6 B)8 C)2 D)5 E)4 SOLUTION:Explanation: Mary and her sister complete half work in 2.5 days => they can complete whole work in 5 days Answer: Option D #### D QUESTION:Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer) options: A)Rs. 8167 B)Rs. 4261 C)Rs. 4269 D)Rs. 4266 E)Rs. 4262 SOLUTION:Explanation: CI = 14800{ [ 1 + 13.5/100]2 - 1 } = 14800 { [1 + 27/200]2 - 1 = 14800 { 2 + 27/200}{27/200} = (74)[2 + 27/200](27) = 1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266 Answer:D #### D QUESTION:What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345? options: A)2345 B)4500 C)5000 D)6000 E)7000 SOLUTION:2000 + 300 + 40 + 5 = 2345 ANSWER A #### A QUESTION:A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? options: A)2.5 min B)3 min C)3.2 min D)3.5 min E)4 min SOLUTION:Total distance = (7/2 + 1/4) miles = 15/4 miles time taken = 15/475 hrs =1/20 hrs = 3 min ANSWER B #### B QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9) SOLUTION:The number of possible 4-digit codes is 36^4. The number of possible 5-digit codes is 36^5. The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4) The answer is A. #### A QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)42.3 B)560.45m C)79m D)26m E)111.12m SOLUTION:Explanation: A runs 1000 m while B runs 900 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. B can give C = 1000 - 888.88 = 111.12 m. ANSWER E #### E QUESTION:What is the difference between the local value of 1 and 2 in the number 2124? options: A)70 B)75 C)20 D)80 E)60 SOLUTION:Explanation: 100 â€“ 20 = 80 Answer: D #### D QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 1060 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack? options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13 SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits. Probability of getting spade or a jack: = (13 + 3)/52 = 16/52 = 4/13 Therefore, the probability of getting neither a spade nor a jack: = 1 − 4/13 = 9/13 ANSWER:A #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m options: A)II,III only B)I,III only C)I only D)III only E)II only SOLUTION:n > 1. So, option II, III is not possible. So, Option I is correct. Answer : C #### C QUESTION:9log9(5) = ? options: A)1 B)2 C)3 D)5 E)8 SOLUTION:Exponential and log functions are inverse of each other. Hence aloga(x) = x , for all x real and positive. and therefore 9log9(5) = 5 correct answer D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)227 B)350 C)881 D)277 E)271 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 172+37+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:Yesterday, a pie shop sold 6 apple pies, 5 peach pies, and 6 pumpkin pies. How many pies did the shop sell in all? options: A)21 B)37 C)13 D)17 E)32 SOLUTION:Add the number of pies 6+5+6 =17. Answer is D. #### D QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work? options: A)20days B)15days C)30days D)45days E)50days SOLUTION:10days work of A = 10/40 = 1/4 remaining work = 1-1/4 = 3/4 B can finish 3/4 work = 603/4 = 45days Answer is D #### D QUESTION:If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%. options: A)4% B)5% C)6% D)3% E)5.5% SOLUTION:sol. cp=rs490,sp= 465.50. loss=rs(490-465.50)=rs 24.50. loss%=[(24.50/490)100]%=5% Answer is B. #### B QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85 Speed of the train is 85 kmph. Answer: Option C #### C QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour? options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2 SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same. Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of: R = (100 mi)/(1.5) = 66.67 mph That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars. One of the speeds is x, and let's call the other y. We want y. x + y = 66.67 y = 66.67 - x Answer =(A) #### A QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ? options: A)160 B)180 C)200 D)220 E)None SOLUTION:Answer Let the number be N. Then, (N/5) + 4 = (N/4) - 4 â‡’ (N/4) - (N/5) = 8 â‡’ (5N - 4N)/20 = 8 âˆ´ N = 160 Option: A #### A QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? options: A)50 % B)60 % C)70 % D)80 % E)40 % SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:B #### B QUESTION:For all positive integers n and m, the function A(n) equals the following product: (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8 SOLUTION:For all positive integers n and m, A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2) B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive. A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...} A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2) The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ... missing numbers are 1/8, 1/13, 1/16, .... B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25) here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values The largest reciprocal that present in B(25) but not in A(5) is 1/3 Answer A #### A QUESTION:Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:Let x be the amount of soup at the beginning. After lunch, the remaining soup was (4/5)x. After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x. The answer is B. #### B QUESTION:Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is options: A)2 : 3 B)4 : 3 C)6 : 7 D)9 : 16 E)None SOLUTION:Sol. Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3. Answer B #### B QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 24th September was a Monday. The answer is A. #### A QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000100/120000 = 40% Answer: option D #### D QUESTION:A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 9.33% D) 10.67% E) 11.7% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500100=~9.33% of the remaining solution of 7,500 gallons. Answer: C. #### C QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? options: A)2400 B)2880 C)2787 D)3087 E)0728 SOLUTION:1200 * 12: x * 9 = 2:3 x = 2400 Answer: A #### A QUESTION:Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder options: A)1235 B)1456 C)1567 D)1678 E)1631 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 35 5x = 1330 x = 266 Large number = 266+1365 = 1631 E #### E QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 700/20 S = 35 M/Sec Speed= 3518/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 126 Kmph Answer: A #### A QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is: options: A)180 B)1800 C)18 D)18000 E)1350 SOLUTION:Area of the hall= 36001500 Area of each stone= (8050) Therefore, number of stones= (36001500/ 8050)= 1350 ANSWER:E #### E QUESTION:The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is? options: A)2379 B)2889 C)5625 D)9000 E)28311 SOLUTION:Let their prices be 3x, 5x and 7x. Then, 2x + 6x + 8x = (15000 3) or x = 2812.5. Cost of cheapest item = 2x = Rs. 5625. Answer: C #### C QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible? options: A)20 B)40 C)C=50 D)C=80 E)C=120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10. But these 3 chosen couples can send two persons (either husband or wife): 222=2^3=8. Total # of ways: 5C32^3=80. Answer: D. #### D QUESTION:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be options: A)(1.5)^4 B)(1.05)^5 C)(1.05)^4 D)1 + (0.05)^4 E)1 + 4(0.05) SOLUTION:In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have.... Answer :B #### B QUESTION:What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, x options: A)214 B)215 C)213 D)320 E)216 SOLUTION:Go on dividing by 6 to the next number Answer : E #### E QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? options: A)287 B)27 C)28 D)25 E)28 SOLUTION:[50/x + 50/(x/2)] – 100/x = 2 x = 25 Answer: D #### D QUESTION:10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people? options: A)9 B)13 C)21 D)24 E)23 SOLUTION:work per day epr hour per person= 55/(12810) // eq-1 people=48; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 198/(p848) // eq-2 eq-1==eq-2; p= 9 ANSWER:A #### A QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good? options: A)20/67 B)20/63 C)20/19 D)20/18 E)20/28 SOLUTION:Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 4)/126 = 20/63 Answer: B #### B QUESTION:Ravi's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ravi's average score on the 5 tests to be 80? options: A) 80 B) 82 C) 84 D) 86 E) 88 SOLUTION:E. 88 Ravi must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88. #### E QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ? options: A)7.76 kms B)8.76 kms C)5.76 kms D)3.76 kms E)4.76 kms SOLUTION:Explanation: Speed in still water = 6 kmph Stream speed = 1.2 kmph Down stream = 7.2 kmph Up Stream = 4.8 kmph x/7.2 + x/4.8 = 1 x = 2.88 Total Distance = 2.88 x 2 = 5.76 kms Answer: C #### C QUESTION:1398 x 1398 = ? options: A)1624404 B)1851404 C)1951404 D)1954404 E)None of these SOLUTION:Explanation : 1398 x 1398 = (1398)2 = (1400 - 2)2 = 14002 - (2 × 1400 × 2) + 22 = 1960000 - 5600 + 4 = 1954404. Answer : Option D #### D QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph SOLUTION:30 --- 3 DS = 10 ? ---- 1 18 ---- 3 US = 6 ? ---- 1 M = ? M = (10 + 6)/2 = 8 ANSWER:B #### B QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water? options: A)29 B)92 C)30 D)32 E)23 SOLUTION:US = 22 DS = 42 M = (42 + 22)/2 = 32 Answer:D #### D QUESTION:In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? options: A)18 B)36 C)42 D)52 E)56 SOLUTION:All options other than 'D' are factors of 2013. Hence, 'D' is the answer #### D QUESTION:The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 10 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? options: A)20 km B)30 km C)40 km D)50 km E)60 km SOLUTION:Number of stops in an hour: 60/5 = 12 Distance between stops: 60/12 = 5 km Distance between Yahya's house and Pinedale Mall: 5 x 10 = 50 km IMO, correct answer is "D." #### D QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop. The cost of the bomber is quite interesting. The Cost of 1st bomber is: 2 The Cost of 2nd bomber is: 4 The Cost of 3rd bomber is: 6 The Cost of 4th bomber is: 8 The Cost of 5th bomber is: 10 i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins. How many bombers can you buy using 1000 coins ? ? options: A)61 B)62 C)63 D)64 E)65 SOLUTION:Solution 62 The Cost of 1st bomber is: 2 i.e Total coins spend: 2 The Cost of 2nd bomber is: 4 i.e Total coins spend: 6 The Cost of 3rd bomber is: 6 i.e Total coins spend: 12 The Cost of 4th bomber is: 8 i.e Total coins spend: 20 The Cost of 5th bomber is: 10 i.e Total coins spend: 30 The Cost of 6th bomber is: 12 i.e Total coins spend: 42 The Cost of 7th bomber is: 14 i.e Total coins spend: 56 The Cost of 8th bomber is: 16 i.e Total coins spend: 72 The Cost of 9th bomber is: 18 i.e Total coins spend: 90 The Cost of 10th bomber is: 20 i.e Total coins spend: 110 The Cost of 11th bomber is: 22 i.e Total coins spend: 132 The Cost of 12th bomber is: 24 i.e Total coins spend: 156 The Cost of 13th bomber is: 26 i.e Total coins spend: 182 The Cost of 14th bomber is: 28 i.e Total coins spend: 210 The Cost of 15th bomber is: 30 i.e Total coins spend: 240 The Cost of 16th bomber is: 32 i.e Total coins spend: 272 The Cost of 17th bomber is: 34 i.e Total coins spend: 306 The Cost of 18th bomber is: 36 i.e Total coins spend: 342 The Cost of 19th bomber is: 38 i.e Total coins spend: 380 The Cost of 20th bomber is: 40 i.e Total coins spend: 420 The Cost of 21st bomber is: 42 i.e Total coins spend: 462 The Cost of 22nd bomber is: 44 i.e Total coins spend: 506 The Cost of 23rd bomber is: 46 i.e Total coins spend: 552 The Cost of 24th bomber is: 48 i.e Total coins spend: 600 The Cost of 25th bomber is: 50 i.e Total coins spend: 650 The Cost of 26th bomber is: 52 i.e Total coins spend: 702 The Cost of 27th bomber is: 54 i.e Total coins spend: 756 The Cost of 28th bomber is: 56 i.e Total coins spend: 812 The Cost of 29th bomber is: 58 i.e Total coins spend: 870 The Cost of 30th bomber is: 60 i.e Total coins spend: 930 The Cost of 31st bomber is: 62 i.e Total coins spend: 992 Answer B #### B QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters? options: A)50 B)51 C)52 D)53 E)54 SOLUTION:50000 ->1 41000 ->5 31100 ->10 32000 ->10 21110 ->10 22100 ->15 11111 ->1 1+5+10+10+10+30+1=52 ANSWER:C #### C QUESTION:AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 16.0 grams 4:00 P.M. x grams 7:00 P.M. 20.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.? options: A)12.0 B)18.1 C)12.2 D)12.3 E)18.0 SOLUTION:The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours. Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm: Fractional increase from 1 PM to 4 PM = X / 16.0 Fractional increase from 4 PM to 7 PM = 20.4 / X X \ 16 = 20.4 \ X X^2 = 20.4 * 16 X = 18 answer : E #### E QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)Rs.24028 B)Rs.24000 C)Rs.24003 D)Rs.24029 E)Rs.24029 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs.24000 Answer: B #### B QUESTION:Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow? options: A)1/2 B)1/5 C)3/4 D)1/3 E)3/5 SOLUTION:This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow. So, possible options for this other ball would be: W, W, B, B (as one yellow is already picked) So the probability for that ball to be yellow too is 2/4=1/2. Option A #### A QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %? options: A)30% B)40% C)50% D)56% E)78% SOLUTION:Gain=16 apples Total 56 apples CP 56-16=40 (16/40)100 =40% Ans B #### B QUESTION:A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? options: A)116 B)132 C)148 D)164 E)180 SOLUTION:3/10P are ponies with horseshoes, so P is a multiple of 10. 5/83/10P = 3/16P are Icelandic ponies with horseshoes, so P is a multiple of 16. The minimum value of P is 80. Then H = P+4 = 84. The minimum number of horses and ponies is 164. The answer is D. #### D QUESTION:A city with a population of 173,460 is to be divided into 9 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)17,400 B)17,500 C)17,600 D)17,700 E)17,800 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 173,460 = p + 8(1.1)p 9.8p=173,460 p = 17,700 The answer is D. #### D QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/7 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x? options: A)x/3 B)5x/2 C)2x/3 D)3x/2 E)2x SOLUTION:x/(x+y) = 2/7 7x = 2x+2y 5x = 2y y = 5x/2 Answer B #### B QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be options: A)21 B)5193 C)77 D)9275 E)19 SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!. So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!. So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320) So remainder is 5193. Answer:B #### B QUESTION:The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area? options: A)298 B)148 C)289 D)987 E)282 SOLUTION:2(45 + 56 + 46) = 148 Answer:B #### B QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order? options: A)6720 B)5280 C)6240 D)5202 E)4020 SOLUTION:three letters can be arranged in 3! ways. only one combination AEI is required. 8 letters can be arranged in 8! ways. thus 8!/ 3! * 1 = 6720. A #### A QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.95 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.915 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33100 = 180% of 3.33. Answer: E. #### E QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 125 cm 64 cm. What is the perimeter of the square? options: A)600 cm B)800 cm C)400 cm D)1000 cm E)None of these SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. ANSWER:B #### B QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 7 employees to 2 different offices? options: A)215 B)310 C)343 D)243 E)123 SOLUTION:Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 777=7^3=343. Answer: C. #### C QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? options: A)3/7 B)3/2 C)3/1 D)3/9 E)3/4 SOLUTION:Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. Answer:B #### B QUESTION:A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: options: A)49 B)4 C)12 D)9 E)27 SOLUTION:Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 14 : 6 :: 21 : x 14 x = 6 x 21 x = (6 x 21)/14 x = 9. Answer is D. #### D QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 1045 900 = 2045 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:Two trains 150 meters and 180 meters long are running in the same direction with speeds of 102 km/hr, 66km/hr. In how much time will the first train cross the second options: A)37 sec B)22 sec C)27 sec D)35 sec E)33 sec SOLUTION:Explanation: Relative speed of the trains = (102 - 66) km/hr = 36 km/hr = (36Ã— 5/18) m/sec = 10 m/sec. Time taken by the trains to cross each other = Time taken to cover (150 + 180) m at 10 m /sec = (330/10) sec = 33 sec. Answer: Option E #### E QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.66 feet C)3.3 feet D)3.4 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+10=40 44/12=3.66 feet ANSWER:B #### B QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!22= 480 The answer is C. #### C QUESTION:A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)28 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=224/32=28/4=7 m/sDistance covered by B in 4 seconds = Speed × time =7×4=28 metre i.e., A beat B by 28 metre Answer is B #### B QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:John earned 40% more per month than Oscar. If john salary is decreased 10% and Oscar’s salary is increased by 10%, then john would be earning what percent more than Oscar? options: A)10% B)9.09% C)15.54% D)14.54% E)It cannot be determined from the information given. SOLUTION:This Q is all about taking the correct BASE for taking %s.. the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 60 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 140.. 100 increases 10% =110.. 140 decreases 10%=126.. so the increase is 16.. again the BASE is 110, so answer 16/110 * 100= 14.54% C without calculations, answer cannot be equal to or greater than 16, as 16 is on 110.. so D is the only one left #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 11000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)14 B)21 C)22 D)23 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (10000 × 7) + 6000 ( x – 7) ‹=› 2000x = 28000 ‹=› x = 14. Answer A #### A QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:In track last week, the boys ran 15 laps. The girls ran 5 more laps. Each lap is a one-fifth of a mile. How many miles did the girls run? options: A)2 miles B)3 miles C)4 miles D)5 miles E)6 miles SOLUTION:The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4. The girls ran 4 miles correct answer C #### C QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ? options: A)76 B)29 C)26 D)19 E)11 SOLUTION:Explanation: Average = total runs / no.of innings = 32 So, total = Average x no.of innings = 32 x 10 = 320. Now increase in avg = 4runs. So, new avg = 32+4 = 36runs Total runs = new avg x new no. of innings = 36 x 11 = 396 Runs made in the 11th inning = 396 - 320 = 76 Answer: A #### A QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent? options: A)25% B)5% C)10% D)15% E)20% SOLUTION:3000 --- 600 100 --- ? => 20% Answer: E #### E QUESTION:Among the answers given below, which is nearly equal to √7? options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0 SOLUTION:2.6 is nearly equal to the square root of 7 2.62.6=6.76 2.52.5=6.25 difference 7 - 6.76=0.24 7 - 6.25=0.75 Since 0.24 is lesser of both, 2.6 is closer. Answer is C #### C QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 3 = Rs.2025 Answer:C #### C QUESTION:In what time a debt of Rs.7920 due may be cleared by immediate cash down payment of Rs.3600 at 1/2% per month options: A)10years B)20years C)30years D)40years E)50years SOLUTION:Explanation: PW=100x Amount/100+(RxT) Answer: B #### B QUESTION:Bookman purchased 55 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 360, how many paperback copies were sold? options: A)8 B)10 C)12 D)19 E)16 SOLUTION:The bookman had 10 hardback ad 55-10=45 paperback copies; 14 copies were sold, hence 55-14=41 copies were left. Let # of paperback copies left be p then 10p+20(41-p)=560 --> 10 p=260 --> p=26 # of paperback copies sold is 45-26=19 Answer: D #### D QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x4x=900 x^2= 225 x= 15 Length= 415= 60 difference= 60-15= 45 E is the answer #### E QUESTION:A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 55% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight? options: A) 7/12 B) 1/4 C) 1/2 D) 7/24 E) 17/24 SOLUTION:In probability questions the trap answer is just the multiple of the numbers in the question. i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct. C #### C QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c âˆ’ a? options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=160 --2 subtracting 1 from 2 we have c-a=70; ANSWER:B #### B QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit. options: A)487 B)15 C)76 D)29 E)12 SOLUTION:If x is speed limit, Speed of first person = x + 10 Speed of 2nd person = x + 20 But speed of 2nd person = 35 kmph x + 20 = 35 x = 15 kmph. so speed limit is 15 kmph option D Answer: B #### B QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? options: A)1/12 B)0 C)12/212 D)11/12 E)11/13 SOLUTION:0 If one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope. ANSWER:B #### B QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D <<<Examples ends QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5% Answer (C) #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)1752 B)1799 C)1719 D)1750 E)1800 SOLUTION:Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2 = 1800 Answer: E #### E QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:How many 3 digit positive integers T exist that when divided by 7 leave a remainder of 5? options: A)128 B)142 C)143 D)141 E)129 SOLUTION:Minimum three digit number is 100 and maximum three digit number is 999. The first three digit number that leaves remainder 5 when divided by 7 is 103. 14 * 7 = 98 +5 = 103 The second three digit number that leaves remainder 5 when divided by 7 is 110. 15 * 7 = 105 +5 =110 The third three digit number that leaves remainder 5 when divided by 7 is 117 and so on The last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 Therefore, we identify the sequence 103,110,117.....999 use the formula of last term Last term = first term + (n - 1) * common difference you will get the answer 129 that is definitely E. #### E QUESTION:The 7th grade French and Spanish classes each have 26 students in them, and there are nine students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes? options: A)26 B)28 C)30 D)32 E)34 SOLUTION:French class + Spanish class = 52 students. Nine students are in both classes so they were counted twice. The number of students taking just one class is 52 - 2(9) = 34. The answer is E. #### E QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ? options: A)10 hr B)50 C)20 D)250 E)260 SOLUTION:Explanation: 6C4 * 7C3 = 50 B #### B QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 2460 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? options: A)25 B)37 C)36 D)29 E)21 SOLUTION:Explanation: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get 4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60. We know that SI = , where p is the principal, n the number of years and r the rate percent of interest. In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60. Therefore, 60 =(60n4)/100 => n = 100/4 = 25 years. Answer: A) 25years #### A QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/19 B)1/20 C)1/23 D)2/17 E)1/17 SOLUTION:(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 B) #### B QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)? options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k) SOLUTION:f(k) = k^3 /16 f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k). So answer is B. #### B QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -. options: A)7/18 B)7/19 C)7/11 D)7/12 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ways. 7/15 Answer: E #### E QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? options: A)330 B)650 C)729 D)800 E)890 SOLUTION:Choose 4 starters from a team of 11 players. Order is not important. \inline {\color{Black} 11C_{4}}= 330 A #### A QUESTION:Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 60 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ? options: A)2hrs, 48mins B)7hrs, C)7hrs, 12mins D)13hrs, 4mins E)14hrs, 24mins SOLUTION:The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/60 --> x=1/420--> (time) = (reciprocal of rate) = 392 minutes = 7 hours Answer: B. #### B QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x? options: A)(1-x)/x B)(x - 1)/x C)x/(x + 1) D)(x + 1)/x E)x/(1-x) SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: E #### E QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:If -1 < x < 0, which of the following must be true? I. x^4 < x^3 II. x^6 < 1 – x III. x^5 < x^2 options: A)I only B)II only C)III only D)II,III only E)I,II,III only SOLUTION:Answer : E #### E QUESTION:There are different 15 circles. What is the number of the greatest possible points with which the circles intersect? options: A)390 B)100 C)110 D)180 E)210 SOLUTION:Maximum points of intersection between n different circles = n(n - 1) = 1514 = 210 Answer: E #### E QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C? options: A)2250 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 75/247 7410 = 2250 Answer: A #### A QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1â„7 hours B)6 2â„7 hours C)8 2â„7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 Ã— 2 = 16 km Distance covered in next two hours = 10 Ã— 2 = 20 km Distance covered in next two hours = 12 Ã— 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 â€“ 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. âˆ´ Time taken = 4â„12 = 1â„3 hour. Total time= 6 + 1â„3 = 6 1â„3 hour Answer E #### E QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C QUESTION:What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, x options: A)214 B)215 C)213 D)320 E)216 SOLUTION:Go on dividing by 6 to the next number Answer : E #### E QUESTION:An old priest fell on a bottom of the well of a church. The well is 16 inches deep. At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches. In how many days priest will come out of the well ? options: A)12-days B)14-days C)11-days D)19-days E)10-days SOLUTION:A 12-days In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-) #### A QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Sandy can do 1/12 of the job each day. Molly can do 1/24 of the job each day. The combined rate is 1/12 + 1/24 = 1/8 of the job each day. The job will take 8 days. The answer is C. #### C QUESTION:One type of liquid contains 10% of water and the second type of liquid contains 15% of water. A glass is filled with 5 parts of 1st liquid and 2 parts of 2nd liquid. The percentage of water in the new mixture in the glass is? options: A)5.6% B)11.4% C)15.6% D)21.3% E)18.9% SOLUTION:Required percentage = (10% of 5 + 15% of 2)/5+2 100 = 0.8/7 100 = 11.4% Answer is B #### B QUESTION:Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work. If it takes him exactly 8 minutes more to walk to work than to ride his bicycle, then x equals options: A)4 B)7 C)12 D)15 E)20 SOLUTION:The best way would be... Per km, he takes 40 secs extra if he walks So he will take 8 mins or 860 secs in 860/40 =12 km ANSWER:C #### C QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)-2 D)2 E)-3 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches? options: A)Rs 900 B)Rs 800 C)Rs 1,800 D)Rs 2,800 E)None of these SOLUTION:Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425 Profit = Rs (425 - 200) = Rs 225 Profit of 8 watches = Rs 225 x 8 = Rs 1,800 ANSWER:B #### B QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum? options: A)337 B)268 C)198 D)697 E)168 SOLUTION:1200 = P [1 + (126)/100] P = 697' Answer:D #### D QUESTION:If a = 105 and a^3= 21 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 3 5 b Therefore (3 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 b Therefore, b = 3^3 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 57 = 35 Correct answer A. #### A QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All two 2. One symmetry and other two non 4. All the two letters can be arranged in 2 ways ( 11c2+ 11c1 * 15c2) 2 ( 1110/ 2 + 11 * 15 * 14 / 2 ) * 2 2420 IMO option D is the correct answer.. OA please...will correct if I missed anything..D #### D QUESTION:R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour? options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m; The rest caught a combined total of n fish. Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2. Answer: D. #### D QUESTION:The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7) options: A)60 m2 B)64 m2 C)68 m2 D)66 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 3 = 66 m2 Answer D #### D QUESTION:A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 kmph B)108 kmph C)54 kmph D)71 kmph E)88 kmph SOLUTION:S = 480/16 * 18/5 = 108 kmph Answer:B #### B QUESTION:A Cone, a hemisphere and a cylinder stand on equal bases and have the same height .Find ratio of their volumes. options: A)2:1:3 B)2:1:4 C)1:2:3 D)4:1:7 E)5:1:8 SOLUTION:Let R be the radius of each Height of the hemisphere = Its radius = R. Height of each = R. Ratio of volumes = (1/3)∏ R2 x R : (2/3)∏R3 : ∏ R2 x R = 1:2:3 ANSWER C 1:2:3 #### C QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 610=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 37=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3(20/60) = 7 hr Answer is D #### D QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet? options: A)124 sq.ft. B)120 sq.ft. C)126 sq.ft. D)129 sq.ft. E)132 sq.ft. SOLUTION:Let l = 9 ft. Then l + 2b = 37 => 2b = 37 - l = 37 - 9 = 28 => b = 28/2 = 14 ft Area = lb = 9 × 14 = 126 sq. ft. Answer is C. #### C QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)231 B)150 C)200 D)450 E)451 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 5C2) = 200 Ans: C #### C QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)30% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 45 are employed males, hence 19% are employed females. (employed females)/(total employed people)=19/64=30% Answer: C. #### C QUESTION:A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years? options: A)0.400 tons B)0.200 tons C)0.175 tons D)0.160 tons E)0.185 tons SOLUTION:X is the quantity of gold reserves of the mine After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining. So we have: X1=95/100 X X2=95/100 X1 X3=95/100 X2 X4=95/100 X3 By multiplying both ends of the equations we get: X1X2X3X4 = (95/100)^4 XX1X2X3 Simplification leaves us with: X4 = (95/100)^4 X X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4) In this case, given X was: X=2 tons So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton Answer E. #### E QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination. options: A)1 B)159/160 C)157/160 D)0.875 E)0.975 SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975. answer is E #### E QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. options: A)220. B)205. C)250 D)105 E)225 SOLUTION:different ways.. 1) EASIEST approach.. lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220... Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15.. total = 220-15 = 205 ANSWER:B #### B QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers? options: A)3 B)5 C)6 D)7 E)None of these SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3 (A) 3 Can divide 12 or 9 (B) 5 Can divide 10 (C) 6 Can divide 12 (D) 7 can divide 7,21,28 Hence answer will be (E) #### E QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)(C-20)+20=(3/4)C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house? options: A)58 B)5 C)12 D)9 E)7 SOLUTION:Angel can select one or more than one of his 8 gang. => Required number of ways = 2^3 – 1= 7. E #### E QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is : options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 5 SOLUTION:Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 495 99c - 99a = 99(c - a) = 495 495 = 995 = 99(c - a) So c - a = 5 Answer (E) #### E QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number? options: A)20 B)22 C)27 D)28 E)30 SOLUTION:Given Ratio => 2:3 2x - 10 : 3x - 10 = 2 : 4 4[2x - 10] = 2[3x - 10] 8x - 40 = 6x - 20 8x - 6x = 40 - 20 x = 10 Then biggest number is = 3x 3x = 30 Ans = E #### E QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:The least common multiple is 222357=840. 3600 seconds / 840 = 4 + remainder. The answer is A. #### A QUESTION:Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? options: A)2/5 B)1/4 C)1/3 D)1/2 E)2/3 SOLUTION:Let P be the capacity of Jar X. The amount of water in Jar Y is 1/2P/2=P/4 Then the total amount in Jar X is P/4+P/4=P/2 The answer is D. #### D QUESTION:If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:X+Y will be even if X and Y are both even or both odd. P(X and Y are both even) = 3/62/5 = 1/5 P(X and Y are both odd) = 3/63/5 = 3/10 P(X+Y is even) = 1/5 + 3/10 = 1/2 The answer is A. #### A QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? options: A)90 min B)100 min C)110 min D)120 min E)None SOLUTION:Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C #### C QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt? options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36 SOLUTION:The total number of ways the dice can land is 666=216. Bob must get a score of 18=6+6+6. There is only 1 way to do this. P(Bob wins)=1/216 The answer is A. #### A QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap? options: A)7203 B)2403 C)3603 D)4803 E)5803 SOLUTION:LCM of 16, 20, 25, 45 = 3600 1 3600 + 3 = 3603 not divisible by 21 2 * 3600 + 3 = 7203 is divisible by 21 ANSWER:A #### A QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)25 days B)24 C)22 days D)27 days E)21 days SOLUTION:B 24 days B = 1/8 – 1/2 = 1/24 => 24 days #### B QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:Minute hand overlaps hour hand in 65 mins. In how many days it will gain 1440 hours ? options: A)58.384 days B)59.384 days C)57.384 days D)69.384 days E)55.384 days SOLUTION:In this problem , it has considered that 65 mins = 1hr so mins has increased by 5 mins so multiply 524=120 mins extra , That is now per day it adds 2hr extra so divide 1440/26=59.384 days ANSWER:B #### B QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)x years. ((2/5)x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11 SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways. The required probability = (9 4) = 36/78 = 6/13 Answer: B #### B QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A QUESTION:Perimeter of the backwheel is 9 feet and front wheel is 7 feet at a certain distance. The front wheel gets 10 revolutions more than the back wheel. What is the distance? options: A)305 B)310 C)315 D)320 E)325 SOLUTION:If distance=d Number of revolutions by back wheel=d/9 & front wheel=d/7 (d/7)-(d/9)=10 ,2d=630 ,d=315 ANSWER:C #### C QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? options: A)2.04% B)6.12% C)8% D)8.25% E)10% SOLUTION:Per quarter, interest = 2% So for a year, interest = 8% Due to quarter cumulation, effective yield (YTM) would be slight higher than 8% Answer = 8.25% =ANSWER:D #### D QUESTION:A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have? options: A)200 B)125 C)180 D)152 E)250 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 45% % of of employees other than secretaries and salespeople = 100 - 60 = 40% But this number is given as 50 so 40% of x = 50 x = 125 Therefore there a total of 125 employees in the company D Correct answer - B #### B QUESTION:The cost of raw material of a product increases by 30, the manufacturing cost increases by 20 and the selling price of the product increases by 60. The raw material and the manufacturing cost, originally, formed 40 and 60 of the total cost respectively. If the original profit was one-fourth the original manufacturing cost, find the approximation new profit percentage. options: A)48.38% B)54.68% C)62.48% D)42.36% E)None of these SOLUTION:Explanation : Let, the total initial cost of the product be Rs 100. Manufacturing cost = Rs 60 Raw materials cost = Rs 40 Also, original selling price => Rs100+(60/4)= Rs 115. New raw material cost =>Rs 40+30% of 40= Rs 52. New manufacturing cost =>Rs 60+20% of 60= Rs 72 New cost of the product = Rs124 New selling price =>115+60% of 115=Rs 184 New profit percentage =>60/124×100 =>48.38%. Answer : A #### A QUESTION:If C = x% of y and B = y% of x, then which of the following is true? options: A)1) C is smaller than B. B)2) C is greater than B C)3) Relationship between C and B cannot be determined. D)4) If x is smaller than y, then A is greater than B. E)5) None of the above SOLUTION:Basically C = B = xy/100 None of the options mentions this; hence E. #### E QUESTION:AB + CD = JJJ, where AB and CD are two-digit numbers and JJJ is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C? options: A) 1 B) 3 C) 7 D) 9 E) Cannot be determined SOLUTION:AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of JJJ it's 111. So, A=1. 1B+CD=111 Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9 Answer: D. #### D QUESTION:Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan. options: A)Rs.7000 B)Rs.5000 C)Rs.6000 D)Rs.Rs.4000 E)Rs.6500 SOLUTION:3:1 2:1 ------ 6:1 7 ----- Rs.28000 1 ----- ? => Rs.28,000/7=Rs. 4000 Answer: D #### D QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus? options: A)52 B)92 C)95 D)88 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 11 Total People can seat= 81+11=92 ANSWER:B #### B QUESTION:The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is? options: A)48 B)49 C)50 D)51 E)52 SOLUTION:Excluded number = (27 5) - (21 * 4) = 135 - 84 = 51. Answer: D #### D QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x107)/(1002)) – ( (x125)/(1002)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|C\| = -c \|b - 4\| + \|ab - b\| = ? options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab - b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab - b =ab - 2b + 4 Answer: Option B #### B QUESTION:A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is? options: A)90 B)45 C)110 D)40 E)50 SOLUTION:Explanation: milk:water = 6:3 6x : 3x + 10 = 6 : 5 5[6x] = 6[3x + 10] 30x = 18x + 60 30x - 18x = 60 12x = 60 x = 5 The quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9x = 45 Short cut method - 2 : for Only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio -------> 10 liters 9part of ratio -------> 45 liters Answer: Option B #### B QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:The average mark of the students of a class in a particular exam is 90. If 2 students whose average mark in that exam is 45 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam? options: A)10 B)40 C)20 D)30 E)25 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 90 x. Total marks of (x - 2) students = 95(x - 2) 90x - (2 45) = 95(x - 2) 100 = 5x => x = 20 Answer: C #### C QUESTION:suga invested an amount of Rs. 10,500 at the rate of 13% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested? options: A)13650 B)13150 C)13450 D)13900 E)13750 SOLUTION:Let the second amount be Rs. x. Then, (10500 * 13 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100 13650+ 15x= 16800 + 14x x = 3150 Total investment = 10000 + 3150 = Rs. 13150 .Answer: B #### B QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 â€“ 120 = 380 #### D QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match options: A)36 B)37 C)38 D)39 E)40 SOLUTION:Explanation: Let the average after 17th match is x then the average before 17th match is x-3 so 16(x-3) + 87 = 17x => x = 87 - 48 = 39 Answer: Option D #### D QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in options: A)2 days B)1 day C)3 days D)5 days E)7 days SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. B) #### B QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 541=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 5 games? options: A)x + 3y/(n + 3) B)x + y/(n + 3) C)(x + 3y)/(n + 3) D)(nx + 3y)/(n + 5) E)(3x + ny)/(n + 3) SOLUTION:Total points in first n games = nx Total marks in next 3 games is 3y So, Average marks in n + 5 games = (nx+3y)/(n+5) Hence, correct answer will be (D) #### D QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? options: A)72 B)78 C)80 D)82 E)84 SOLUTION:Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 268 - (A + D) = 268 - 132 = 136. B + B -28 = 136 B = (136 + 28)/2 = 82 ANSWER:D #### D QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:At a recent small town election for mayor a total of 971 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place? options: A)134 B)178 C)197 D)166 E)194 SOLUTION:The number of votes the winning candidate received was 971 + 53 + 79 + 105 /4= 302. The second received 302 – 53 = 249, The fourth place received 302 – 105 = 197. C #### C QUESTION:A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many Q apples did each person get before 45 people joined the feast? options: A)20. B)21. C)22. D)23. E)24. SOLUTION:Before solving it algebraically, let us prime factorize 1430 = 251113. Since number of apples per person total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C #### C QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 34 = 12 Answer: C #### C QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)12 B)15 C)20 D)24 E)30 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 60 / (60+x) = 4/5 x = 15 The answer is B. #### B QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item? options: A)17% B)21% C)24% D)29% E)42% SOLUTION:The price decreased by 23.99 - 16.99 = $7. $7 is a bit more than 29% of original price of $24. Answer: D. #### D QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is? options: A)6000 B)4000 C)2000 D)600 E)300 SOLUTION:412 : 236 : 436 2: 3: 6 2/11 3300 = 600 Answer: D #### D QUESTION:A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax? Choices options: A)$22.68 B)$23.94 C)$24 D)$25.20 E)$30 SOLUTION:A. #### A QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? options: A)14 min 80 sec B)14 min 48 sec C)14 min 42 sec D)14 min 40 sec E)14 min 43 sec SOLUTION:Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/20 1/20 : 8/15 :: 1 ; x x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec. The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec. Answer:D #### D QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:If ab-a-b=265 bc-b-c=155 ac-c-a=150 then find a? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:(A-1)(B-1)=AB-A-B+1=265+1=266..(1) (B-1)(C-1)=BC-B-C+1=155+1=156..(2) (C-1)(A-1)=CA-C-A+1=150+1=151..(3) (1)/(2) gives..(A-1)/(C-1)=266/156..(4) (3)(4) gives..(A-1)^2=257.47...A=17.04 Solving other equations..B=17.58 and C=10.4 ANSWER:B #### B QUESTION:A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)7 km D)5 km E)2 km SOLUTION:Let the total distance be 3x km. Then, x/8 + x/9 + x/10 = 47/60 x/3 = 47/60 => x = 2.33. Total distance = 3 2.33 = 6.99 km. Answer:C #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar? options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9) SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg Actual price of sugar = 10100/((100-10 )4) = Rs. 2(7/9) B #### B QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)50 m B)60 m C)65 m D)75 m E)80 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:Find the sum of all odd numbers upto 100. options: A)200 B)1000 C)2500 D)3140 E)3200 SOLUTION:Sol. The given numbers are 1, 3, 5, 7, ..., 99. This is an A.P. with a = 1 and d = 2. Let it contain n terms. Then, 1 + (n - 1) x 2 = 99 or n = 50. Required sum = (n/2) (first term + last term) = 50(1 + 99)/2 = 2500. ANSWER C 2500 #### C <<<Examples ends QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 117 pounds? options: A)8 B)7 C)12 D)9 E)none of the above SOLUTION:Ans is C: 39 pounds --> 6 days 117 pounds --> x days x = 117*6/39 = 18 the animal has already consumed food in 6 days so the the number of days for it's total consumption be 117 pounds is 18-6 = 12 #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:At what rate percent per annum will a sum of money double in 8 years. options: A)12.5% B)13.5% C)11.5% D)14.5% E)21.5% SOLUTION:Let principal = P, Then, S.I.=P and Time=8 years Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum. Answer: A #### A QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol. What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol? options: A)32 B)21 C)27 D)None of these E)18 SOLUTION:Explanation: Let t be the time after Kajol starts, when she meets Ajay, then \inline t=\frac{300}{(x+y)} This should be less than 2.5 or (x+y)>120 Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72 This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol. Answer: D #### D QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-902)/3=340 Answer : C #### C QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 532=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122 SOLUTION:Explanation: Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 Answer: B #### B QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test? options: A)768 B)243 C)246 D)280 E)224 SOLUTION:Let the maximum mark in each test be M. The candidate failed by 66 marks in the second test. pass mark in the second test = 249 + 66 = 315 45/100 M = 315 Pass mark in the first test = 40/100 M = 40/45 * 315 = 280. Answer:D #### D QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ? options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these SOLUTION:Explanation: Relative Speed = 60+40 = 100 Kmph = 100(5/18) = 250/9 m/sec Distance to be covered = 140 + 160 = 300 metres Time = Distance/Speed Time=300∗9/250=54/5=10.8 seconds Option B #### B QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly? options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20 SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/51/4 = 9/10. Answer: D. #### D QUESTION:What percent of a day is 15 hours? options: A)37Ã—1/2% B)16Ã—1/2% C)18Ã—2/3% D)22Ã—1/2% E)None SOLUTION:Solution Required percentage = (15/24Ã—100)% = (75 / 2)%. = 37Ã—1/2%. Answer A #### A QUESTION:The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? options: A)16 B)3/√2 C)8 D)2√2 E)(√2)/3 SOLUTION:800score Official Solution: The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2. The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B). #### B QUESTION:A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ? options: A)30 days B)15 days C)45 days D)24 days E)None of these SOLUTION:Let C completes the work in x days. Work done by (A + B) in 1 day = 1⁄10 Work done by (B + C) in 1 day = 1⁄18 A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1 or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1 or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days Answer C #### C QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+ SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers: L = 200 M = 10 N =20. So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans.. looking the the opion C to E, one can make out that they are incorrect, A. Out of which, i choose A. #### A QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream? options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these SOLUTION:Explanation : Speed downstream = 96⁄8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12-4 = 8 kmph Speed upstream = 8-4 = 4 kmph Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B QUESTION:In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder. options: A)A)4 B)B)3 C)C)2 D)D)5 E)E)6 SOLUTION:Explanation: 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 Answer: Option D #### D QUESTION:What is the different between the place value and face value of 6 in the numeral 5468? options: A)45 B)54 C)60 D)36 E)44 SOLUTION:place value of 6 = 6 * 10 = 60 face value of 6 = 6 60 - 6 = 54 Answer is B #### B QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king? options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26 SOLUTION:There are 26 black cards and 2 red kings. P(black card or king) = 28/52 = 7/13 The answer is D. #### D QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is? options: A)625 B)298 C)269 D)200 E)267 SOLUTION:Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3? options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml SOLUTION:concentration of water in mixture1 =2/9 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =3/10 By rule of alligation, concentration of water in mixture1 (2/9) concentration of water in pure water (1) Mean concentration (3/10) 1−3/10=7/10 =1:19 => Quantity of water =630×1/9=70 ml C #### C QUESTION:What is the remainder when 1014104710501053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24242730 break them into pairs 2424/33 gives remainder 15 and 2730/33 gives remainder 18 so 1518/33 gives remainder 6. B #### B QUESTION:Two coins are tossed, find the probability that two Tails are obtained options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3 SOLUTION:The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(T,T)} P(E) = n(E) / n(S) = 1/4 B #### B QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 17. D #### D QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:If you throw two dice at a same time. Can you find the probability of getting sum as 10 of the two numbers shown ? options: A)1/16 B)2/14 C)1/12 D)1/19 E)1/17 SOLUTION:C 1/12 All possible cases can be 36 (66) Case we need : [(4,6), (5,5), (6,4)] = 3 probability => 3/36 = 1/12 #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)11 B)77 C)36 D)47 E)99 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)1000 B)3000 C)3500 D)2500 E)2250 SOLUTION:For 20 staffs: 30010020 = 60000 for driver and cleaning staff: 3001002 =6000 From petty Cash : 1000 Answer is 1000 #### A QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= lw = 1/2 wd (l=1/2 d or d=2l) top face area= wd side face area= wd = 1.5 dl (w=1.5l) Volume = lwd= 192 l1.5l2l= 192 l=4 Side face area= ld= l2l= 424 =32 E is the answer #### E QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is options: A)60 B)75 C)90 D)105 E)120 SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 # of terms = (11 + 19)/2 * 9 = 15 9 = 135 sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75 Answer: B #### B QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ? options: A)4/17 B)4/18 C)4/76 D)4/13 E)4/29 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer: D #### D QUESTION:The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is? options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9 SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B #### B QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten? options: A)30 B)25 C)20 D)15 E)10 SOLUTION:There are two conditions: 1. Roslin got at least one score of each of 1, 2, 3, 4, and 5. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30. Answer: A. #### A QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits? options: A)36 B)77 C)88 D)99 E)22 SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1) Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2) Multiplying equation (1) by 2 and subtracting it from equation (2), we get => 2r = 72 => r = 36. Answer: A #### A QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:What is the area of a square field whose diagonal of length 20 m? options: A)228 B)271 C)200 D)277 E)181 SOLUTION:d2/2 = (20 * 20)/2 = 200 Answer:C #### C QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B? options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above SOLUTION:et ratio of A and B be 6x & 7x so net loss = 6x+7x= 7800 x=600 A=6x=6(600)=3600 B= 7x=7(600)=4200 so, B= 4200 ANSWER:A #### A QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:If w is a positive integer, then 3^w + 3^(w +1) = options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a(a − 1) E)4(3^w) SOLUTION:3^w + 3^(w +1) = 3^w + (3^w 3^1) = 3^w (1 + 3) = 3^w(4) Ans. E) 4(3^w) #### E QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=23322 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:If a person throw 2 dice simultaneously then find the probability of the sum of dots is 3 multiply ? options: A)1/2 B)1/3 C)2/5 D)7/9 E)1/4 SOLUTION:If 2 dies are thrown E = event of getting a prime number = 12 total number of possible out comes = 36 probability = 12/36 = 1/3 Answer is B #### B QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4? options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters SOLUTION:4:1 --- 60 1:4 2:8 --------------- 5 5 ----------- 60 5 ----------- ? => 60 liters ANSWER:A #### A QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%? options: A)8 B)3 C)5 D)6 E)None SOLUTION:C.P. of 9 Headphones= Rs100 S.P. of 9 Headphones = 150% of Rs 100 = Rs150 For Rs.150 , Headphones sold = 9. For Rs. 100,Pens sold=(9/150)100=6 Answer: Option D #### D QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ? options: A)28years B)29years C)30years D)31years E)32years SOLUTION:Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 25) years = 35 years. Ayush's father's present age = (35+ 5) years = 40 years. Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years. Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years. Answer: A) 28 year #### A QUESTION:Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute? options: A)4:5 B)9:25 C)5:4 D)25:9 E)Cannot be determined from the information provided SOLUTION:Same circumferential rate means that a point on both the gears would take same time to come back to the same position again. Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B Time A = 2pi25/Speed A Time B = 2pi20/Speed B Since the times are same, 50pi/Speed A = 40pi/Speed B SpeedA/Speed B = 50pi/30pi = 5/4 Correct Option: C #### C QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 5050 = 2500m = 2.5km Speed = 602.5=150km/hr Answer is D #### D QUESTION:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 140800, how many purple chips were selected? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:140800 = 15^28^311 The factors of 8 must come from the purple point value, so there are 3 purple chips. The answer is C. #### C QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours Answer: Option D #### D QUESTION:Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The total number in the three clubs is 17+24+22=63. All 50 students signed up for at least one club. 3 of those students signed up for exactly one more club. 63 - 53 = 10 so 5 students must have signed up for exactly three clubs. The answer is A. #### A QUESTION:Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? options: A)32 : 48 B)32 : 42 C)32 : 45 D)32 : 41 E)42 : 45 SOLUTION:Explanation: A : B (80004)+(40008) : (90006)+(60006) 64000 : 90000 32 : 45 Answer:C #### C QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12.5N E)20 SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 + 1.5x$500 = $500 + $750 =$1250 This is 12.5 times the 1992 number, so the correct answer is 12.5N. D #### D QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 37/1002100 = 441. D #### D QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:Which is greater than -1? options: A)-5 B)-4 C)-3 D)-2 E)0 SOLUTION:-1 greater than 0. Answer: E #### E QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ? options: A)6 B)3 C)2 D)1 E)5 SOLUTION:There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options. So, we start with a=1, we get b as -ve. out a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions) a=3, we get b as 3. Yes (Now we have 3 possible solutions) a=4, we get b as fraction. Out a=5, we get b again as some fraction. Out a=6 already taken. We have A,B options left. C,D,E are out. A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b. When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible. So, answer will be E. #### E QUESTION:As part of a game, two people each must secretly choose an integer between 1 and 2, inclusive. What is the approximate likelihood that all two people will choose different numbers? options: A)9% B)12% C)16% D)20% E)50% SOLUTION:Ans:E 1st person has option no's- (1,2) - there fore probability of getting a no = 2c1/2c1 = 1 2nd person has only one option - there fore probability of getting a no = 1c1/2c1 =1/2 =11/2 =50% #### E QUESTION:In a fuel station the service costs $1.65 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? options: A)320$ B)380$ C)420$ D)448.8$ E)480$ SOLUTION:Total Cost = ( 1.6512 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 => 448.8 Hence answer will be (D) #### D QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago? options: A)152460 B)214560 C)131632 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^6 Answer is C #### C QUESTION:The equation of line q is y = 4/3x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.510075=0.5125* x => x=60; SO answer is 60=C #### C QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ? options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4 SOLUTION:Say a = 2. Then: a/b = 1/3 --> b = 6; b/c = 2 --> c = 3; c/d = 1/2 --> d = 6; d/e = 3 --> e = 2; e/f = 1 --> f = 2. abc/def = (263)/(622) = 3/2. Answer: D. #### D QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")(Number of ways the vocalist can sing "new songs")= 1510=150 Answer: C #### C QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles? options: A)4329 B)2799 C)4312 D)2799 E)2712 SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: C #### C QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(8400047/2)/100 = i i = 11760 Answer: D #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 105 ⇒ 1.75x = 105 ⇒ x = 60 coins Answer D #### D QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:What is the sum of this series? 1, 3, 5, 7, 9, ...... 45. options: A)600 B)529 C)612 D)512 E)589 SOLUTION:Number of odd numbers between 1 and 45 is (45+1)/2=23 Therefore Sum of odd numbers 2323= 529 ANSWER: B #### B QUESTION:S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the tenth digit of p, counting right to left from the units digit? options: A)1 B)2 C)4 D)6 E)9 SOLUTION:C Sum of unit digits of first 30 terms = 60 Sum of tens digits of first 30 terms = 58 Sum of thousands digits of first 30 terms = 56 and so on.. p1 = 0 p2 = (6+58) = 4 p3 = (6+56) = 2 p4 = (6+54) = 0 p5 = (6+52) = 8 p6 = (5+50) = 5 p7 = (5+48) = 3 p8 = (5+46) = 1 p9 = (5+44) = 9 p10= (4+42) = 6 ANSWER : D #### D QUESTION:Which is the middle even number between 6 and 14? options: A)10 B)6 C)8 D)14 E)26 SOLUTION:6+x = 14-x 2 x = 8 X = 4 Now 6+x = 10 ANSWER:A #### A QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+1112) = 12!11!(133) = 12!11!(719) The greatest prime factor is 19. The answer is C. #### C QUESTION:Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)s.225 B)s.288 C)s.485 D)s.279 E)s.282 SOLUTION:Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5 SP = CP[(100 + profit%)/100] = 232.5 [(100 + 20)/100] = Rs.279. Answer:D #### D QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? options: A)120 cm2 B)187 cm2 C)178 cm2 D)189 cm2 E)176 cm2 SOLUTION:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A #### A QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)4.1 B)3.6 C)2.6 D)5.0 E)5.5 SOLUTION:B 3.6 In this simple subtraction series, each number decreases by 0.4. #### B QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years? options: A)Between 20 and 21 B)Between 21 and 22 C)Between 22 and 23 D)Between 23 and 24 E)None of these SOLUTION:Required sum = 20(1+8/100)2=20×27×27/25×25=23.3 Answer D #### D QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 12=45,0008 1:1 Madhu's share=1/260,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)20 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=20%. Answer: E. #### E QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:14 To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible. 75-yes 72 -yes 69 and 66 -no 63 - yes 60 -no 57, 54, and 51 -yes 48 - no 45 and 42 - yes 39 - no 36 - yes 33 and 30 - no 27, 24, and 21 - yes 18 -no 15 and 12 yes Correct answer is E. #### E QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:139 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 93+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:3+33+333+33.33=? options: A)362.33 B)372.33 C)402.33 D)702 E)None of them SOLUTION:3 33 333 33.33 ---------- 402.33 ---------- Answer is C #### C QUESTION:Half of 5 percent written as decimal is options: A)5 B)0.5 C)0.05 D)0.025 E)None of these SOLUTION:Explanation: It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025 Answer: Option D #### D QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage? options: A)50% B)100% C)45% D)55% E)65% SOLUTION:Let the C.P of each book be Re 1. Then, S.P of 5 books= C.P of 10 books= Rs. 10 Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10 Gain = Rs ( 10 -5 ) = Rs 5. Gain% = ( 5/5× 100 ) % = 100% Answer : B #### B QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)1/10=80.5+7.51/10 80.5+0.75=81.25 E #### E QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:Find the value of 72519 x 9999 = m. options: A)233243413 B)354545451 C)343435451 D)565656767 E)725117481 SOLUTION:72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 E #### E QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 115=55 Answer : B #### B QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:Two planes take off from neighboring runways at the same time. The British Airways Jet heads directly East at 300 Km/Hr, while the American Airlines Jet takes off heading directly west at 250km/hr. At this speed, how long before the two planes are 2,000 Km away from each other? options: A)4 hours B)3.75 hours C)3.0 hours D)3.5 hours E)3.63 Hours SOLUTION:For every hour the planes travel in opposite directions, they are 550 Km away from each other. So to be 2,000 Km away, it would take (2,000 Km/550 Km/Hour= 3.63 Hours). Answer is E #### E QUESTION:When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n? options: A)9 B)20 C)55 D)70 E)81 SOLUTION:Here's an approach that's based on Number Properties and a bit ofbrute forcemath: We're told that K and N are both INTEGERS. Since K/N = 81.2, we can say that K = 81.2(N) N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E. With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11) Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH. Final Answer: B #### B QUESTION:What is the perimeter of a triangle with sides 5 and 4 that has the maximum possible area? options: A)9 + 3√2 B)9 + √41 C)16 D)9 + √37 E)9 + 3√6 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(25+16) = √41 The perimeter is 9 + √41 The answer is B. #### B QUESTION:A student completes a 3 part exam as follows. The student completes sections A in 6 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour? options: A)7:1 B)9:2 C)8:3 D)5:2 E)6:1 SOLUTION:The time spent on section B and section C is 27 minutes each. The ratio of C to A is 27:6 = 9:2 The answer is B. #### B QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 75 = 20.93 ANSWER:D #### D QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:The total marks obtained by a student in Mathematics and Physics is 32 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)26 C)27 D)28 E)22 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 32 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (32 + 20) / 2 = 26.Answer:B #### B QUESTION:How many positive integers less than 254 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)43 E)64 SOLUTION:252/4=63 Multiples of 4 which are a multiple of 6 will be of the form 223=12n where n>0 240/12=20 63-20=43 Answer: D #### D QUESTION:Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 50 yr. How old is E? options: A)50 yr B)40 yr C)45yr D)64 yr E)NOne SOLUTION:Solution: Total present age of A, B, C and D, = (454)+(45) = 200 yr; Total age present age of A, B, C, D and E, = 505 = 250 yr. So, age of E = 50 yr. Answer: Option A #### A QUESTION:If an article is sold at 19% profit instead of 12% profit, then the profit would be $84 more. What is the cost price? options: A)$900 B)$1200 C)$1500 D)$1800 E)$2100 SOLUTION:7% cost price = $84 1% * cost price = $84 / 7 = $12 The cost price is $1200. The answer is B. #### B QUESTION:There are 100 wine glasses. I offered my servant to 3 paise for every broken glass to be delivered safely and forfeit 9 paisa for every glass broken at the end of day. He recieved Rs.2.40 .how many glass did he break. a. 20 b. 73 c. 5 d. 8 options: A)22 B)281 C)29 D)28 E)191 SOLUTION:Answer:B #### B QUESTION:(786×74) ÷ ? = 1211.75 options: A)4.8 B)48 C)58 D)68 E)48 SOLUTION:Explanation: 58164/x = 1211.75 => x = 58164/1211.75 = 48 Answer: Option B #### B <<<Examples ends QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? options: A)3.625 B)3 C)4.5 D)4 E)3.5 SOLUTION:Set up two R x T =D cases. 1. 1/12 km/ min x T = 2.75 from which T= 33 mins. We know total journey time now is 51 +33 =84. The rate is the same ie 1/12km/min. set up second R x T =D case. 1/12 km/min x 84 = 7 km Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5 E. #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed. options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec SOLUTION:If length of train is l and speed of train is s, then l/s = 10 (l+180)/s = 20 (l+180)/l = 20/10 =2 l+180 =2l l= 180 l=180 mtrs s= l/10 = 180/8 = 10 m/sec ANSWER:A #### A QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:If a^x = b^y, then options: A)log a/b= x/y B)log a/ log b = x/y C)log a/ log b = y/x D)log b/a = x/y E)log b/a = y/x SOLUTION:a^x = b^y => log a^x = log b^y => x log a = y log b => log a/ log b = y/x ANSWER:C #### C QUESTION:A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group? options: A)5.55% B)16.67% C)15.75% D)20.45% E)25% SOLUTION:The question basically asks about the probability that Bob and Lisa sit at the ends. The total # of sitting arrangements is 4!. Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 22!. P=(favorable)/(total)=(22!)/4!=1/6. Answer: B. #### B QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pir^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)2121/4 = 346.5 sq m answer :C #### C QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:168: x4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? options: A)87 sec B)89 sec C)17 sec D)18 sec E)97 sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 650)/10 = 89 sec. Answer:B #### B QUESTION:Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount. options: A)680 B)700 C)720 D)730 E)750 SOLUTION:From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal. As the annual Interest is to be calculated, the time period T =1. Plugging these values in the simple Interest formula, I = P x T x R = 8,000 x 1 x 0.09 = 720.00 Annual Interest to be paid = $720 answer :C #### C QUESTION:In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is: options: A)4 B)5 C)6 D)7 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 15 : 9 :: 12 : x => 12 x 15 x x = 10 x 8 x 12 => x = 10 x 9 x 12 / (12 x 15) => x = 7 Answer : D #### D QUESTION:In the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r = options: A)6 B)5 C)4 D)3 E)2 SOLUTION:An easy way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units (both points are on y=-1 line so the distance will simply be 1-(-2)=3) So the radius must be more than 3 units. The distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units (both points are on x=-2 line so the distance will simply be 4-(-1)=5) So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4. Answer: C. #### C QUESTION:A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room? options: A)10:00am B)10:45am C)12:00pm D)12:30pm E)1:30pm SOLUTION:In 6 hours the entrance door is opened to fill the room equal to 61/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours. Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm. Answer: D. #### D QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 * 15 * 15 = 1350 Answer: A #### A QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:How many ways could two people sit at a table with four seats in which two of the four seats will remain empty? options: A)60 B)12 C)112 D)118 E)120 SOLUTION:ways in which 2 seats out 4 can be selected = 4C2 ways in which 2 people can be arranged in 2 seats = 2! Total ways of arrangement = 4C22! =43 =12 Ans = B #### B QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? options: A)662 B)678 C)652 D)642 E)721 SOLUTION:8 86 = 688 – 10 = 678 ANSWER:B #### B QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 6046 = 2760 runs Now excluding the two innings the runs scored = 5844 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is: options: A)260 B)262 C)270 D)272 E)None of these SOLUTION:Explanation: Volume will be length * breadth * height, but in this case two heights are given so we will take average, Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3 Option C #### C QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:55 + 40 + 20 = 115 This number includes some people counted twice and some people counted three times. 115 - 88 = 27, and this number represents people counted twice or three times. 7% of the people are counted two extra times. The percentage of people counted one extra time is 27 - 7(2) = 13. The percentage of people who liked more than one product is 7% + 13% = 20%. The answer is B. #### B QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y? options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6 SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2. and hence answer B #### B QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? options: A)5/6 B)2/7 C)2/8 D)9/2 E)8/9 SOLUTION:P (getting a prize) =10/(10 + 25) = 10/35 = 2/7 . Answer:B #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 34 = 12 Answer: C #### C QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 5/18 = 40/9 m/s Hence time taken to cover 40 m = 409/40 = 9 seconds. Answer: C #### C QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)10years B)12 years C)5 years D)3 years E)24 years SOLUTION:Explanation: 9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 years Answer:D #### D QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n? options: A)8/7 B)8 C)9/8 D)7 E)5 SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 9x+xn and we are told that it equals to 9xn: 9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9 n = 9/8 Answer: C #### C QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother. options: A)24 years B)25 years C)26 years D)27 years E)28 years SOLUTION:At the present, Sara's age is x. Sara's mother's age is y=6x. Next year, Sara's age will be x+1. Sara's mother's age will be y+1=5(x+1). From the two equations, we can calculate Sara's age: y=6x y+1=5 (x+1) 6x+1=5x+5 6x-5x=5-1 x=4 If Sara is currently 4 years old, and her mother is 6 times older, then her age is 6x=6×4=24. ANSWER: A #### A QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km. Speed = Distance/Time Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours] Required speed = 3000 x 3/5 km/hr = 1800 km/hr. Answer: Option B #### B QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 40007 = 28000. Answer : Option A #### A QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:What is the remainder of Q= 3^19 when divided by 10? options: A)0 B)1 C)5 D)7 E)9 SOLUTION:I looked for patterns: ^2 - units digit 9 ^3 - units digit 7 ^4 - units digit 1 ^5 - units digit 3 hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9 and we can then see: ^16 - units digit 1, or ^18 - units digit 9 and ^19 - units digit 7 therefore, Q=when divided by 10, the remainder must be 7.D #### D QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these SOLUTION:Explanation: 2(l+b)/b=5/1 2l + 2b = 5b 3b = 2l b = 2/3 l Then, Area = 216 cm2 l x b = 216 l x (2/3)l = 216 l2 = 324. l = 18 cm. Answer: B #### B QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race? options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters SOLUTION:Answer A runs 25% as fast as B. i.e., if B runs 100 m in a given time, A will run 125 m in the same time. In other words, if A runs 5 m in a given time, then B will run 4 m in the same time. Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat. Ratio of length of start given : length of race :: 1 : 5 In this question, we know that the start given is 7 m. Hence, the length of the race will be 7 * 5 = 35 m. Choice E #### E QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m SOLUTION:D = 70 * 1 ½ = 105 km RS = 85 – 70 = 15 T = 105/15 = 7 h 3.30 + 7 h = 10.30 p.m. Answer:C #### C QUESTION:When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is options: A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002 SOLUTION:It is very easy if x is the diameter, then the magnified length is 1000x. ince 1000x=0.3 then x=0.3/1000=0.0003. The answer is D #### D QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -3 < x < 7 - true because x can be between -3 < x < 7 E. none of the above. Answer: D #### D QUESTION:A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it? options: A)30 days B)35 days C)40 days D)45 days E)50 days SOLUTION:Explanation: Let ‘x’ be the number of days taken by B alone to finish the whole work Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days. Then, working together, 3x/2 × x/3x/2 + x = 18 days 3x × x/5x = 18 3x/5 = 18 Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days. Answer: Option A #### A QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)240 B)377 C)2908 D)287 E)201 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A #### A QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears? options: A)300 B)250 C)130 D)303 E)111 SOLUTION:830-527=303. Answer is D. #### D QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour? options: A)73 B)83 C)12 D)83 E)11 SOLUTION:Explanation: T = 8/45 * 60 = 11 Answer: Option E #### E QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:If x and y are even integers, which of the following is an odd integer? options: A)x+y B)xy C)xy+2 D)x^2+y^2 E)None of these SOLUTION:even+even = even even even = even even+even =even Answer : E #### E QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? options: A)25 B)21 C)20 D)10 E)15 SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B respectively Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4] Quantity of B in mix. left =[5x –5/12 9 ] = [ 5x - 15/4 ] Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9 [5x-15/4]+9 20x+21 252x -189 =140x+147 or 112x =336 , x = 3. Quantity of A in the can initially =73 =21 ANSWER:B #### B QUESTION:Which is the middle even number between 6 and 14? options: A)10 B)6 C)8 D)14 E)26 SOLUTION:6+x = 14-x 2 x = 8 X = 4 Now 6+x = 10 ANSWER:A #### A QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74 SOLUTION:1/5 + 1/15 - 1/x = 1/18 x = 4.74 Answer:E #### E QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 24th September was a Monday. The answer is A. #### A QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5 options: A)40 B)20 C)25 D)30 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40 Answer: Option A #### A QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24 options: A)22 B)62 C)28 D)16 E)11 SOLUTION:Answer:B #### B QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(28-10) kmph = 4 kmph. Answer B #### B QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 13579...99 g(97) = 13579...97 g(99) - g(97) = 13579...99 - 13579...97 = 13579...97(99 - 1) = 13579...9798 hence:A. #### A QUESTION:the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? options: A)20 B)55/4 C)25 D)14 E)13 SOLUTION:After passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles/hour. In those 5 mins the cyclist travels a distance of 5/4 miles. In those 5 mins the hiker travels a distance of 1/3 miles. So the hiker still has to cover 11/12 miles to meet the waiting cyclist. The hiker will need 55/4 mins to cover the remaining 11/12 miles. So the answer is B. #### B QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 245= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 245 + 2y =124 then y=2 244 + 2y = 124 then y=14 243 +2y = 124 then y= 26 242 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:If x = 3^9 and x^x = 3^k, what is k? options: A)3^11 B)3^13 C)3^25 D)3^27 E)3^81 SOLUTION:Solution: We know that x=3^9 which implies x^x = (3^9)^(3^9) = 3^(9 3^9) [because (x^y)^z = x^(yz))] so 3^(3^2 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)] therefore x^x = 3^(3^11) Given that x^x=3^k so 3^(3^11) = 3^k Since the base is same the exponent will also be same therefore k = 3^11 Answer: A #### A QUESTION:A large box contains 19 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)475 B)350 C)450 D)550 E)650 SOLUTION:The number of chocolate bars is equal to 19 * 25 = 475 correct answer A #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:Two pipes A and B can fill a tank in 15 min and 27 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? options: A)14 min 19 sec B)14 min 42 sec C)18 min 24 sec D)14 min 40 sec E)14 min 10 sec SOLUTION:: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/27 1/27 : 8/15 :: 1 ; x x = 8/15 * 1 * 27 = 14 2/5 min = 14 min 24 sec. The tank will be full in (4 min. + 14 min. 24 sec) = 18 min 24 sec.Answer: C #### C QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:What is the sum of natural numbers between 50 and 100 options: A)4800 B)4860 C)3825 D)5500 E)5550 SOLUTION:a = first number l = last number Sn = n/2[a + l] between 50 and 100 numbers = 51 => 100 - 50 = 50 + 1 = 51 Sn = 51/2 Ã— 150 = 51 Ã— 75 = 3825 Answer : C #### C QUESTION:On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday? options: A)0.008 B)0.125 C)0.128 D)0.512 E)0.64 SOLUTION:Re-phrasing the question: What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain Probability of rain = 0.5 Therefore, probability of no rain = 0.5 0.50.50.5 = 0.125 Hence B #### B QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/155297 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:When x divided by 288, the remainder is 47. Find the remainder when the same x is divided by 24? options: A)20 B)21 C)23 D)26 E)29 SOLUTION:23 Option C #### C QUESTION:If x,p,q, and r are positive integers and (p)×(q)×(r)=x^2, which of the following could be the values of p,q, and r? options: A)3, 16, 25 B)9, 25, 24 C)2,16, 32 D)2, 9, 16 E)8, 16, 36 SOLUTION:This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number. C fits the bill. 21632 = 24484 =4488 ans C #### C QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make? options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss SOLUTION:81 ---- 17 100 ----- ? è 20.98%loss Answer: B #### B QUESTION:The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/18% B)18 2/11% C)18 2/91% D)18 9/11% E)12 2/11% SOLUTION:13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B #### B QUESTION:A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved? options: A)2/4 B)3/4 C)4/5 D)5/6 E)6/7 SOLUTION:consider A,B,C events and AA,BB,CC not solving the problems now P(1)=1/2, P(B)=2/3 and P(C)=1/4 Not solving events =1/22/33/4 ==>1-1/4= 3/4 ANSWER B #### B QUESTION:Two clocks are set at 3 0'clock in the morning. If one clock gains 10 minutes per hour and when it shows 6:30 in the morning what does the correct clock show? options: A)5:30 B)5:25 C)7:00 D)6:15 E)6:00 SOLUTION:The faster clock gains 10 minutes per hour. The two clocks at at 3:00 at 3 0'clock in the morning At 4 0'clock - The correct clock is at 4:00 The faster clock is at 4:10 (1 hour + gains 10 minutes) At 5 0'clock - The correct clock is at 5:00 The faster clock is at 5:20 (2 hours + gains 20 minutes) In three hours the faster clock gains 310=30 minutes When the faster clock is at 6:30 the correct clock is at 6:00 in the morning. Answer is E #### E QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)4 D)5 E)6 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph options: A)2 second B)4 second C)6 second D)8 second E)10 second SOLUTION:Explanation: From the given question, we will first calculate the speed of train relative to man, => ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite ) Convert it in metre/second =66Ã—5/18 =55/3m/sec Time it will take to pass man =110Ã—3/55 =6 seconds ANSWER IS C #### C QUESTION:If the speed of a man is 54 km per hour, then what is the distance traveled by him in 25 seconds ? options: A)275m B)360m C)375m D)420 m E)440 m SOLUTION:The distance traveled in 25 sec = 54(5/18) 25 =375m ANSWER:C #### C QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6? options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720 SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6 Seeing the Options After Dividing an Finding the Reminder of 2 My Answer was A #### A QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages options: A)30 B)35 C)37 D)41 E)42 SOLUTION:Explanation: Let A's age 10 years ago = x years. Then, B's age 10 years ago = 2x years. (x + 10) / (2x+ lO) = 3/4 => x = 5. So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years Option B #### B QUESTION:Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum? options: A)20 B)22 C)25 D)27 E)29 SOLUTION:(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131 a + b + c = √625 = 25 C #### C QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 70% total profit if he has already sold one of the four cars at Rs. 1.2 lakh? options: A)1.8 lakh B)1.3 lakh C)1.9 lakh D)8.1 lakh E)6.1 lakh SOLUTION:Explanation: Total cost of 4 cars = 1+2 = 3 lakh Total SP of 4 cars = 3 x 1.7 = 5.1 lakh SP of 1 car = 1.2 lakh SP of rest 3 cars = 5.1 - 1.2 = 3.9 lakh Average SP of all the 3 cars = 1.3 lakh Answer: B) #### B QUESTION:Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? options: A)$1.08 B)$1.41 C)$1.74 D)$1.98 E)$2.16 SOLUTION:2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E. #### E QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). (140/100 5x), (150/100 * 7x) and (175/100* 8x) 7x, 21x/2 and 14x The required ratio = 7x : 21x/2 : 14x 14x : 21x : 28x 2 : 3 : 4 Answer = A #### A QUESTION:The value of (34.310.4731.5)/(0.067323.257.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.310.4731.5)/(0.067323.257.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases Answer: option C #### C QUESTION:In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? options: A)2.5 sec B)4.25 Sec C)5 sec D)12.5 sec E)None SOLUTION:Solution Speed = (144 x 5 /18) m/sec = 40 m / sec Time taken = (100 /40) sec = 2.5 sec. Answer A #### A QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above SOLUTION:5510 = 550 665 = 330 880/15 = 58.66 ANSWER:C #### C QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)Rs. 2000 B)Rs. 2010 C)Rs. 2100 D)Rs. 2200 E)Rs. 2300 SOLUTION:Total expenditure for the first 3 months = 3 × 1600 = 4800 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 4800 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 25200/12 = Rs. 2100 C #### C QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is? options: A)1 B)22 1/7 C)2 D)22 1/2 E)3 SOLUTION:100 --- 10 DS = 10 ? ---- 1 200 ---- 30 US = 8 ? ----- 1 S = (10 - 8)/2 = 1 kmph. Answer:A #### A QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:A committee of 6 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)360/14 E)3/14 SOLUTION:3/84/71/66! = 3/14. We are multiplying by 6! because we can choose secretary,economist, and accountant is several way: Answer: D. #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)Rs.64.18 B)Rs.64.67 C)Rs.64.08 D)Rs.64.10 E)Rs.64.22 SOLUTION:S.I. = (1000 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 25 = 10. So, we need 10 to be in x! at least in power of 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface? options: A)27 B)16 C)12 D)18 E)11 SOLUTION:2 π * 2r * 3r = 12 πr2 Answer:C #### C QUESTION:By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: options: A)Rs. 2,600 B)Rs. 2,700 C)Rs. 2,800 D)Rs. 3000 E)NOne SOLUTION:Solution: Let Cost Price was X. X + 14% of X = 2850 X + 14X/100 = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = 100/1142850 = Rs. 2500; SP for a profit of 8% = 108/1002500 = Rs. 2700. Answer: Option B #### B QUESTION:Find the next term in series - 25, 37, 49, 61, ? options: A)71 B)72 C)73 D)74 E)75 SOLUTION:Series is Increased by 12. 25 +12 =37 37 +12 =49 49 +12 =61 61 +12 =73 ANSWER:C #### C QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)6 B)(P-7)5 C)(P-7)2 D)(P-7)3 E)(P-7)4 SOLUTION:M/84 =(P-7)/21 M = (P-7)84/21 =(P-7)4 E #### E QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792? options: A)1600 B)2777 C)2889 D)27670 E)2771 SOLUTION:1792 = P [1 + (512/5)/100] P= 1600.Answer:A #### A QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 987 / 32 = 84 n(E) = 2C2 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(38+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 9 inches long, how wide is Jordan's rectangle, in inches? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 9x=180x x=20 answer is D #### D QUESTION:Six children â€” A, B, C, D, E, and F â€” are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children? options: A)60 B)180 C)240 D)360 E)720 SOLUTION:If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy. First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? Thatâ€™s a permutation of the 6 items â€”- 6P6 = 6! = 720. Thatâ€™s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, itâ€™s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F. Answer = D. #### D QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? options: A)23 years B)24 years C)25 years D)None of these E)18 years SOLUTION:Let the average age of the whole team by x years. 11x - (26 + 29) = 9(x -1) 11x - 9x = 46 2x = 46 x = 23. So, average age of the team is 23 years. Answer: Option A #### A <<<Examples ends QUESTION:The perimeter of a semi circle is 180 cm then the radius is? options: A)22 B)28 C)35 D)37 E)13 SOLUTION:36/7 r = 180 => r = 35 Answer: C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price? options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050 SOLUTION:C $1000 90% 104% -------- 14% ---- 140 100% ---- ? => $1000 #### C QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 40 km per hour. At what time will Car B be 40 km ahead of Car A? options: A)3:00 pm B)3:30 pm C)4:00 pm D)4:30 pm E)5:00 pm SOLUTION:At 9:30 am, Car A will be 15 km ahead of Car B. Car B travels at a rate 10 km per hour faster than Car A. Car B needs to travel 55 km more than Car A in order to be 40 km ahead. This will take 55 km/10 km per hour=5.5 hours. Car B will be 55 km ahead at 3:00 pm. The answer is A. #### A QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15. How many flies did her frog eat on Thursday? options: A)12 B)14 C)10 D)11 E)13 SOLUTION:A) 12. The frog started eating 3 more flies each day. 3 +3 =6 6+3=9 9+3=12 12+3=15 #### A QUESTION:The volume of a sphere with radius r is (4/3)pir^3 and the surface area is 4pir^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/8001/600=1/4,800. Answer: B. #### B QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and â€“4; #### B QUESTION:After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone? options: A)7 B)4 C)6 D)2 E)7 SOLUTION:Explanation: David and Moore complete half work in 3 days => they can complete whole work in 6 days Answer: Option C #### C QUESTION:On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit? options: A)10.5% B)12.5% C)15% D)25% E)30% SOLUTION:suppose there are X motorists. 10% of them exceeded the speed limit and received the ticket, i.e. X/10. Again, suppose total no. of motorists who exceeded the speed limit are Y. 60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5. it means 2Y/5 received the ticket. hence, 2Y/5 = X/10 or Y/X=1/4 or Y/X 100= 1/4 * 100= 25% D #### D QUESTION:A man can do a piece of work in 5 days, but with the help of his son he can do it in 2 days. In what time can the son do it alone ? options: A)7 1/2 days B)6 1/2 days C)5 1/3 days D)3 1/3 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/2−1/5)=(5−2)/10=3/10 So son will do whole work in 10/3 = 3 1/3 days Answer: D #### D QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5700 = Rs.3500 ANSWER:D #### D QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is: options: A)448 B)488 C)16748 D)548 E)560 SOLUTION:Required number = (L.C.M. of 12, 31, 20, 54) + 8 = 16740+ 8 = 16748. answer :C #### C QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 3^2 * 5 * n = 37K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2235 = 60. So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 607 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 602 or 6032 or 605 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has. Answer (C) #### C QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year? options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155 SOLUTION:cost of type A products next year = 1.3 * 3200 = 4160 cost of type B products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 ANSWER:C #### C QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business? options: A)2:35:16 B)2:15:16 C)2:15:77 D)2:15:98 E)2:15:23 SOLUTION:Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24) = 12:15:16 Answer: B #### B QUESTION:The number which exceeds 16% of it by 63 is : options: A)75 B)52 C)58 D)60 E)62 SOLUTION:Solution Solution Let the number be x. x-16% of x =63 x-16/100x =63 x-4/25x=63 21/25x=63 x=(63x25/21)= 75 Answer A #### A QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:The smallest 2 digit prime number is? options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None SOLUTION:The smallest 3-digit number is 10, which is divisible by 2. 10 is not a prime number. 11 is a prime number. Hence 11 is the smallest 2-digit prime number. A) #### A QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?. options: A)540 m B)178 m C)936 m D)234 m E)713 m SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m. When B covers 960 m, C covers 936 m Option C #### C QUESTION:Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is: options: A)8 B)4 C)12 D)16 E)14 SOLUTION:Explanation : Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4. Number of Knives = 3x = 12. Answer : C #### C QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:In a lottery there are 100 prizes and 300 blanks. A lottery is drawn at random. What is the probability of getting a prize? options: A)1/2 B)5/400 C)1/5 D)1/3 E)1/4 SOLUTION:total draws = prizes+blanks= 100+300=400 probability of getting a prize = 100/400 = 1/4 correct option is E #### E QUESTION:3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days? options: A)18 B)09 C)07 D)19 E)12 SOLUTION:3 M + 10 B ----- 09 days 7 M + 7 B ------- 8 days 9 M + 9 B -------? 21 M + 70 B = 63 M +63 B 7 B= 42 M => 6 M = 1 B =>1 B =6 M 3 M + 60 M = 63 M ---- 9 days 9 M + 54 M = 63 M -----? => 9 days Answer: B #### B QUESTION:The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.) options: A) 1 B) 4 C) 7 D) 11 E) 10 SOLUTION:We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients... 3 ingredient blends: ABC ABD ACD BCD Total blends = 4 B #### B QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 610=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 37=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n? options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2 SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2. In an AP, Last term = First term + (n-1)common difference w = First term + (n-1)2 First term = w - 2(n-1) ANSWER:C #### C QUESTION:A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share? options: A)8239 B)2900 C)2000 D)2393 E)2009 SOLUTION:Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively. Then, 4x - 3x = 1000 => x = 1000. B's share = Rs. 2x = 2 * 1000 = Rs. 2000. Answer: C #### C QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68 E)None of these SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. ANSWER:A #### A QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The distance between the nest and the ditch is 250 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 250 = 7500. D = ST 7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km) D) #### D QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z? options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)% SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1 z is m% of y MEANS z= (m/100 )* y------------------------eq2 Find equation of xz substitute value of y from 2nd equation into Ist equation so x= (n/100)(100z/m) so x= (n/m)z or x= (100n/m)z/100 so answer E is 100n/m %.E #### E QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54 SOLUTION:Let the required means score be x. Then, 20 80 + 25 * 31 + 55 * x = 52 * 100 = 1600 + 775 + 55x = 5200 = 55x = 2825 = x = 565/11 = 51.4. ANSWER:C #### C QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code? options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D SOLUTION:D = S : = L S = A P = { P = { Y = U Correct Answer: A #### A QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability. options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53 SOLUTION:Explanation : There are total 4 letters. The probability that P gets the first position is 1/4. The probability that O is in the second position is 1/3. Likewise, probability for C and Y are 1/2 and 1/1. Hence, the required probability is:- => (1/4) x (1/3) x (1/2) x 1. => 1/24. Answer : C #### C QUESTION:Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project? options: A)120 B)80 C)48 D)192 E)40 SOLUTION:Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x. But we are told that one of these individual works is 15hrs. hence, possible scenarios, if (1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40 Hence Answer is D 192 which can not be any of these. #### D QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)35 B)45 C)25 D)15 E)55 SOLUTION:A : B : C =10×7:12×5:15×3 =2×7:12×1:3×3 =14:12:9 Amount that C should pay =175×9/35=5×9=45 Answer is B. #### B QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01$330=$333.30. The answer is D. #### D QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: options: A)30 B)28 C)24 D)20 E)35 SOLUTION:Product of two nos = product of HCF and LCM Let one number = x => 25 * x = 5 * 150 x=5150/25=30 ANSWER A #### A QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)100 = 25% ANSWER:A #### A QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000? options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000 SOLUTION:Saving = (45-30)% of 48000 = 7200. Answer:D #### D QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 = options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 22^7 we would have: sum=9(22^7)=182^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C. Answer: C #### C QUESTION:Find 30 % of 240 options: A)72 B)94 C)86 D)74 E)110 SOLUTION:We know that R % of m is equal to R/100 × m. So, we have 30 % of 240 30/100 × 240 = 72 Answer:A #### A QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good? options: A)7/21 B)10/21 C)9/21 D)8/21 E)5/21 SOLUTION:Required probability = (5C2 . 5C2)/10C4 = (10 * 10)/210 = 10/21 Answer:B #### B QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Let the number of men be m and so the number of women = 15-m Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start. Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days). Let the total work be 360 units (LCM of 180 and 120). 1 man does 360/120 = 3 units per day 1 woman does 360/180 = 2 units per day Based on above facts, Total work by men + women in these 17 days = 360 units m93 + (15-m)62 = 360, 27m + 180 -12m = 360, Solving m=12. Num of men = 12 and number of women = 15-12 = 3 ANSWER:C #### C QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63 SOLUTION:Required probability = 1 - 1/126 = 125/126 ANSWER:C #### C QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than SOLUTION:Correct answer is (A). This year, the price of a tree is price1=P/N. If this price increases by 50% it becomes price2=P/N1.50 Then with P dollars, you can grow P/price2 tress i.e. P/(P/N1.50) i.e. N/1.5 i.e. .67% less* A #### A QUESTION:Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months. options: A)Rs. 9009 B)Rs. 9008 C)Rs. 9002 D)Rs. 9202 E)Rs. 9001 SOLUTION:Explanation: P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years Therefore, S.I = (PRT)/100 = (78000* 77/5 * ¾ * 1/100) = Rs. 9009 ANSWER: A #### A QUESTION:Find the one which does not belong to that group ? options: A)237 B)232 C)223 D)426 E)111 SOLUTION:Explanation: 525 => 5 52, 39 => 3 32, 24 => 2 22, 636 => 6 62. The above pattern is not followed in 426. Answer: D #### D QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)14 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m. Answer C #### C QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average? options: A)69 B)70 C)71 D)72 E)75 SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D #### D QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. options: A)5113 B)5117 C)5120 D)8119 E)10115 SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year. If x = initial number of trees = 5120 Year 1 = 5/4x Year 2 = (5/4)(5/4)x Year 3 = (5/4)(5/4)(5/4)x Year 4 = (5/4)(5/4)(5/4)(5/4)x Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500 Hence, correct answer = C #### C QUESTION:David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going six times as fast. His new time compared with the old time was: options: A)twice as much B)three times as much C)the same D)half as much E)a fourth as much SOLUTION:Let t be the time of the first trip. On the later trip, David can travel 300 miles in time t. The trip of 75 miles takes t/4. The answer is E. #### E QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? options: A)26 B)30 C)34 D)38 E)42 SOLUTION:The first number is 22 = 16+6(1). We can continue adding 6 to make a list: 22, 28, 34,... The last number is 196 = 16+6(30) There are 30 numbers in the list. The answer is B. #### B QUESTION:In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks : options: A)300 B)350 C)400 D)450 E)550 SOLUTION:total marks:1500 for three exams 70% of 1500=1050 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =1050 X=550 ANSWER:E #### E QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7? options: A)35 B)16 C)17 D)can’t be determined E)None of these SOLUTION:Answer C Solution In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is (770-210/35)+ 1 = 17 Hence option C #### C QUESTION:John bought 9.25m of cloth for $397.75. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)43 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $397.75 Cost per metre = 397.75 ÷ 9.25 The cost of the cloth per metre = $ 43 Answers: E #### E QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:A reward of $1400 was divided among a group of 36 rescue workers such that each male in the group received $50. How much did each of the 16 females receive? options: A)$10 B)$12.50 C)$25 D)$37.50 E)$50 SOLUTION:x = amount each female received amount each male received = 50 number of females = 16 number of males = 36 - 16 = 20 total to males = 20(50) = 1000 total to females = 16x reward = total to males + total to females 1400 = 1000 + 16x 1400 - 1000 = 16x 400 = 16x 25 = x Answer: C #### C QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers? I. LCM : 24; HCF : 6 II. LCM : 18; HCF : 8 III. LCM : 16; HCF : 9 options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III SOLUTION:We need to keep two things in mind here: 1. Product of two numbers = LCMHCF 2. LCM should be a multiple of HCF Only Statement I follows these two rules. Correct Option A #### A QUESTION:The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output? options: A)20% B)27% C)30% D)32% E)79% SOLUTION:The original output increases by 15% and then 20%. Total % change = a + b + ab/100 Total % change = 15 + 20 + 1520/100 = 38% Now, you want to change it to 0, so, 0 = 38 + x + 38x/100 x = -38(100)/138 = 27% approximately Answer is B #### B QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 3200 = 400.Answer: D #### D QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C? options: A)3377 B)2899 C)5000 D)2778 E)1991 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 400 C's capital = 300001/6 = 5000 Answer: C #### C QUESTION:Find the simple interest on Rs.620 for 10 months at 10 paisa per month? options: A)277 B)620 C)640 D)678 E)121 SOLUTION:I = (6201010)/100 = 620 Answer: B #### B QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ? options: A)64 B)1/8 C)1 D)4 E)1/64 SOLUTION:Say r=2 => V1 = 1/16 when r=1; V2 = 1/4 V2 = 4V1. Answer : D #### D QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:What will be the product of (50-1)(50-2)(50-3)..............(50-99)(50-100)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:How many times in a day, the hands of a clock are straight? options: A)22 B)44 C)48 D)24 E)36 SOLUTION:The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 'o clock only. Hence the hands point in the opposite directions 22 times in a day. The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 o'clock). Hence the hands coincide 22 times in a day. So In 24 hours, the hands come in opposite direction or coincide 44 times. This is already given as a formula and it's is better to learn the answer by heart as 44 which can save time in competitive exams.(However you should know the theory behind). Answer: Option B #### B QUESTION:The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability W that exactly two visitors will buy a pack of candy? options: A)0.343 B)0.147 C)0.189 D)0.063 E)0.027 SOLUTION:3C2 (3/10)^2 * 7/10 = 3 * 9/100 * 7/10 = 189/1000 = 0.189=W Answer - C #### C QUESTION:In an election contested by two parties, Party ADMK secured 24% of the total votes more than Party DMK. If party DMK got 266,000 votes, by how many votes did it lose the election? options: A)34,000 B)56,000 C)164,000 D)168,000 E)200,000 SOLUTION:ADMK + DMK = 100 ---- (1) ADMK - DMK = 24 ---- (2) Solving (1) and (2) ADMK = 62% and DMK = 38% 38% of Total = 266000 Total = 700000 ADMK = 434000 Difference = 434000 - 266000 = 168000 Answer: D #### D QUESTION:Find a sum for first 12 prime no's from number series? options: A)190 B)178 C)197 D)189 E)100 SOLUTION:Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197 Note: 1 is not a prime number Option C #### C QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)7.5% B)8% C)9.7% D)10% E)None of these SOLUTION:By investing Rs. 1552, income = Rs. 128 By investing Rs. 97, income = Rs. (128/1552 * 97) = Rs. 8 Dividend = 8% Answer = B #### B QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:Find the odd man out 864, 420, 200, 96, 40, 16, 6 options: A)420 B)200 C)96 D)40 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. ANSWER:C #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 34? options: A)3 B)4 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 34m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 3 more to make it 34m + 34 Answer - A #### A QUESTION:If a - b =4 and a2+b2=52 , find the value of ab. options: A)8 B)26 C)18 D)42 E)36 SOLUTION:Explanation: We know 2ab=(a2+b2)âˆ’(aâˆ’b)2 2ab=52âˆ’16=36 =>ab=18 Option C #### C QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=2726^2 The answer is C. #### C QUESTION:If x + \| x \| = 0, which of the following must be true? options: A)x > 0 B)x≥0 C)x < 0 D)x≤0 E)x = 0 SOLUTION:Manipulate the equations: x + \| x \| = 0 \|x\| = -x -x > 0 OR -x = 0 This means x could be 0 or x is less than 0. D. x≤0 E. x=0 Answer: D #### D QUESTION:The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number? options: A)40 B)45 C)55 D)45 E)50 SOLUTION:a1 = 120/3 = 40 a2 = a1 -5 = 35 sum of second list = 353 = 105 therefore the number = 105 -60 = 45 D #### D QUESTION:The following sets each have a mean of 10 and the standard deviations are given in variable form. Set I = {6, 6, 6, 14, 14, 14}, standard deviation = P Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q Set III = {7, 8, 9, 11, 12, 13}, standard deviation = R Rank these three standard deviations from least to greatest. options: A)P, Q, R B)P, R, Q C)Q, P, R D)Q, R, P E)R, Q, P SOLUTION:SD is minimum when the terms are closer to the mean. In set 2, we have all terms equal to mean. hence, its SD is 0.(The Lowest) Comparing Set 1 and Set 3, Set 3 has terms more closer to mean than set 1. hence, Set 1 Sd is the highest. So, Answer is D #### D QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x1/10 + Nx1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted? options: A)8 B)5 C)15 D)22 E)6 SOLUTION:Let the two numbers be 6x and 5x. Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k. (6x - k) / (5x - k) = 5/4 => 24x - 4k = 25x - 5k => k = x. 6x - 5x = 5 => x = 5 k = x = 5. Answer:B #### B QUESTION:Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? options: A)$760 B)$750 C)$810 D)$800 E)$780 SOLUTION:50 pages typed 1x 30 pages typed 2x (original + one revision) 20 pages typed 3x (original + two revisions) 50(5)+30(5+4)+20(5+4+4)=250+270+260=780 Answer - E #### E QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:4,25,49,121,169,289, options: A)361 B)169 C)189 D)209 E)219 SOLUTION:19^2= 361 because follow sequence of square of the prime numbers ANSWER:A #### A QUESTION:A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours? options: A)48/75 B)20/75 C)27/75 D)28/75 E)16/75 SOLUTION:Number of questions A can answer per hour: 7 Number of questions B can answer per hour: 5 Number of questions A and B can answer per hour: 7+5=12 Number of questions A and B can answer in 4 hours: 4x12=48 Fraction of the study guide that is incomplete = 1-48/75=27/75 Answer is C #### C QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ? options: A)24 B)25 C)26 D)27 E)29 SOLUTION:x/2y=3/2 =>x=6y/2=3y =>(7x+8y)/(x-2y)=((7(3y))+8y)/(3y-2y) =>29y/y=29 ANSWER:E #### E QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ? options: A)50 meter B)100 meter C)220 meter D)120 meter E)350 meter SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes = 1/60∗6=1/10=100meters So distance between them after 6 minutes = 450 - 100 = 350 meters Option E #### E QUESTION:A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? options: A)3.75 days B)3.99 days C)2.67 days D)2.98 days E)2.44 days SOLUTION:1/4 + 1/8 = 3/8 8/3 = 2.67 days Answer: C #### C QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:If one cat eats 1.5 rats in 1.5 days, then in howmany days 3 cats will eat 3 rats?? options: A)1 Day B)2 Days C)3 Days D)4 Days E)5 Days SOLUTION:1Cat ------ 3/2 Rat --------- 3/2 Days 1 Cat ------(3/2)2 Rat -----(3/2)2 Days (Rat doubled, days doubled) 13 Cat----- 3 Rat -----------3/3=1 Day (Cat3 , Same rat , Days/3 ) ANSWER:A #### A QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:14 To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible. 75-yes 72 -yes 69 and 66 -no 63 - yes 60 -no 57, 54, and 51 -yes 48 - no 45 and 42 - yes 39 - no 36 - yes 33 and 30 - no 27, 24, and 21 - yes 18 -no 15 and 12 yes Correct answer is E. #### E QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West options: A)I,II only B)II,III only C)II only D)I and III only E)III only SOLUTION:It's evident if we make a diagram for the Movement of N respect to M. From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range. Thus it can only move north or west or anything in that curve. Answer : D #### D QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? options: A)8300 B)14500 C)7700 D)13000 E)5900 SOLUTION:Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 #### C QUESTION:If x^2+4x+3 is odd, then which one of the following could be the value of x. options: A)3 B)4 C)5 D)6 E)9 SOLUTION:for any x, 4x+3->odd so x^2 should be even, means x should be even; only ans we have 4 as even. ANSWER:B #### B QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? options: A)2100 B)1800 C)1245 D)3210 E)4521 SOLUTION:5 subjects can be arranged in 6 periods in 6P5 ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements = 6P5× 5C1 /2!=1800 Ans: B #### B QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 512 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (410/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (1010/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (510)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (210/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B <<<Examples ends QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? options: A)25 B)30 C)45 D)20 E)50 SOLUTION:6p2 = 6 x 5 = 30 B) #### B QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is? options: A)8 kmph B)9 kmph C)2 kmph D)4 kmph E)1 kmph SOLUTION:DS = 16 US = 14 S = ? S = (16 - 2)/2 = 2 kmph Answer:C #### C QUESTION:A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)120 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (9 - 8) = 1 km/hr. Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m. .'. Distance between the criminal and policeman = (265 - 50) m = 215 m. Answer : E #### E QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)205 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 * 8 * 4) = 160. Therefore, 160 * 2.40 + x * 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER:B #### B QUESTION:B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement? K9D 2$M JUR ? options: A)Î´KW B)Î´K5 C)Î´56 D)Î´W6 E)None of these SOLUTION:Explanation: K +6 2 +6 J +6 Î´ 9 +6 S +6 U +6 5 D +6 M +6 R +6 W ANSWER IS E #### E QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)4 B)5 C)34 D)7 E)9 SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 Answer:D #### D QUESTION:In a bag, there are 4 white, 1 brown and 5 red pens. One pen is picked up randomly. What is the probability that it is neither white nor red? options: A)1/5 B)1/10 C)1/2 D)1/3 E)1/4 SOLUTION:Explanation : Neither white nor red means the pen drawn is brown. Total number of outcomes = (4+1+5) = 10. Number of Favourable outcomes = 1 = Number of brown pens. Hence, Probability of the event = 1/10. Answer : B #### B QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 2460 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year. options: A)62.5 B)150 C)225 D)112.5 E)212.5 SOLUTION:Explanation : The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest Simple interest that he needs to pay = PRT/100=5000×5×2/100=500 He also lends it at 6 1⁄4% p.a for 2 years Simple interest that he gets = PRT/100=5000×25/4×2/100=625 His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125 His overall gain in 1 year = 125/2 = Rs.62.5 Answer : Option A #### A QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is: options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons SOLUTION:Explanation: Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying] Volume of {\color{Black} \frac{1}{40}} part = 3 gallons Volume of whole = (3 x 40) gallons = 120 gallons. Answer: C #### C QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B. options: A)16 years B)24 years C)8 years D)12 years E)18 years SOLUTION:let present age of A be A let presennt age of B be B in 6 yrs A+6:B+6=3(B-4):B=6 ie A+6=3(B-4) but given A=B+6 so B+6+6=3(B-4) B=12 ANSWER:D #### D QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/1233 = 33 cents. Answer: C. #### C QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who speak both the languages? options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32 SOLUTION:let the student who speaks tamil-x let the student who speaks telugu-y as (xuy)-(xny)=total 30+30-(xny)=50 =10 B) #### B QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 12=45,0008 1:1 Madhu's share=1/260,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 11030=3,300 copies. Answer: C. #### C QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”? options: A)5 B)10 C)16 D)20 E)9 SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum). E #### E QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? options: A)65 B)21 C)78 D)67 E)51 SOLUTION:Let the total number of workers be x. Then, 8000x = (12000 7) + 6000(x - 7) = 2000x = 42000 = x = 21. Answer: B #### B QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel? options: A)400 B)450 C)500 D)550 E)600 SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour. The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours. The answer is A. #### A QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full. After 28 days, the dish was one quarter full. After 27 days, the dish was one eighth full. After 26 days, the dish was one sixteenth full. After 25 days, the dish was 1/32 full. After 24 days, the dish was 1/64 full. The answer is C. #### C QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)277 B)277 C)120 D)882 E)272 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true? I. c is even II. ab is even III. ab > 0 options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above. II only.letter B #### B QUESTION:A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article? options: A)$25 B)$12.50 C)$29.65 D)$35.95 E)$45.62 SOLUTION:S.P. of each of the article = 50/2 = $25 Let M.P = $x 50% of x = 25 x = 25.5 =$12.50 Answer is B #### B QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r1^2 . h1/r2^2. h2 => 1/15 = (1)^2h1/(2)^2h2 => h1/h2 = 3/5 i.e. h1 : h2 = 3:5 Answer: A #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these SOLUTION:Explanation : Total numbers = 70 Total numbers in 1 to 70 which has 1 in the unit digit = 7 Total numbers in 1 to 70 which has 9 in the unit digit = 7 Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14 Required percentage = (14/70) × 100 = 140/7 = 20% Answer : Option B #### B QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)230 B)244 C)245 D)238 E)235 SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m. Answer: Option E #### E QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest? options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33% SOLUTION:T = 30 years P= principle amount = x A = total amount = 2x SI = simple interest = A-P = 2x-x = x R = 100SI/PT = 100x/30x =3.33% Answer is B #### B QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)70 B)80 C)90 D)50 E)60 SOLUTION:Solution Let x be the original price. x - 20 = 50 x - 20 + 20 = 50 + 20 x + 0 = 70 x = 70 Answer A #### A QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 8011/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be? options: A)1 : 9 B)1 : 3 C)1 : 2 D)1 : 1 E)3 : 3 SOLUTION:Suppose age of Laxmi is x years. The difference of their ages \inline \therefore Ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 Answer:B #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer B #### B QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:9log9(5) = ? options: A)1 B)2 C)3 D)5 E)8 SOLUTION:Exponential and log functions are inverse of each other. Hence aloga(x) = x , for all x real and positive. and therefore 9log9(5) = 5 correct answer D #### D QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)P(B) = 2/5 4/7 = 8/35 ANSWER IS A #### A QUESTION:A large research project was scheduled over the course of a 25-month period, and a budget of $100,000 was allotted for the course of the entire project. After 9 months, the project had spent $35,800. Was the project at this point over budget or under budget, and by how much? options: A)under, $200 B)under, $1200 C)under, $7000 D)over $1800 E)over $5800 SOLUTION:cost per month = 100,000/25 = 4,000. Now, multiply by nine months: 9($4000) = $36,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget. $36,000 â€“ #35,800 = $200 Answer = (A) #### A QUESTION:A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? options: A)0.09 B)0.15 C)0.54 D)0.75 E)0.91 SOLUTION:According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 5)/60 = 45/60 = 0.75. Answer: D. #### D QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (12523+16225)/125+162 = 24 years Answer is D #### D QUESTION:After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article? options: A)12000 B)15000 C)1200 D)1000 E)10000 SOLUTION:CP (44/100) =4400 CP= 100 * 100 => CP = 10000 Answer:E #### E QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ? options: A)10.2 Days B)15.2 Days C)16.2 Days D)18 Days E)20 Days SOLUTION:Let us assume that the work is laying 40 bricks. Jane = 4 bricks per day Ashley = 1 brick per day Together = 5 bricks per day Let's say first 8 days Ashley works alone, No of bricks = 8 Last 4 days Jane works alone, No. of bricks = 16 Remaining bricks = 40 - 24= 16 So together, they would take 16/5 = 3.2 Total no. of days = 8 + 4 + 3.2 = 15.2 Answer is B #### B QUESTION:How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) options: A)37×260^2 B)36×260^2 C)36×270^2 D)10^2×26^3 E)10^3×26^2 SOLUTION:We are given that License plate could be either of the form DDLLL or DDDLL Now, every D could be filled in 10 ways and every L could be filled in 26 ways. or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1) Number of ways for DDDLL = 10 10102626 --(2) Total ways = (1) + (2) = $36×260^2$ Answer s B. #### B QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14Ã—30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—14) Ratio of the capacity of a man and woman =1/(15Ã—14) : 1/(14Ã—30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x) Solve the equation. 262.85(32)+3,104.35x = 1,399.45(32 + x) 8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x 8,411.2 + 1,704.9x = 44,782.4 1,704.9x = 36,371.2 x ≈ 21.3 Answer is B. #### B QUESTION:What is the sum of all the prime numbers greater than 30 but less than 50? options: A)126 B)199 C)198 D)188 E)122 SOLUTION:Required sum = (31 + 37 + 41 + 43 + 47) = 199 Note: 1 is not a prime number Answer B #### B QUESTION:Find the area of a parallelogram with base 24 cm and height 16 cm? options: A)198 cm2 B)384 cm2 C)279 cm2 D)128 cm2 E)297 cm2 SOLUTION:Area of a parallelogram = base * height = 24 * 16 = 384 cm2 Answer:B #### B QUESTION:Find the value of a from (15)^2 x 8^3 Ã· 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 Ã· 256 = a = 225 x 512 Ã· 256 = 450 E #### E QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)? options: A)190 B)200 C)210 D)220 E)230 SOLUTION:Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 140 = 25(x / 15) 10x = 2100 x = 210 meters The answer is C. #### C QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1800 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 9x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700. Hence, (R - p) = (2700 - 900) = 1800 Answer : A #### A QUESTION:A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms? options: A) 6 B) 4.8 C) 2.5 D) 2 E) 1 SOLUTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms? (A) 6 (B) 4.8 (C) 2.5 (D) 2 (E) 1 If A is the answer, then the question means that the concentration of water the newt day became 96%. Out of 12 kilograms 98%, or 11.76 kilograms was water and 0.24 kilograms was non-water. The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.24 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x0.04=0.24 --> x=6 kilograms. Answer: A. #### A QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2 SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec.Answer: B #### B QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 70 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/8,100 C)7/48,000 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 70/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=70/8001/600=7/48,000. Answer: C. #### C QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? options: A)20 B)98 C)66 D)54 E)12 SOLUTION:Let C.P. of each article be Re. 1. Then, C.P. of 50 articles = Rs. 50; S.P. of 50 articles = Rs. 40. Loss % = 10/50 100 = 20% Answer: A #### A QUESTION:From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed? options: A)720 B)625 C)30 D)960 E)255 SOLUTION:Potential combinations of 4 numbers that will yield positive product ++++ 4C6 ---- 4C6 ++-- 2C62C6 4C6 + 4C6 + 2C62C6 F=15 +15 + 1515 = 255=E #### E QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D QUESTION:20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)7/30 B)3/14 C)9/38 D)4/21 E)5/26 SOLUTION:P(1st ball is even) = 10/20 P(2nd ball is also even) = 9/19 P(both balls are even) = 10/20 9/19 = 9/38 The answer is C. #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:What is the next number in the given series 4,18,100,294,....? options: A)1210 B)1220 C)1230 D)1240 E)1250 SOLUTION:The given series is difference of cubes and squares of consecutive prime numbers. 222-22=4, 333-33=18, 555-55=100, 777-77=294, 111111-1111=1210 ANSWER:A #### A QUESTION:Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance. What is the distance traveled by each tyre? options: A)75000 B)80000 C)90000 D)67800 E)50000 SOLUTION:B 80,000. The distance traveled by each tyre: 4/5 1, 00, 000km = 80,000 km. #### B QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)187 B)180 C)289 D)216 E)279 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B #### B QUESTION:If $25,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years? options: A) compounding daily B) compounding quarterly C) compounding monthly D) compounding annually E) All four of these would produce the same total SOLUTION:This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest. This process will be repeated every day till the amount matures Compounding annually will give least returns Answer = A #### A QUESTION:By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: options: A)Rs. 2,600 B)Rs. 2,700 C)Rs. 2,800 D)Rs. 3000 E)NOne SOLUTION:Solution: Let Cost Price was X. X + 14% of X = 2850 X + 14X/100 = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = 100/1142850 = Rs. 2500; SP for a profit of 8% = 108/1002500 = Rs. 2700. Answer: Option B #### B QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:How many terminating zeroes T does 200! have? options: A) 40 B) 48 C) 49 D) 55 E) 64 SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C QUESTION:Which of the following points falls outside of the region defined by 2y≤6x−10? options: A)(5, 1) B)(3, -8) C)(2, 0) D)(0, -2) E)(0, -14) SOLUTION:Equation given is 2y<=6x-10 Simplifying this; y<=3x-5 Plug in the values provided in the options, A. 1<=10 B. -8<=4 C. 0<=1 D.-2<=-5 E. -14<=-12 Option C is the answer. #### C QUESTION:In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? options: A)25 B)43 C)64 D)78 E)98 SOLUTION:Ans.(C) Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways #### C QUESTION:The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches? options: A)25 B)27 C)30 D)35 E)36 SOLUTION:Average in 5 matches = (230 + 340)/2+3 = 60+120 / 5 = 180/5 = 36 Answer is E #### E QUESTION:In a manufacturing plant, it takes 48 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:the choices give away the answer.. 48 machines take 4 hours to fill 8 standard orders.. in next eq we are doubling the machines from 48 to 72, but the work is not doubling(only 1 1/2 times), = 448/7212/8 =4 Ans A #### A QUESTION:Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is options: A)42 B)36 C)28 D)20 E)24 SOLUTION:Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10×36/10 km/hr = 36 km/hr Answer: Option B #### B QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double (5,5)? options: A)1/24 B)1/36 C)1/12 D)1/18 E)1/3! SOLUTION:total no. in two dice (1,1) ,(2,2) .....(6,) Total number of events= 66 Total events of getting same pair(5,5) = 6 Probability= 6/66= 1/6=1/3! E #### E QUESTION:161?85?65?89=100 then use + or - in place of ? and take + as m,- as n then find value of m-n options: A)3 B)-1 C)1 D)-3 E)2 SOLUTION:161-85-65+89=100 so m=1, n=2 => (m-n)=-1 ANSWER:B #### B QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)8:8 B)9:8 C)9:6 D)9:5 E)9:13 SOLUTION:(36 + 66): (6.512) 54:78 => 9:13 Answer: E #### E QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C? options: A)3√2 B)5 C)5√2 D)√(67) E)√(73) SOLUTION:height of cone=3 radius of base=4 so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle Hence the distance is sqrt(3^2+4^2)= 5 ANSWER:B #### B QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:if a no. is divided by 342 then remainder is 47.then if that no. is divided by 18 then what will be the remainder? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:let quotient be k if that no. is divided by 342 and remainder 47. that no.= 342k+47 = (1819k)+(182)+11 =18(19k+2)+11 so remainder when divided by 18=11 answer A #### A QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 16.0 grams 4:00 P.M. x grams 7:00 P.M. 20.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.? options: A)12.0 B)18.1 C)12.2 D)12.3 E)18.0 SOLUTION:The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours. Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm: Fractional increase from 1 PM to 4 PM = X / 16.0 Fractional increase from 4 PM to 7 PM = 20.4 / X X \ 16 = 20.4 \ X X^2 = 20.4 16 X = 18 answer : E #### E QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1x X=11.81% Answer D) #### D QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock? options: A)60 miles B)70 miles C)90 miles D)120 miles E)400 miles SOLUTION:Answer = B. 70 miles Relational speed = 130 - 100 = 30 miles per hour In 3 hours, difference = 30 3 = 90 miles Fast train trailing 20 miles, so effective difference = 90 - 20 = 70 miles #### B QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y? options: A)1/7 B)14 C)15 D)52/7 E)60/7 SOLUTION:3x-y=6 ...equation 1 x+2y=8 ...equation 2 adding both the equations 4x+y=14 correct answer option B #### B QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N? options: A)107 B)331 C)511 D)691 E)871 SOLUTION:N/P=10 7/P= 20P+7 N/(P+2)=15 2/(P+2)=15P+30+2 solving these two equations we get P=5 N= 107 answer is A. #### A QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)50 m B)60 m C)65 m D)75 m E)80 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? options: A)6 B)9 C)12 D)15 E)18 SOLUTION:2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 3024 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 3024 / 80 oxen = 9 days The answer is B. #### B QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate? options: A)69 B)70 C)71 D)72 E)73 SOLUTION:number of ways = 23!3! = 72 Answer is D #### D QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)42.5% E)Can't be calculated SOLUTION:The owner buys 100 kg but actually gets 114kg; The owner sells 100 kg but actually gives 80kg; Profit: (114-80)/80100=~42.5% Answer: D. #### D QUESTION:The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the width of the rectangle? options: A)10 cm B)12 cm C)14 cm D)16 cm E)18 cm SOLUTION:2L+2W = 5W L = 3W/2 WL = 150 3W^2/2 = 150 W^2 = 100 W = 10 The answer is A. #### A QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:A- B = 120 Miles B - C = 60 Miles Avg Speed = 45 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 45 = 180/4t t = 60 B-C = 60 mph Answer E #### E QUESTION:How many possible integer values are there for x if \|4x - 3\| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: \|4x-3\| < 6 let 4x=a therefore we have \|a-3\| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool? options: A)4 2/3 B)9 1/4 C)9 1/3 D)8 3/4 E)10 1/2 SOLUTION:The answer is D 7 pumps take 5 hours. 1 Pump will take 57 hours . Hence 4 pumps will take (57)/4 = 8 75/100 = 8 3/4 hours #### D QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5700 = Rs.3500 ANSWER:D #### D QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 > b^2 > c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=1, b=2, and c=3. None of the options must be true. Answer: A. #### A QUESTION:The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9300 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7500 Ã— 100/90 Ã— 100/90 = 9259 A) #### A QUESTION:Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long? options: A)1/6 B)1/4 C)2/3 D)3/4 E)11/12 SOLUTION:So please: Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/31/4=11/12. Answer: E. #### E QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/19 B)1/20 C)1/23 D)2/17 E)1/17 SOLUTION:(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 B) #### B <<<Examples ends QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h? options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these SOLUTION:Explanation: Let the length of the train be L. Then, => (450 + L)/42 = (650+L)/50. => L= 600 m. Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25(18/5) = 90 Km /hr. ANSWER IS A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the sides of a triangle are 52 cm, 48 cm and 20 cm, what is its area? options: A)480 cm2 B)765 cm2 C)216 cm2 D)197 cm2 E)275 cm2 SOLUTION:The triangle with sides 52 cm, 48 cm and 20 cm is right angled, where the hypotenuse is 52 cm. Area of the triangle = 1/2 * 48 * 20 = 480 cm2 Answer: A #### A QUESTION:If the area of a circle is 81pi square feet, find its circumference. options: A)48 B)38 C)51 D)92 E)18 SOLUTION:The area is given by pi pi × r × r = 81 pi r × r = 81 ; hence r = 81 feet The circumference is given by 2 × pi × r = 2 × pi × 9 = 18 pi feet correct answer is E) 18 #### E QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:Tough and Tricky questions: Work/Rate Problems. If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)8 E)9/7 SOLUTION:80 Workers = 3 hours then, 1 Worker = 380 Hours 30 Workers = (380) /(30) = 8 Answer.D #### D QUESTION:Which number should replace both the asterisks in (* /18) x (/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 15 = 75 ways. Answer: A #### A QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum? options: A)8 B)2 C)10 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150 15000[(1 + R/100)2 - 1 - 2R/100] = 150 15000[(100 + R)2 - 10000 - 200R]/10000 = 150 R2 = (159 * 2)/3 = 100 => R = 10 Rate = 10% Answer: Option C #### C QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:What is the value of: -9^7 + 9^9 ? options: A) 9^2 B) -18^16 C) 63(9^7) D) -80(9^7) E) 80(9^7) SOLUTION:-9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E. #### E QUESTION:How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:A is followed by B means : A comes first,B comes next A preceded by B means : B comes first, A comes next The sets which satisfy the condition is: 5 3 8 1 3 8 7 3 4 ANSWER:C #### C QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None SOLUTION:Sol. Man's rate in still in water = (12- 2) km / hr = 10km / hr. Man's rate against the current = (10 - 2) km / hr = 8 km / hr. Answer A #### A QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is options: A)100 B)250 C)260 D)416 E)None of these SOLUTION:Explanation: Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 × 32 = 416. Answer: D #### D QUESTION:The sum of three consecutive integers is 102. Find the lowest of the three? options: A)18 B)67 C)98 D)33 E)26 SOLUTION:Three consecutive numbers can be taken as (P - 1), P, (P + 1). So, (P - 1) + P + (P + 1) = 102 3P = 102 => P = 34. The lowest of the three = (P - 1) = 34 - 1 = 33. Answer: D #### D QUESTION:In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing? options: A)2 B)4 C)12 D)0 E)13 SOLUTION:E 13 This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next. #### E QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d? options: A) 16% B) 32% C) 48% D) 84% E) 92% SOLUTION:16% ________________________________________________ a+d 34% ________________________________________________ a 34% ________________________________________________ a-d 16% since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a. thus 16% lie below a-d and 16% lie above a+d now below a+d = 16+34+34 = 84% hence D #### D QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)3000 - (1/10)%3000 = 300 - (1/1000)3000 = 300 - 3 = 297 The answer is B. #### B QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2 SOLUTION:(y^2 − xy)/x=y-x => y^2 − xy = xy -x^2 => x^2 - 2xy + y^2 = 0 => (x-y)^2 = 0 Answer E #### E QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 43/32 = 2:1''Answer: 2:1; #### A QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y? options: A)6 B)3 C)4 D)5 E)7 SOLUTION:lets start from z, as per the question stem z + 5 + 7 = 16 -->> z= 4 similarly, y + 4 + 5 = 7 --> y = -2 similarly,, x + -2 + 4 = 5 --> x = 3 hence , x-y = 3+2 = 5 ANSWER:D #### D QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)891 E)1,001 SOLUTION:James = (0.5/100)2000 = 10 Votes to win = (45/100)Total Votes +1 = (45/100)2000 +1 = 901 Remaining Voted needed to win election = 901 - 10 = 891 Answer: option D #### D QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7100/83.3 =20% ANSWER:C #### C QUESTION:The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? options: A)4/19 B)1/9 C)2/3 D)1 1/9 E)2 1/9 SOLUTION:Total bought = 4/19+2/13 left part 4/26--->2/13 so used part 4/19+2/13-2/13=4/19 ANSWER:A #### A QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? options: A)2/3 B)1 C)3/4 D)3/2 E)2 SOLUTION:Rate of A = 1/2 tank/hour; Rate of B = 1/3 tank/hour; Rate of C = 1/6 tank/hour. Combined rate when A and B are used to pump-out water, while C is used to fill water into the tank is 1/2+1/3-1/6=2/3 tank hour. So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the half-full tank half of that time would be needed: 1/23/2=3/4 hours. Answer: C. #### C QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:If 5 < x < 11 and y = x + 7, what is the greatest possible integer value of x + y? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:x+y = x+x+7 = 2x+7 We need to maximize this value and it needs to be an integer. 2x is an integer when the decimal of x is .0 or .5 The largest such value is 10.5 Then x+y = 10.5 + 17.5 = 28. The answer is C. #### C QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100? options: A)33 B)67 C)25 D)66 E)81 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (100 - 75) = 25 points to C. Answer: C #### C QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9 SOLUTION:Speed of Peter = x/9 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x Option D The values 100m and 200m have no role to play here and are just given to confuse you. #### D QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speedâˆ—Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)51 23/27% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27% Answer B #### B QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)? options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k) SOLUTION:f(k) = k^3 /16 f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k). So answer is B. #### B QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 â€“ 4xy (x- y)2 = 625 â€“ 576 => (x â€“ y) = 7 ANSWER: A #### A QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:The greatest common factor of two positive integers is P. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other? options: A)PY⁄Z B)XZ + YZ C)X⁄Z + Y D)X + Y⁄Z E)X + Z⁄Y SOLUTION:Say other integer is W Formula GCF(WZ)LCM(WZ) = WZ PY = WZ So W= PY/Z Answer A #### A QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in options: A)2 days B)1 day C)3 days D)5 days E)7 days SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. B) #### B QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre. options: A)Rs. 15,000 B)Rs. 15,500 C)Rs. 15,600 D)Rs. 20,625 E)None SOLUTION:Solution Area of the floor = (5.5 x 3.75)m² = 20.635m ² Cost of paying = Rs. (1000 x 20.625) = Rs.20625. Answer D #### D QUESTION:A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest? options: A)5% p.a. B)7.5% p.a. C)10% p.a. D)12.5% p.a. E)None of these SOLUTION:Explanation: Given: 800 = (P * R * 2) / 100 S.I. For 1 year = Rs. 400 Thus, (840 – 800) = S.I. on Rs. 400 for 1 year 40 = (400 * R * 1) / 100 R = 10% p.a. ANSWER C #### C QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg? options: A)4/7 B)5/6 C)5/9 D)4/8 E)3/8 SOLUTION:B 5/6 Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 #### B QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:If a fair die is rolled once, what is the probability that a 3 occurs on at least one roll? options: A)25/36 B)125/216 C)1/6 D)1/36 E)5/6 SOLUTION:Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N) Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6) = 1-5/6 = 1/6 5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities. C is thus the correct answer. #### C QUESTION:In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled? options: A)1200 B)1400 C)1600 D)1500 E)1540 SOLUTION:Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %) 20 % = 60 % - 40 % 20% -----> 280 (20×14 = 280 ) 100% -----> 1400 (100×14 = 1400) Option 'B' #### B QUESTION:Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer. options: A)115 × 8 ÷ 10 + 8 B)425 ÷ 17 × 4 C)36 × 5 ÷ 6 + 17 × 4 D)2(6) + √256 + 20 E)35 × 12 ÷ 14 + 14 × 5 SOLUTION:All others are equal to 100. But option (c) gives a value equal to 98. Answer C #### C QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joined them. How many days will they take to complete the remaining work? options: A)3days B)4days C)2days D)8days E)5days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 days work = 6/9 = 2/3 remaining work = 1 – 2/3 = 1/3 18 men's 1 days work = 18/108 = 1/6 1/6 work is done by them in 1 day therefore, 1/3 work is done by them in 6/3 = 2 days. ANSWER C 2days #### C QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area? options: A)2:1 B)3:1 C)4:1 D)6:1 E)8:1 SOLUTION:Let x be the length of the small cube's side. The total surface area of the small cube is 6x^2. The total surface area of the large cube is 6(2x)^2=24x^2. The ratio of surface areas is 4:1. The answer is C. #### C QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago? options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4 SOLUTION:3x-25/2x-25 = 4/3 Therefore x=-25 Age cannot be negative. Answer: D #### D QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=prt/100 Amount = SI+p = 4p (pr15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area? options: A)158 B)129 C)150 D)123 E)60 SOLUTION:1/2 * 12 * 10 = 60 Answer:E #### E QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? options: A)6 B)8 C)6 D)5 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer:B #### B QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+ SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers: L = 200 M = 10 N =20. So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans.. looking the the opion C to E, one can make out that they are incorrect, A. Out of which, i choose A. #### A QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)120 E)200 SOLUTION:6C34C2 =120=D #### D QUESTION:If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is options: A)Rs.48,000 B)Rs.45,000 C)Rs.30,000 D)Rs.50,000 E)None of the above SOLUTION:investment by B=(590000)/(4+5) =50000 ANSWER:D #### D QUESTION:If one-third of one-fourth of a number is 15, then three-tenth of that number is options: A)35 B)15 C)60 D)54 E)57 SOLUTION:Let the number be x. then 1/3 of ¼ of x=15 X=15x12=180 The required number=(3/10)180=54 ANSWER D 54 #### D QUESTION:In how many Q ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6666= 1296 ------(1) Total number of passwords in which no letter repeats = 6C44!= 1524=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)2789 B)2772 C)1991 D)6725 E)2099 SOLUTION:CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725. Answer: D #### D QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor? options: A)11 B)17 C)13 D)23 E)37 SOLUTION:let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27. now 242-15=227 =kx (k is an integer and 234 is divisble by x) similarly 698-27=671 = lx (l is an integer and 689 is divisible by x) adding both 698 and 242 = (227+671)+15+27 =x(k+l) + 42 when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37 hence E #### E QUESTION:P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P? options: A)80 B)70 C)85 D)90 E)95 SOLUTION:The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3. Since, they work together, the share of P = 6/13 * 195 = Rs.90 Answer: D #### D QUESTION:In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number Q of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85? options: A)144 B)189 C)234 D)279 E)309 SOLUTION:Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2. Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant. If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279. (10x+18x) < 85. 28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3. (45x+48x) = 93x. Max (93x) Q= 279. Answer is D. #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)18 days B)20 days C)24 days D)30 days E)32 days SOLUTION:2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days ANSWER:C #### C QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:Kunal electronic services assemble computers. Over a period of time the engineers made the following observation regarding the two vital components - the USB port and CD drive. The probability that USB port is defective is 0.1, that both the USB port and CD drive are defective is 0.02, while the probability that only the CD drive is defective is 0.03 . The probability that the USB port is defective when the CD drive has been found to be defective is? options: A)0.2 B)0.3 C)0.25 D)0.4 E)0.6 SOLUTION:Explanation : USB Defective USB OK Total CD Defective 0.02 0.03 (0.05) CD OK (0.08) (0.87) (0.95) Total 0.1 (0.9) The figures enclosed in brackets follow as conclusions. The probability that USB part is defective, when the CD drive is found to be defective is 0.02/0.02+0.03 = 2/5 = 0.40 Answer : D #### D QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was: options: A)10 years. B)14 years. C)17 years. D)16 years. E)12 years. SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22 Son's age 10 years back (22 - 10) = 12 years. ANSWER :E #### E QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)5:4 B)4:5 C)2:5 D)5:2 E)None of them SOLUTION:Let the third number be x. Then, first number = 120% of x = 120x/100 = 6x/5 Second number = 150% of x = 150x/100 = 3x/2 Therefore, Ratio of first two numbers = (6x/5 : 3x/2) = 12x : 15x = 4 : 5. Answer is B. #### B QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10? options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18 SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once. There are 66=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12. D #### D QUESTION:A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? options: A)4 sec B)6 sec C)7 sec D)3 sec E)2 sec SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 =6 sec. Answer:B #### B QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:If f(x) = -2x2 + 8x - 4, which of the follwoing is true? options: A)The maximum value of f(x) is -4. B)The graph of f opens upward. C)The graph of f has no x-intercept D)f is not a one to one function. E)The maximum value of f(x) is 4. SOLUTION:f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D correct answer D #### D QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x107)/(1002)) – ( (x125)/(1002)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/72/61/5=1/35. Ans E #### E QUESTION:A box contains 3 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors? options: A)1/2 B)3/5 C)7/12 D)2/3 E)7/10 SOLUTION:Total selection ways: 5C2=5!/2!3!=10 Selecting one blue chip out of two: 2C1=2!/1!1!=2 Selecting one red chip out of four: 3C1=3!/2!1!=3 Thus, (2C13C1)/5C2=(23)/10=6/10=3/5=B #### B QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7? options: A)35 B)16 C)17 D)can’t be determined E)None of these SOLUTION:Answer C Solution In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is (770-210/35)+ 1 = 17 Hence option C #### C QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3. options: A)27 B)26 C)28 D)25 E)24 SOLUTION:1/2(6+12)3=27 ANSWER:A #### A QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!2! or 43/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 375,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes? options: A)a) 500 B)b) 750 C)c) 1,000 D)d) 1,250 E)e) 1,500 SOLUTION:Since N = 2F, no of Florida zip codes (F) will be N/2. Since N = 4A, no of Arizona zip codes (A) will be N/4 Since N = (4/3)C, no of California zip codes (C) will be 3N/4 N + N/2 + N/4 + 3N/4 = 5N/2 = 250 N = 100 C = 3N/4 = 75 No of orders is 25% of 375,000 = 93,750 So required ratio = 93,750/75 =1,250 Answer D #### D QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^327 + 26^5. Answer: D. #### D QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = xx is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:Which of the following number is divisible by 24 ? options: A)22 B)24 C)26 D)27 E)28 SOLUTION:24 = 3 x8, where 3 and 8 co-prime. Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8. Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8. Consider option (D), Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3. Also, 736 is divisible by 8. 3125736 is divisible by (3 x 8), i.e., 24. B #### B QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is? options: A)187 B)169 C)152 D)178 E)175 SOLUTION:200(80/100)(95/100) = 152 Answer:C #### C QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel? options: A)400 B)450 C)500 D)550 E)600 SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour. The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours. The answer is A. #### A QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:Find the average of first 20 natural numbers? options: A)5.5 B)7.2 C)10.5 D)12.3 E)15.5 SOLUTION:Sum of first n natural numbers = n(n+1)/2 sum of first 20 natural numbers = 2021/2 =210 average = 210/20 = 10.5 Answer is C #### C QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? options: A)776 B)864 C)299 D)257 E)125 SOLUTION:W = 60% L = 40% 60% - 40% = 20% 20% -------- 288 60% -------- ? => 864 Answer:B #### B QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 34 = 12 Answer: C #### C QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: options: A)1.8h B)3h C)4h D)5h E)None of these SOLUTION:Explanation: Upstream speed = B-S Downstream speed = B + s B - S = 15/5 = 3 km/h Again B = 4S Therefore B - S = 3 = 3S => S = 1 and B = 4 km/h Therefore B + S = 5km/h Therefore, Time during downstream = 15/5 = 3h Answer: B #### B QUESTION:The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is: options: A)270 B)300 C)299 D)322 E)345 SOLUTION:the numbers are (18 x 11) and (18 x 15). Larger number = (18 x 15) = 270. ANSWER :A #### A QUESTION:If a, b, and c are positive numbers such that (a/(a+b))(10) + (b/(a+b))(20)=c and if a<b which of the following could be the value of c? options: A)10 B)12 C)15 D)18 E)30 SOLUTION:The answer is D. For any positive a and b, c is a number between 10 and 20. Since a < b, weight of 10 is inferior of weight of 20 -> c is > 15 -> 18 is the answer. #### D QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed. options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above SOLUTION:My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 57 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 #### D QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is: options: A)0 B)10 C)20 D)30 E)40 SOLUTION:You can calculate the LCM (10,14) = 70. After that you should check which of the possible X values will result in a number divisible by 70. The only possibility for this is 30 ( because 250 + 30 = 280 = 704) Answer D #### D QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a quarter of its new value. What is the stock's value at the end of Monday? options: A)X. B)3X/8. C)2X/3. D)X/3. E)X/4. SOLUTION:Stock value= X AT sunday end= x+.5X= 1.5 X On monday the value drop to 1/4rd of its value on sunday 1.5x/4= 3X/8 B is the answer #### B QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:A train 150 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)108 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [150/5] m/sec = [30 18/5] km/hr = 108 km/hr. Answer B #### B QUESTION:The perimeter of one face of a cube is 48 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 48/4 = 12 cm Volume = aaa = 121212 = 1728 cm cube Option E #### E QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.500 D)s.450 E)s.420 SOLUTION:SP = 700 Profit = 25% CP = (SP)[100/(100+P)] = 700 [100/125] = 560 Loss = 25% = 25% of 560 = Rs.140 SP = CP - Loss = 560 - 140 = Rs.420 ANSWER:E #### E QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:Sum of the local value and the face value of 4 in the numeral 153489216 is options: A)40004 B)4004 C)4000004 D)400004 E)44 SOLUTION:(Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 D #### D QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/4 %, then the amount invested at 11% was? options: A)12500 B)37500 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100) (9x + 1100000 - 11x) = 37000/4 = 925000 x = 87500 Sum invested at 9% = Rs. 87500 Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500. Answer: A #### A <<<Examples ends QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)12 greater B)12 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/6 * 480 =80 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 80-68 =12>>> therfore answer is 28 fewer B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years? options: A)100 B)120 C)200 D)220 E)264 SOLUTION:P = 240 R = 10% Required population of town = P(1 + R/100)^T = 240(1 + 10/100) = 240(11/10) = 264 Answer is E #### E QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day? options: A)10 B)15 C)20 D)25 E)None of them SOLUTION:Let the required number of days be x. More men, Less days (indirect proportion) Less hours per day, More days (indirect proportion) Men 18 : 15 Hours per day 8: 9 } : :16 : x (18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15 Hence, required number of days = 15. Answer is B. #### B QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q\|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q\|Q) = 3/51 P(A\|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A\|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q\|Q) P(A\|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:The H.C.F. of two numbers is 12 and their difference is 12. The numbers are : options: A)66, 78 B)70, 82 C)94, 106 D)84, 96 E)None of these SOLUTION:Explanation: Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96. ANSWER IS D #### D QUESTION:The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip? options: A)300/(x + y) B)600/(x + y) C)150/x + 150/y D)300/x + 300/y E)600/x + 600/y SOLUTION:Time taken to cover first half i.e 300 miles of a 600 mile trip = x time taken to cover the second half i.e 300 miles of a 600 mile trip = y Total time taken = x+y Average speed for the entire trip =total distance /total time =600/(x+y) Answer B #### B QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is options: A)28 B)H C)27 D)29 E)271 SOLUTION:Answer:B #### B QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 505/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 50018/250 = 36sec Answer is C #### C QUESTION:Tough and Tricky questions: Number Properties. If (z + 3)/6 is an integer, what is remainder when z is divided by 6? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:6/6=1 Ans B #### B QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)P +(1/4)Q = (3/8)P+(3/4)Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3. options: A)27 B)26 C)28 D)25 E)24 SOLUTION:1/2(6+12)3=27 ANSWER:A #### A QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 14.5 II. 15.3 III. 9.5 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+21.3 = 14.6 2 SD below mean = 12-21.3 = 9.4 14.5 and 9.5 lies in the range of 2SD from mean Answer: Option C #### C QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=66 = 36 (6^3)= 366 = .16 (6^4)= .166 = ..96 (6^5) = ..966 = ..76 (6^6) = ..766 = ...56 (6^7) = ....566 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)30 C)88 D)266 E)121 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B: #### B QUESTION:The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? options: A)76 B)88 C)66 D)55 E)35 SOLUTION:Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 28/2 = 35 cm2 Answer:E #### E QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum? options: A)8 B)2 C)10 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150 15000[(1 + R/100)2 - 1 - 2R/100] = 150 15000[(100 + R)2 - 10000 - 200R]/10000 = 150 R2 = (159 * 2)/3 = 100 => R = 10 Rate = 10% Answer: Option C #### C QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail? options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27 SOLUTION:Probability of getting least one tail at the coin tossed five times. = There is not even a single tail. = 1/32 ; P(T) = 1 - 1/32 = 31/32 ANSWER B #### B QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 9 = 150 meter Answer:A #### A QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 34 = 12 Answer: C #### C QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married? options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70 SOLUTION:--------------------M------W--------Total Marrried----------20-----20---------40 Not married-----10-----50---------60 Total-------------30-----70--------100 need married woman/total woman, so 20/70=2/7 C #### C QUESTION:Which of the following number is divisible by 24 ? options: A)3100000 B)3115832 C)3115800 D)3125832 E)3125834 SOLUTION:31214 is not divisible by 3 and 8 => 31214 is not divisible 24 61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24 512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24 3125832 is divisible by 3 and 8 => 3125832 is divisible 24 D) #### D QUESTION:A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls? options: A)1/12 B)5/36 C)1/9 D)1/3 E)17/36 SOLUTION:no. of possible outcomes = 66 = 36 no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) ) So, the probability = 1/9 (Option C) #### C QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres? options: A)18000 B)40000 C)31000 D)19000 E)16000 SOLUTION:Let breadth is x then length is 30+x Now the perimeter=2(x+30+x)=540 solving this we get x=120 Now the area is 120150=18000 ANSWER:A #### A QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.78 B)5.79 C)5.76 D)5.74 E)5.721 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 2 = 5.76.Answer: C #### C QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3? options: A)14 B)13 C)12 D)11 E)10 SOLUTION:The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A #### A QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:Find the value of a from (15)^2 x 8^3 Ã· 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 Ã· 256 = a = 225 x 512 Ã· 256 = 450 E #### E QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 8015010 cu.ft ,100% full = 60100101 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80150101/ 60 min= 2000 min E #### E QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table? options: A)120 B)480 C)960 D)2520 E)5080 SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E QUESTION:Select the one which is different from other Four alternatives. options: A)988 B)1140 C)1064 D)1197 E)1352 SOLUTION:E (A) 988 ÷ 19 = 52 (B) 1352 ÷ 19 = 71.15 (C) 1064 ÷ 19 = 56 (D) 1197 ÷ 19 = 63 (E) 1140 ÷ 19 = 60 #### E QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. options: A)237 B)126 C)971 D)611 E)150 SOLUTION:Explanation: ANSWER: E #### E QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later? options: A)2(10^5) B)9(10^5) C)(2^9)(10^5) D)(10^9)(10^5) E)(10^5)^9 SOLUTION:Every 10 minutes, the population is double the previous population. In 90 minutes, the population doubles 9 times. The population then is 2^910^5. The answer is C. #### C QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is? options: A)4452 B)4445 C)4330 D)4334 E)4336 SOLUTION:Divisor = (5 42) = 210 = 10 * Quotient = Divisor => Quotient = 210/10 = 21 Dividend = (Divisor * Quotient) + Remainder Dividend = (210 * 21) + 42 = 4452 A #### A QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water? options: A)29 B)92 C)30 D)32 E)23 SOLUTION:US = 22 DS = 42 M = (42 + 22)/2 = 32 Answer:D #### D QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was? options: A)120000 B)120029 C)187899 D)178968 E)200000 SOLUTION:X * (105/100) * (105/100) * (105/100) = 231525 X = 231525/1.157625 X = 200000 Answer:E #### E QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/5 = 3x => x = 20/3. So, speed of the faster train = 40/3 = 40/3 18/5 = 42 km/hr. Answer:D #### D QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate? options: A)69 B)70 C)71 D)72 E)73 SOLUTION:number of ways = 23!3! = 72 Answer is D #### D QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105. options: A)18 B)8 C)12 D)16 E)None of these SOLUTION:105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 The H.C.F of 32, 48 and 80 is 16. ANSWER:D #### D QUESTION:A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? options: A)20 B)24 C)25 D)26 E)30 SOLUTION:Ans.(A) Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways #### A QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km options: A)200 Km B)222 Km C)224 Km D)248 Km E)None of these SOLUTION:Explanation: Let time taken to travel the first half = x hr Then time taken to travel the second half = (10 - x) hr Distance covered in the the first half = 21x [because, distance = timespeed] Distance covered in the the second half = 24(10 - x) Distance covered in the the first half = Distance covered in the the second half So, 21x = 24(10 - x) => 45x = 240 => x = 16/3 Total Distance = 221(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way] Option C #### C QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:What is the remainder when you divide 2^200-1 by 7? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:answer is C. this is very similar to the 32^32^32-1 divided by 7 question. #### C QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? options: A)65 B)44 C)86 D)29 E)26 SOLUTION:Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Answer: B #### B QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 256/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:Yesterday, a pie shop sold 6 apple pies, 5 peach pies, and 6 pumpkin pies. How many pies did the shop sell in all? options: A)21 B)37 C)13 D)17 E)32 SOLUTION:Add the number of pies 6+5+6 =17. Answer is D. #### D QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)35 SOLUTION:Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr =(60 x(5/18)) m/sec =50/3 m/sec. Therefore Time taken to pass the man =(500 x(3/50))sec = 30 sec. Answer :B #### B QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D QUESTION:Magnabulk Corp sells boxes holding i magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate? options: A)100bi/m B)bi/(100m) C)100bi/m D)m/(bi) E)bi/m SOLUTION:We're given some facts to work with: 1) Magnabulk Corp sells boxes holding I magnets each. 2) The boxes are shipped in crates, each holding B boxes. 3) Magnabulk charges M DOLLARS for each crate We're asked for the price charged per magnet, in CENTS.... IF.... I = 2 B = 3 M = 12 (2 magnets per crate)(3 crates) = 6 magnets $12 for 6 magnets = $2 per magnet = 200 cents per magnet So we're looking for an answer that equals 200 when I=2, B=3 and M=12. There's only one answer that matches... Answer is C #### C QUESTION:A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? options: A)76 sec B)89 sec C)87 sec D)95 sec E)16 sec SOLUTION:Speed = 360/30 = 12 m/sec. Required time = (360 + 780)/12 = 95 sec. Answer:D #### D QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15? options: A)2 B)4 C)7 D)8 E)9 SOLUTION:Explanation: 35 + 25 = 60/15 = 4 (Remainder) B #### B QUESTION:The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)52 years E)None of these SOLUTION:Explanation: Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D #### D QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)30 C)99 D)77 E)62 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B #### B QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)8837 C)2377 D)3772 E)3881 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer: A #### A QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7? options: A)35 B)16 C)17 D)can’t be determined E)None of these SOLUTION:Answer C Solution In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is (770-210/35)+ 1 = 17 Hence option C #### C QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:Which of the following inequalities is equivalent to −1 < x < 5? options: A)\|x - 1\| < 7 B)\|x + 2\| < 3 C)\|x + 3\| < 5 D)\|x - 2\| < 3 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -1 < x < 5, let's say by adding y to this inequality we will get into the above format -1+y < x+y < 5+y Now, to move this into the mod format, we need to have (-1+y) + (5+y) = 0 => y = -2 Thus, -3< x-2 < 3 => \|x-2\| < 3. Hence, answer is D #### D QUESTION:A worker's daily wage is increased by 50% and the new wage is $30 per day. What was the worker's daily wage before the increase? options: A)$15 B)$18 C)$20 D)$22 E)$25 SOLUTION:Let x be the daily wage before the increase. 1.5x = $30 x = $20 The answer is C. #### C QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 17=7.Also 172 gives 1 Hence unit's digit in the product =71=7. Option A #### A QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.66 feet C)3.3 feet D)3.4 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+10=40 44/12=3.66 feet ANSWER:B #### B QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1065 C)1070 D)1075 E)1080 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 A #### A QUESTION:If A(k)=(k+1)^-k, and k=0, what is the value of A(A(A(k)))? options: A)0 B)(2/3)^(1/2) C)1 D)(3/2)^(1/2) E)(2/3)^-2 SOLUTION:A(A(A(0)))=A(A(1))=A(1/2)=(1/2+1)^-1/2=(2/3)^(1/2) Thus, the answer is B. #### B QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)96 C)100 D)125 E)250 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 5.6 , so radius is 2.8 New area = 7.84π Increase in area is 3.84π % increase in area = 3.84/4100 So, % increase is 96% Answer will be (B) #### B QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ? options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these SOLUTION:Explanation: Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24) =12:15:16=12:15:16. ANSWER IS D #### D QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant. options: A)250 m B)560 m C)100 m D)320 m E)240 m SOLUTION:Explanation : Abhishek's speed = 100/5=20 m/s. Time taken by Abhishek to cover 500 m =500/20=25 seconds. Dishu's speed = 500/20 or 25 m/s Prashant's speed = 15 m/s Time taken by Dishu to meet Prashant in 500m race in opposite direction: Distance covered by Abhishek: =>500/(15+25). =>12.5 sec. =>12.5(20)= 250 m. Answer : A #### A QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 23=6 as well. Answer: C. #### C QUESTION:Sum of two numbers prime to each other is 20 and their L.C.M. is 99. What are the numbers? options: A)8 and 12 B)14 and 6 C)19 and 1 D)11 and 9 E)12 and 9 SOLUTION:As two numbers are prime, only two options satisfy ie option C and D. but option C will not make the product of numbers i.e 99 ANSWER:D #### D QUESTION:In a certain store, the profit is 350% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)72.2% B)70% C)100% D)250% E)120% SOLUTION:Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 450 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 450 - 125 = Rs. 325 Required percentage = 295/420 100 = 72.2% ANSWER:A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:A total of 22 men and 30 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women? options: A) 31 B) 31.5 C) 32.8 D) 32.5 E) 33 SOLUTION:Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 52 = 22 * 38 + 30 * Aw =>1820 = 836 + 30 Aw => 30 Aw = 984 =>Aw = 32.8 Answer C #### C QUESTION:3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is: options: A)2/9 B)1/9 C)8/9 D)7/9 E)1/4 SOLUTION:let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house there will be 1 case when x,y,z will buy house a another when they buy house b and another when they buy house c so the prob that they buy same house is 31/27=1/9 ANSWER:B #### B QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:If a and b are integers and (2^a)(3^b) is a factor of 900^40, what is the largest possible value of ab? options: A)2a B)5a C)20a D)40a E)80a SOLUTION:(2^a)(3^b) is a factor of 900^40 We need to find the largest possible value of ab. We know that 900 = 2^25^23^2 Therefore 900^40 will have 2 powers of 3 in it. Hence in (2^a)(3^b), b has to 2 Therefore value of ab = 2a Correct Option: A #### A QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 â€“ 4xy (x- y)2 = 625 â€“ 576 => (x â€“ y) = 7 ANSWER: A #### A QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 98 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 76 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14Ã—30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—14) Ratio of the capacity of a man and woman =1/(15Ã—14) : 1/(14Ã—30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is: A 6, B 12, C 24, D 36, E 48 n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B #### B QUESTION:What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345? options: A)2345 B)4500 C)5000 D)6000 E)7000 SOLUTION:2000 + 300 + 40 + 5 = 2345 ANSWER A #### A QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (44)+(11)=17 MASS = 13+1+19+19=52 i.e (55)+(22)=29 DON = 4+14+15=33 i.e(33)+(33)=18 Hence (C) is correct Answer : C #### C QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27 SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30 We can write 30 as product of two numbers in following ways 130 215 310 56 4 cases = 42 i.e. 8 factors (including 1) Factors greater than 1 = 7 Answer: Option D #### D QUESTION:A group of four women and two men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in two adjacent seats, how many possible different seating arrangements are there for these 6 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C)6! – 5!2! D) 7 × 2!3!2! E) 2!3!2! SOLUTION:6 people can sit in 6! different ways. But because 2 men cannot sit together, we take them as a unit. This unit of men, among themselves can sit in 2! ways. Hence, 6! - 2!. This unit of men along with 4 women can sit in 5! different ways which also needs to be eliminated. Hence 6! - 5!2! C #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ? options: A)5 B)10 C)22 D)25 E)30 SOLUTION:Let's TEST Answer C: 22 seashells... With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer. C #### C QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1X2X3 = (1/3)^3 XX1X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed) options: A)4443 B)5980 C)5992 D)5990 E)5994 SOLUTION:n = 333 = 27 <x> = (333 + 111) / 2 = 222 Sum = number of integers x average value n * <x> = 27 * 222 = 5994 answer = E #### E QUESTION:A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long? options: A)52 B)94 C)71 D)68 E)88 SOLUTION:Speed = 280/28 = 10 m/sec. Required time = (280 + 660)/10 = 94 sec. Answer: B #### B QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 --> In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6. Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8. Answer: B. #### B QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)2 months B)7 months C)8 months D)10 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 months ANSWER:B #### B QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)(100%-19%) = 1.07.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)3 B)7 C)8 D)5 E)1 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 804 / 60 = 5 hours 33 mins Answer â€“ B #### B QUESTION:Sum of 42 odd numbers is? options: A)1764 B)1774 C)1784 D)1794 E)1754 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 42 odd numbers = 42^2 = 1764 ANSWER:A #### A QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 83= 24 tubes A is the answer #### A <<<Examples ends QUESTION:What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube. options: A)30 B)45 C)60 D)75 E)90 SOLUTION:C.. 60 degrees All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides. options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16 SOLUTION:CM=3 AREA=PMCM/2, thus PM=12 By Pythagorean Theorem, we can now find the value of PC. D is the correct option. #### D QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 52 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 5034 = 1700 >> 49 remains which will be adjusted with the 34 members 51 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price? options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050 SOLUTION:C $1000 90% 104% -------- 14% ---- 140 100% ---- ? => $1000 #### C QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y? options: A)2 B)1 C)0 D)5 E)6 SOLUTION:Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x can not equal 0 D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer. Answer A #### A QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:5 3 -2 -5 -3 2....What is the sum of first thirty number sequence? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 => 50-50=0. ANSWER:A #### A QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 (2/25) = 40 seconds Answer:C #### C QUESTION:A coin is tossed six times. What is the probability that there is at the least one tail? options: A)63/64 B)31/64 C)31/67 D)31/64 E)63/31 SOLUTION:Let P(T) be the probability of getting least one tail when the coin is tossed six times. = There is not even a single tail. i.e. all the outcomes are heads. = 1/64 ; P(T) = 1 - 1/64 = 63/64 Answer: A #### A QUESTION:Consider below info to be a table: AMOUNT OF BACTERIA TIME - AMOUNT 1PM - 10gms 4PM - x gms 7PM - 10.0 gms Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ? options: A)12.0 B)12.1 C)10.0 D)12.3 E)12.4 SOLUTION:let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =10.0 => x^2 =1.00 or x = 1.0 => @4PM quantity = 10x =101.0 =10. Answer C #### C QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 302928 = 24360 Answer: E #### E QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)28 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (14000 × 7) + 6000 ( x – 7) ‹=› 2000x = 56000 ‹=› x = 28. Answer D #### D QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(7206)=4320. Answer is E #### E QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25110)+(3580)+(4065) = 2750+2800+2600= $8150 required percentage = (2800/8150)100=33.35% C #### C QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)\|x - 1\| < 7 B)\|x + 2\| < 6 C)\|x + 3\| < 5 D)\|x - 2\| < 6 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => \|x-2\| < 6. Hence, answer is D #### D QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is? options: A)22 B)99 C)27 D)11 E)37 SOLUTION:Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30. S.I for one year = Rs. 330. S.I. on Rs. 330 for 1 year = Rs. 36.30 Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D #### D QUESTION:In how many no. between 10 and 50 exactly Two of the digits is 5? options: A)47 B)65 C)1 D)35 E)65 SOLUTION:It's simple can be solved by elimination of answer choices. Option B and D are too large, not possible. Even AE are large to have correct choice. Ans : C #### C QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is: options: A)600 B)450 C)350 D)500 E)620 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 40 Ã— 30) Cm(power)2 = 40 Ã— 15 = 600 Cm(power)2 Answer is A. #### A QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3\|X^3-3 options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1 SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t\|(t+3)^2-3, which is equivalent to the condition t\|3^3-3, or t\|24. Therefore, it is necessary and sufficient for t to be an integer divisor of 24, hence t must be equal to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7, 9, 11, 15, and 27. Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B QUESTION:If d<0, which of the following represents a positive number? options: A)d\|d\| B)\|d\|d C)\|d\|/d D)-d\|d\| E)d/ \|d\| SOLUTION:Answer : D #### D QUESTION:A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? options: A)76 hrs B)99 hrs C)55 hrs D)90 hrs E)11 hrs SOLUTION:1/9 - 1/x = 1/10 => 90 hrs Answer: D #### D QUESTION:How many figures are required to number the pages the pages of a book containing 365 pages? options: A)987 B)977 C)967 D)897 E)997 SOLUTION:1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 ----------- 987 ANSWER:A #### A QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36, find P (E\|F) and P(F\|E) options: A)5 B)8 C)2 D)6 E)12 SOLUTION:Here, E and F are events P(E\|F) = P(EnF)/P(F) = 36/36 = 1 P(F\|E) = P(EnF)/P(E) = 36/24 = 2. C) #### C QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)15 B)30 C)36 D)72 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 16) = (x + 8) or x = 24. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72. Answer: D #### D QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5100 000 = X 500 000 = X Answer: A) #### A QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4. 6000 /4 = 1500 toys correct answer B #### B QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed? options: A)502 B)512 C)523 D)521 E)500 SOLUTION:Let n be the total number of children. More children, less notebooks(Indirect proportion) If the number children = n, number of books each child will get = n/8 If the number children = n/2, number of books each child will get = 16 Hence we can write as children n:n/2}::16:n/8 ⇒n×n/8=n/2×16 ⇒n8=16/2=8 ⇒n=8×8=64 Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512 Answer is B. #### B QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have? options: A)5 B)10 C)30 D)40 E)50 SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)100% = 60% Now by Alligation Rule: A . ......... B 20% . . . 80% . . 60% . . (80-60) . (60-20) =20 : =40 Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration) So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%) So as per above ration Qty B mixed will be 50 gallons. Qty of water in mixture B = 20% of 50 = 10 gallons. ANSWER:B #### B QUESTION:The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip? options: A)300/(x + y) B)600/(x + y) C)150/x + 150/y D)300/x + 300/y E)600/x + 600/y SOLUTION:Time taken to cover first half i.e 300 miles of a 600 mile trip = x time taken to cover the second half i.e 300 miles of a 600 mile trip = y Total time taken = x+y Average speed for the entire trip =total distance /total time =600/(x+y) Answer B #### B QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result? options: A)600 B)480 C)538 D)650 E)560 SOLUTION:23th result = sum of 45results - sum of 44 results 1045-1622+2022 = 450-352+440 = 538 Answer is C #### C QUESTION:Half of 2 percent written as decimal is options: A)5 B)0.01 C)0.05 D)0.005 E)None of these SOLUTION:Explanation: It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01 Answer: Option B #### B QUESTION:If a is a positive integer, which of the following could NOT be the square of a? options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752 SOLUTION:A number ending with 2 can never be a perfect square. Units digit of a perfect square must be: 1,4,9,6,5 Answer E) #### E QUESTION:The wheel of an engine 30/7 metres in circumference makes seven revolutions in 4seconds. Find the speed of the train in km per hour? options: A)15km/hr B)25km/hr C)32km/hr D)18km/hr E)27km/hr SOLUTION:Distance travelled by the train in 4 seconds = 307/7 = 30 metres speed of the train = 30/4 = 15/2 m/s = 27 km/hr Answer is E #### E QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=2726^2 The answer is C. #### C QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)7 D)82 E)43 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? options: A)356 B)250 C)127 D)279 E)150 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 15 = 250 m Answer: B #### B QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y? options: A)96 B)75 C)50 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 6.12 and remainder is 6 So .12 X y = 6 hence y= 50 Ans C #### C QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width? options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3 SOLUTION:2x+2y=50 x+y=25 x+4x=25 5x=25 x=5 Answer C #### C QUESTION:Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop? options: A)128 B)64 C)32 D)16 E)8 SOLUTION:Before stop 3, there were 2 passengers on the bus. Before stop 2, there were 4 passengers on the bus. Before stop 1, there were 8 passengers on the bus. The answer is E. #### E QUESTION:Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: options: A)50 B)54 C)47 D)40 E)45 SOLUTION:Area of tile = 6056 = 3360 Area of floor = 560240 = 134400 No of tiles = 134400/3360 = 40 So, the no of tile = 40 ANSWER:D #### D QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)100 = (0.9)100 = 90%. A #### A QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5 options: A)40 B)20 C)25 D)30 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40 Answer: Option A #### A QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Let the number of men be m and so the number of women = 15-m Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start. Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days). Let the total work be 360 units (LCM of 180 and 120). 1 man does 360/120 = 3 units per day 1 woman does 360/180 = 2 units per day Based on above facts, Total work by men + women in these 17 days = 360 units m93 + (15-m)62 = 360, 27m + 180 -12m = 360, Solving m=12. Num of men = 12 and number of women = 15-12 = 3 ANSWER:C #### C QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter? options: A)15 B)25 C)30 D)45 E)60 SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach... We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats. Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as... 15X/7X When we add the 16 cats and factor in the 'ending ratio', we have an equation.... 15X/(7X+16) = 15/11 Here we have 1 variable and 1 equation, so we can solve for X.... (15X)(11) = (7X+16)(15) (X)(11) = (7X+16)(1) 11X = 7X + 16 4X = 16 X = 4 With this X, we can figure out the initial number of dogs and cats... Initial dogs = 15X = 15(4) = 60 Final Answer: D #### D QUESTION:The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? options: A)2888 B)1266 C)1000 D)2779 E)2661 SOLUTION:X * (110/100) * (95/100) = 1045 X * (11/10) * (1/100) = 11 X = 1000 Answer: C #### C QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E QUESTION:What is the tens digit of 7^1415? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit ) 0 , 4 , 4 , 0 . 1415= 4353 + 3 The ten's digit will be 4 . Answer E #### E QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)1752 B)1799 C)1719 D)1750 E)1800 SOLUTION:Speed = [216 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2 = 1800 Answer: E #### E QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)9.30 a.m B)10 a.m C)10.40 a.m D)11 a.m E)11.40 am SOLUTION:Suppose they meet x hours after 7 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 10 a.m. answer B #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen? options: A)1.34 B)2.84 C)3.84 D)4.34 E)5 SOLUTION:40(40/100) = 16 --- 50 ? --- 12 => Rs.3.84 Answer: C #### C QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 66 = Rs. 16.50 Answer: Option D #### D QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number. options: A)42 B)48 C)72 D)67 E)54 SOLUTION:Sol: Let the third number be x. Then second number = 3x. First number=3x/2. Therefore x+3x+(3x/2)=(443) or x=24 So largest number= 2nd number=3x=72 ANSWER :C #### C QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? options: A)3: 5 B)3: 9 C)3: 4 D)3: 1 E)3: 2 SOLUTION:d = 3d d = d a√2 = 3d a√2 = d a = 3d/√2 a = d/√2 => 3: 1 Answer: D #### D QUESTION:A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours. What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). options: A)1 hour B)2 hour C)3 hour D)4 hour E)5 hour SOLUTION:In one hour, Soln 1: the large inlet tube fills 1 / 3 of the tank; the small inlet tube fills 1 / 6 of the tank; the outlet tube empties 1 / 9 of the tank; and therefore all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. Soln 2: Let V be the total volume of the tank. From equation (1), Flow Rate (large inlet tube) = V / 3 Flow Rate (small inlet tube) = V / 6 Flow Rate (outlet tube) = V / 9. Substituting in equation (2), Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9). Using the above result in equation (1), Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ]. Note that V cancels out on simplifying the above expression. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. #### A QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now? options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Q = P+10 Q-20 = 2(P-20) P-10 = 2P-40 P = 30 The answer is A. #### A QUESTION:A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple? options: A)1/5 B)2/7 C)2/9 D)3/5 E)4/11 SOLUTION:The total number of ways to choose 2 apples is 7C2 = 21 The number of ways that include the spoiled apple is 6C1 = 6 P(the spoiled apple is included) = 6/21 = 2/7 The answer is B. #### B QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000 SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? for first 5000 , 8% tax then we get 400$ as tax. Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount. A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount) 550+400 = 950$...hence this is the option. ANSWER :option A. #### A QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 100 = 700 #### C QUESTION:As part of a game, two people each must secretly choose an integer between 1 and 2, inclusive. What is the approximate likelihood that all two people will choose different numbers? options: A)9% B)12% C)16% D)20% E)50% SOLUTION:Ans:E 1st person has option no's- (1,2) - there fore probability of getting a no = 2c1/2c1 = 1 2nd person has only one option - there fore probability of getting a no = 1c1/2c1 =1/2 =11/2 =50% #### E QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)100 = 25% ANSWER:A #### A QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected. What is the probability that a smartphone bundle that will be rejected by quality control? options: A) 0.25 B) .05^10 C) 1-0.94^10 D) 1-0.05^10 E) 0.95^10 SOLUTION:Find the probability of the opposite event and subtract from 1. The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10. P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10. Answer: C. #### C QUESTION:In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (12, 2), (12,-7)? options: A)64 B)68 C)72 D)76 E)80 SOLUTION:By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is: Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides. We can now determine the area of the quadrilateral: Area = 1/2 × (10 + 9) × 8 = 76. The answer is D. #### D QUESTION:Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 6 and the product of the given number and the sum of its digits is equal to 136. options: A)82 B)93 C)39 D)28 E)17 SOLUTION:Using the elimination method the option that fits this description is 17 7-1 = 3 (unit's digit that exceeds its ten's digit by 3) 178 = 136 (the product of the given number and the sum of its digits is equal to 175) answer :E #### E QUESTION:Today Joelle opened an interest-bearing savings account and deposited $10,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$12025 B)$11075 C)$11025 D)$11095 E)$11015 SOLUTION:Interest for 1st year =100005/100 = 500 Interest for 2nd year = 10500 5/100 = 525 Total =10000+500+525 = 11025 Answer : C #### C QUESTION:Three houses of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house. options: A)1/4 B)1/6 C)1/8 D)1/9 E)3/256 SOLUTION:Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 4 men choose House no 1 So for First men it will be 1/4,second men 1/4 , third men also 1/4 and fourth man 1/4 So probability of selecting house no 1 is 1/41/41/41/4= 1/256 And since there are 3 such house so probability that each men select the same house is 31/256 Ans is E #### E QUESTION:A box contains 8 pairs of shoes (16 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/19 D)1/10 E)1/15 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 16, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/11/15(as after taking one at random there are 15 shoes left and only one is the pair of the first one)=1/15 Answer: E. #### E QUESTION:A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long? options: A)2.5 B)3 C)5 D)7 E)9 SOLUTION:D = 25 * 60 + 1000 = 2500 m T = 2500/60 * 18/5 = 150 sec = 2.5 mins Answer: A #### A QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 12 (1!)^3=1 2!=2, therefore (2!)^3=222=8 3!=6, therefore (3!)^3=666=216 4!=24 therefore (4!)^3= 242424 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9m = 150 m. ANSWER:D #### D QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)120 E)200 SOLUTION:6C34C2 =120=D #### D QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item? options: A)17% B)21% C)24% D)29% E)42% SOLUTION:The price decreased by 23.99 - 16.99 = $7. $7 is a bit more than 29% of original price of $24. Answer: D. #### D QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is: options: A)28 B)30 C)40 D)50 E)72 SOLUTION:Let the numbers be 1x and 2x. Then, their L.C.M = 2x. So, 2x = 48 or x = 24. The numbers are 24 and 48. Hence, required sum = (24 + 48) = 72. ANSWER:E #### E QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1: 96 B)1: 98 C)1: 97 D)1: 95 E)1: 91 SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. Answer:A #### A QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(82003))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer? options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1 SOLUTION:9x^2-16y^2=3x+4y (3x+4y)(3x-4y)=3x+4y 3x-4y=(3x+4y)/(3x+4y) 3x-4y=1 Answer is option C #### C QUESTION:The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half? options: A)44.2 B)47.8 C)50.5 D)53.6 E)56.9 SOLUTION:The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. #### B QUESTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible? options: A)5 B)6 C)9 D)24 E)26 SOLUTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 01 + 11 + 21 + 11 + 11 + 01 = 5 cases...A #### A QUESTION:The forth proportional to 6,8,15 is? options: A)15 B)12 C)18 D)20 E)24 SOLUTION:Let the fourth proportional to 6,8,15 be x then 6:8::15:x 6x = 815 x = 20 Answer is D #### D QUESTION:If X = the product of three distinct prime numbers, how many factors does X have besides 1 and itself? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:Since X has 3 distinct prime factors, X has a total of 2^3 = 8 factors. Besides 1 and itself, X has 6 factors. The answer is A. #### A QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k? options: A)3/4 B)1 C)4/3 D)2 E)7/2 SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k. {{k + 4}/4} = k k + 4 = 4k 4 = 3k k = 4/3 Answer = C #### C QUESTION:Evaluate 30!/28! options: A)720 B)600 C)870 D)910 E)650 SOLUTION:we have 30!/28! = 302928!/28! = 3029 = 870 Answer is C #### C QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? options: A)35 B)20 C)47 D)36 E)30 SOLUTION:1: 2/5 = 5: 2 2/7 * 70 =20 Answer:B #### B QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9 SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E âˆ© H) = (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2 D #### D QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)10 B)11 C)12 D)14 E)15 SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = \| (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 14555 + 3555 = 2375 ANSWER:C #### C QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 45!. Answer: C. #### C QUESTION:At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? options: A)62.5 B)62.8 C)62.1 D)62.9 E)32.5 SOLUTION:Explanation: CP = 47.50 SP = 47.50(125/100) = 59.375 MP(95/100) = 59.375 MP = 62.5 Answer: A #### A QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? options: A)12 B)9 C)3 D)7.5 E)2.5 SOLUTION:we have 2 equations 1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B #### B QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: options: A)50 m B)150 m C)200 m D)data inadequate E)None of these SOLUTION:Explanation: Let the length of the train be x metres and its speed be y m/sec. Then, (x/y)= 15 y =(x/15) =x+100/25=x/15 => 15(x + 100) = 25x => 15x + 1500 = 25x => 1500 = 10x => x = 150 m. Answer: B #### B QUESTION:A train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train? options: A)322 B)324 C)326 D)328 E)330 SOLUTION:Length = Speed * time Speed = L/T S = 2000/25 S = 80 M/Sec Speed= 8018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 324 Kmph Answer: B #### B QUESTION:A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 5/18 = 20 = 400 â€“ 250 = 150m ANSWER:A #### A QUESTION:There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have? options: A)7/17 B)5/12 C)4/11 D)3/10 E)2/9 SOLUTION:P(first stamp is different) = 5/10 P(second stamp is different) = 4/9 P(both stamps are different) = 5/104/9 = 2/9 The answer is E. #### E QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? options: A)299 B)277 C)276 D)370 E)281 SOLUTION:Speed = 72 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 150)/26 = 20 x = 370 m. Answer: D #### D <<<Examples ends QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? options: A)4 B)16 C)8 D)1 E)2 SOLUTION:Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000 SOLUTION:0.7(x-600)=0.6(x-400) 0.1x=420-240 x=1800 The answer is D. #### D QUESTION:Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? options: A)1/6 B)1/2 C)5/8 D)5/4 E)15/16 SOLUTION:X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.7(X) + 0.5(1-X) = 0.75 0.2X = 0.75 - 0.5 X = 0.25/0.2 X = 5/4 Therefore the answer is D: 5/4. #### D QUESTION:Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank? options: A)10 min. 20 sec. B)11 min. 45 sec. C)12 min. 30 sec. D)14 min. 40 sec. E)15 min. 40 sec. SOLUTION:Take LCM of 15 and 20 and get the total capacity of tank as 60 . Then A will fill 4li in 1 min and B will fill 3 li in 1 min so total will be 7 . A left after 4 min so they worked together for 4 min so 74= 28 . now subtract it from 60.(60-38=32). This will be filled by b so time taken would be..10 min 20 sec. ANSWER:A #### A QUESTION:If x is less than y by 45% then y exceed x by: options: A)33.33% B)25% C)81.81% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)100) where x is Percentage decrease (here it is 25%) => 45/(100-45)100 =81.81% ANSWER:C #### C QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 18/5 = 8 sec ANSWER:C #### C QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)65 B)69 C)30 D)31 E)32 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers The answer is D. #### D QUESTION:A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by : options: A)7 only B)13 only C)11 only D)1001 only E)1003 only SOLUTION:256256 = 256 x 1001; 678678 = 678 x 1001, etc. So, any number of this form is divisible by 1001 ANSWER:D #### D QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4 and 5). Make the 4 number as large as possible and make the 5 number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6 and 7). Make the 6 number as large as possible and make the 7 number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class? options: A)40 B)50 C)28 D)38 E)48 SOLUTION:As half the circle shape consist of 33-8=25 boys, So total number of boys in full circle=225=50 ANSWER: B #### B QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 1/2 hours B)20 1/7 hours C)20 1/3 hours D)20 3/2 hours E)20 1/4 hours SOLUTION:1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours Answer: A #### A QUESTION:In track last week, the boys ran 15 laps. The girls ran 5 more laps. Each lap is a one-fifth of a mile. How many miles did the girls run? options: A)2 miles B)3 miles C)4 miles D)5 miles E)6 miles SOLUTION:The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4. The girls ran 4 miles correct answer C #### C QUESTION:The area of a triangle is with base 18m and height 6m? options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2 SOLUTION:1/2 * 18 * 6 = 54 m2 Answer: D #### D QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this?? options: A)360 B)430 C)510 D)540 E)630 SOLUTION:we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives. then we have to arrange 3 different sets in 3! ways. so, 5c14c13c13!=360 ANSWER:A #### A QUESTION:If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by options: A)15% B)20% C)25% D)30% E)40% SOLUTION:Sol. Let the original consumption = 100 kg and new consumption = x kg. So, 100 x 3 = x × 5 = x = 60 kg. ∴ Reduction in consumption = 40%. Answer E #### E QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be options: A)21 B)5193 C)77 D)9275 E)19 SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!. So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!. So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320) So remainder is 5193. Answer:B #### B QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph. answer :C #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2) options: A)1296 B)4 C)8 D)16 E)32 SOLUTION:(x+y)^2 - (x-y)^2 (x+y+x-y)(x+y-x+y) (2x)(2y) 4xy 4 6^4 = 1296 Answer A #### A QUESTION:The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area? options: A)1:1 B)1:9 C)1:3 D)1:4 E)1:3 SOLUTION:1:4 Answer: D #### D QUESTION:What is the place value of 0 in the numeral 2074? options: A)0 B)1 C)2 D)5 E)6 SOLUTION:Note : The place value of zero (0) is always 0. It may hold any place in a number, its value is always 0. A #### A QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 * 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters? options: A)174.2 B)212 C)288.1 D)296 E)302 SOLUTION:1.5 inch = 2.541.5 cm. So, 2.541.5 represents 24 miles. So for 48 cm.: 48/(2.541.5) = x / 24 ---> x = 2447/(3.81) = 302 Answer will be E. #### E QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 12 = 84 Answer is A #### A QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 81 hours respectively. The ratio of their speeds is? options: A)4:9 B)9:4 C)4:5 D)4:1 E)4:2 SOLUTION:Let us name the trains A and B. Then, (A's speed) : (B's speed) = √b : √a = √81 : √16 = 9:4 Answer:B #### B QUESTION:How many words can be formed by using all letters of the word “BIHAR” options: A)452 B)320 C)365 D)456 E)120 SOLUTION:The word BIHAR contains 5 different letters. Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120 Ans: E #### E QUESTION:The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is options: A)5 B)10 C)12 D)40 E)50 SOLUTION:Solution Let the initial number of persons be x. Then 16x + 12 x 15 = 15.5(x+20) = 0.5x = 6 x = 12. Answer C #### C QUESTION:How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants? options: A)4!5c2 21c2 B)4!5c3 21c2 C)5!5c2 21c2 D)7!5c2 21c5 E)6!5c2 21c2 SOLUTION:combination for 2 vowels out of 5 = 5c2 ways combination for 5 consonants of 21 = 21c5 ways Additionally the arrangement can be = 7! total arrangements =7!5c2 21c5 D #### D QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun? options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these SOLUTION:EXPLANATION Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg Answer A #### A QUESTION:The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.2 D)36.4 E)None SOLUTION:Solution Correct sum= (36x50+43-23) = 1820. âˆ´ Correct mean= 1820 / 50 = 36.4. Answer D #### D QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)500 B)350 C)828 D)277 E)122 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/489 = 50/3 3x + 900 = 2400 => x = 500 m. Answer: A #### A QUESTION:Convert the 9/36 m/s into kilometers per hour? options: A)0.9 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:9/36 m/s = 9/36 18/5 = 9/10 = 0.9 kmph. Answer: A #### A QUESTION:4 shepherds were watching over the flocks and they were commenting on how many sheep they each had. If ram had 3 more sheep than he would have one less than rahul. wheras akar has the same number as the other 3 shepherds put togeher. If john had 3 less sheep he would have exactly trile the number of ram. If they were evenly distributed if they would each have 11 seep how many sheep did ram have? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:akar has=ram+rahul+john after evenly distribution each has 11. so, total no. is 44 so, akar has=22 & ram+rahul+john=22 also ram=rahul-4 & john-3=3ram solving these we get the sol. ANSWER:B #### B QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? options: A)11 s B)10 s C)8 s D)12 s E)None of these SOLUTION:We know from the formula Time = Distance/ Speed Thus, Time = 120/ 54 x 5/18 or, Time = 8 sec. ANSWER:C #### C QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty five paise coins are in the ratio of 3:2:4, add up to Rs 75. Then how many 1 rupee coins he have? options: A)10 B)20 C)45 D)128 E)49 SOLUTION:Explanation : Given ratio = 3:2:4. Let us assume that there are 3 one rupee coins,2 fifty paise coins and 4 twenty-five paise coins in all. Their value=(31)+(2.50)+(4.25)=3+1+1=Rs 5 If the total is Rs 5, number of 1 rupee coins are 3. If the total is Rs 75, number of 1 rupee coins would be 753/5=45. Answer : C #### C QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 12 = 15552 Answer: E #### E QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ? options: A)x + 2000 = 1/3(x - 3000) B)1/3(x - 3000) = x C)x + 3000 = 1/3x D)x - 7000 = 1/3x E)x - 3000 = 1/5x SOLUTION:Plane's original altitude = x Plane's new altitude after ascending 2000 ft = x+2000 Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000 So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5 Answer (E) #### E QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)2: 7 B)2: 0 C)2: 4 D)2: 3 E)2: 1 SOLUTION:80 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280.Answer:D #### D QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year? options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155 SOLUTION:cost of type A products next year = 1.3 3200 = 4160 cost of type B products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 ANSWER:C #### C QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C QUESTION:A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 85 on the S scale? options: A)39 B)41 C)43 D)45 E)47 SOLUTION:A change of +18 on the R scale is a change of +30 on the S scale. R = (18/30)S + K = 3S/5 + K 6 = 3(30)/5 + K K = -12 R = 3S/5 - 12 R = 3(85)/5 - 12 = 51-12 = 39 The answer is A. #### A QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution? options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30 SOLUTION:Water:soap = 3:4 Soap:Salt=15:20 => For 15 soap, salt = 20 => For 4 Soap, salt = (20/15)4 = 80/15=16/3 So, water:soap:salt = 3:4:16/3= 9:12:16 After open container, water:soap:salt =4.5:12:16 So, water:salt = 4.5:16 = 9:32 ANSWER:A #### A QUESTION:6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is options: A)Rs. 150 B)Rs. 170 C)Rs. 180 D)Rs. 190 E)None of these SOLUTION:Explanation: Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2 = 24 : 24 : 12 = 2 : 2 : 1 Money earned by children = 950 x (1/5) = Rs. 190 Answer: Option D #### D QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in only mean being modified but not the median. A) A is removed B) A and J are removed C) B and I are removed D) A,B,C,H,I,J are removed E) A and E are removed options: A)1) A and B B)2) A and E C)3) A,C,E D)4) All of them E)5) None of them SOLUTION:There are 10 equidistant numbers on the number line. Mean and median will be the average of middle two numbers. If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where mean will change and median will not change. Answer: E #### E QUESTION:In the x-y plane, the area of the region bounded by the graph of \|x+y\| + \|x-y\| = 10 is options: A)8 B)625 C)16 D)20 E)24 SOLUTION:I've never seen such kind of question in GMAT before. OK there can be 4 cases: \|x+y\| + \|x-y\| = 10 A. x+y+x-y = 10 --> x=5 B. x+y-x+y = 10 --> y=5 C. -x-y +x-y= 10 --> y=-5 D. -x-y-x+y=10 --> x=-5 The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be2525=625 Answer: B #### B QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A? options: A)1 B)3 C)4 D)6 E)14 SOLUTION:6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 70 = 6K+4k =>k=7 Total Red's in bag A will be 2K = 14 E #### E QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600 SOLUTION:let investment is x... den remaining investment is (9800-x) x9/75= (9800-x)10/80 x=4800 9800-x=5000 ANSWER:B #### B QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? options: A)25 B)30 C)45 D)20 E)50 SOLUTION:6p2 = 6 x 5 = 30 B) #### B QUESTION:If \|x + 132\| = 32 what is the sum of all the values of x. options: A)-264 B)200 C)-64 D)0 E)-328 SOLUTION:There will be two cases x+132 = 32 and x+132 = -32 Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164 The sum of both values will be -164 + -100 = -264 Answer is A #### A QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? options: A)$110 B)$152.3 C)$180 D)$220 E)$260 SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition. A-E = 1/10(A+E) ==> 9A = 11E ------------ (1) Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E 1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2) Substituting (1) in (2): 11E/911 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 2209/13 =152.3 B #### B QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25Ã—26/2=325 Correct Option: B #### B QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)300 B)368 C)375 D)337 E)639 SOLUTION:A+B+C = 1200 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1200 => 300 Answer:A #### A QUESTION:If a man walks at the rate of 4 kmph, he misses a train by only 6 min. However, if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is options: A)3 km B)4 km C)5 km D)6 km E)7 km SOLUTION:Let the distance covered be d and time taken to reach the station in time t d/4 = t+6/60---(1) d/5 = t-6/60---(2) (1)-(2) gives d/4 - d/5 = (6+6)/60 d/20 = 12/60 d = 1220/60 =4 km ANSWER:B #### B QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.) options: A)1/5 B)1/2 C)2/3 D)4/5 E)6/5 SOLUTION:Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B FOR THE FIRST BUCKET ... Red color - 2 Blue color - 2 FOR THE SECOND BUCKET Red color - 3 Blue color -2 In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios : Scenario I - He picks Red color from List A and Blue color from List B Scenario II - He picks Blue color from List A and Red color from List B Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5 Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ... Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ... We get 1/5 + 3/10 = 2/3 (C) #### C QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)230 B)244 C)245 D)238 E)235 SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m. Answer: Option E #### E QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result? options: A)21 B)56 C)18 D)25 E)23 SOLUTION:1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6th = 294 + 312 – 550 = 56 Answer:B #### B QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60? options: A)426 B)430 C)443 D)470 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D #### D QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1 options: A)I,III only B)III only C)I only D)II only E)II,III only SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+36=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1; I. y<3x --> is not always true. Answer: E #### E QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? options: A)2% B)17% C)25% D)65% E)83% SOLUTION:New Value – Old Value)/Old Value x 100 We are given: February sales this year = 400 million February sales last year = 320 million We need to determine the percent increase between sales from last year to sales this year. Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula. (New Value – Old Value)/Old Value x 100 [(400 – 320)/320] x 100 = 25%. The answer is C. #### C QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:What Is The Next Number 12 13 15 17 111 113 117 119 ? options: A)123 B)220 C)129 D)428 E)224 SOLUTION:123. These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1 Answer : A #### A QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:A tap can fill a tank in 8 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hrs B)6 hrs C)8 hrs D)7.5 hrs E)4 hrs SOLUTION:Time taken by one tap to fill the tank = 4 hrs. Part filled by the taps in 1 hour = 4 1/8 = 1/2 Remaining part = 1 - 1/2 = 1/2 1/2 : 1/2 :: 1 : x x = 1/2 * 1 * 2 = 1 hrs. i.e., 60 min So, total time taken = 3 hrs 60 min = 4 hrs ANSWER: E #### E QUESTION:Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? options: A)320 B)384 C)400 D)408.3 E)440 SOLUTION:The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed. The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles. Answer B. #### B QUESTION:If k^2 = h^2, which of the following must be true? options: A)k = m B)\|k\| = \|h\| C)k = \|m\| D)k = -\|m\| E)k = -m SOLUTION:Solution: We are given that k^2 = h^2, and we can start by simplifying the equation by taking the square root of both sides. √k^2 = √h^2 When we take the square root of a variable squared, the result is the absolute value of that variable. Thus: √k^2 = √h^2 is \|k\| = \|h\| Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true. Answer: E #### E QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Monday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Tuesday, Monday C)Thursday, Monday D)Monday, Friday E)none SOLUTION:Rajat returned on Monday -i.e. 3 days earlier so actual day to return home is Thursday. Rohit returned after days so Monday ANSWER:C #### C QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =2516=400 Answer: E #### E QUESTION:If -1 < x < 0, which of the following must be true? I. x^4 < x^3 II. x^6 < 1 – x III. x^5 < x^2 options: A)I only B)II only C)III only D)II,III only E)I,II,III only SOLUTION:Answer : E #### E QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? options: A)2.04% B)6.12% C)8% D)8.25% E)10% SOLUTION:Per quarter, interest = 2% So for a year, interest = 8% Due to quarter cumulation, effective yield (YTM) would be slight higher than 8% Answer = 8.25% =ANSWER:D #### D QUESTION:Convert 0.30 in to a vulgar fraction ? options: A)18/50 B)16/50 C)3/10 D)19/50 E)None SOLUTION:Answer 0.30 = 30/100 = 3/10 Correct Option: C #### C QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)35 kmph D)23 kmph E)14 kmph SOLUTION:S = (10 + 60)/2 = 35 kmph Answer:C #### C QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled? options: A)600 B)700 C)800 D)850 E)None of these SOLUTION:Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 280 (406 = 240) 100% -----> 600 (1006 = 600) Answer: Option A #### A QUESTION:How much is 90% of 40 is greater than 4/5 of 25? options: A)29 B)776 C)66 D)16 E)99 SOLUTION:(90/100) * 40 – (4/5) * 25 36 - 20 = 16 Answer: D #### D QUESTION:If x+y=20, x-y=10, for integers of x and y, x=? options: A)15 B)20 C)25 D)13 E)42 SOLUTION:x+y =20 x-y = 10 2x = 30 x = 15 Answer is A #### A QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 3 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)3/23 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 3x Hence, a1+a2+..+a20+n = 23x So, the fraction asked = 3x/23x =3/23 Answer E #### E QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .250+.6x=.5(50+x) x=150 Answer E #### E QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 1334 = 156 Answer: E #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? options: A)32 B)36 C)40 D)45 E)50 SOLUTION:A = 9k+3 = 5j+4 B = 9m+3 = 5n+4 A-B = 9(k-m) = 5(j-n) Thus A-B is a multiple of 9 and 5, so it is multiple of 45. The answer is D. #### D QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these SOLUTION:The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer : B #### B QUESTION:The price of 2 sarees and 4 shirts is 16000. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall one have to pay? options: A)2,400 B)4,800 C)1,200 D)Cannot be determined E)None of these SOLUTION:Let the price of one saree and one shirt be x and y respectively. Then, 2x + 4y = 1600 or, x + 2y = 800 ... (i) Also, x + 6y = 1600 ... (ii) Solving equations (i) and (ii), we get 4y = 800 or,y = 200 ∴ cost of 12 shirts = 12 × 200 = 2400 Answer A #### A QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:A student has 7 trousers and 9 shirts. In how many different ways can the student select a trouser and a shirt? options: A)45 B)51 C)57 D)63 E)69 SOLUTION:The student can select one trouser in 7 ways. The student can select one shirt in 9 ways. The number of ways to select one trouser and one shirt is 7 * 9 = 63 ways The answer is D. #### D QUESTION:judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row. Can you find out how many girls are practicing together? options: A)4 B)9 C)11 D)6 E)8 SOLUTION:As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other. 5 + 5 + 1(judith herself) = 11. Hence, 11 girls are practicing the dance together. correct answer is C)11 #### C QUESTION:A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long? options: A)34 Seconds B)22 Seconds C)41 Seconds D)24 Seconds E)27 Seconds SOLUTION:27 Seconds Distance travelled = 140 + 310m = 450m Speed = 60 * 5/8 = 50/3m Time = 450 * 3/50 = 27 Seconds ANSWER E #### E QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price? options: A)(YP)/100X B)100X/(YP) C)(YP)+100X D)(YP)-100X E)(YP)100X SOLUTION:Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P 100 = 100X/(YP) Answer : B #### B QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 999998 = 472392 Hence option (A). #### A <<<Examples ends QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positivenegative = negative. Thus option C is always negative. #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))? options: A)81 B)16 C)300 D)256 E)625 SOLUTION:f(c)=c^2 f(f(c)) = (c^2)^2 = c^4 Therefore f(f(c)) will be numbers that are 4th power of other numbers. Checking the options: 81 = 3^4 16 = 2^4 300. This cannot be written as the 4th power of any number 256 = 4^4 625 = 5^4 Answer: C #### C QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)15 B)30 C)36 D)72 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 16) = (x + 8) or x = 24. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72. Answer: D #### D QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/8001/600=1/4,800. Answer: B. #### B QUESTION:If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 287 pounds. What is Jake’s present weight, in pounds? options: A)178 B)182 C)186 D)190 E)194 SOLUTION:J + K = 287 and so K = 287 - J J - 8 = 2K J - 8 = 2(287-J) 3J = 582 J = 194 The answer is E. #### E QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:How many integers between 263,205and 658,805 have tens digit 1 and units digit 3? options: A)3,955 B)3,925 C)3,956 D)3,926 E)3,915 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ... The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956 Answer:C. #### C QUESTION:Three unbased coins are tossed. the probability of getting at least two head is ? options: A)1/4 B)1/2 C)3/4 D)2/3 E)2/5 SOLUTION:S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH} E be the event of getting at least two head is {THH,HTH,HHT,HHH} P(E)=n(E)/n(S)=4/8=1/2 Answer(B) #### B QUESTION:There has been successive increases of 25% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change? options: A)23% B)27% C)31% D)35% E)39% SOLUTION:Let P be the original price per unit of gas. Let x be the original gas consumption. Let y be the reduced gas consumption. y1.11.25P = xP y = x / (1.11.25) which is about 0.73x which is a decrease of about 27%. The answer is B. #### B QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ? options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8 SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed) let E is the event of getting at least 1 head and 1 tail n(E) = TTH , HTT, THT, HHT, HTH, THH = 6 P(E) = n(E) / n(s) = 6/8 = 3/4 Ans- C #### C QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol. What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol? options: A)32 B)21 C)27 D)None of these E)18 SOLUTION:Explanation: Let t be the time after Kajol starts, when she meets Ajay, then \inline t=\frac{300}{(x+y)} This should be less than 2.5 or (x+y)>120 Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72 This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol. Answer: D #### D QUESTION:If n is a positive integer, which of the following is a possible value of \|36 - 5n\|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then \|36- 5n\| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then \|36- 5n\| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/51400 = 280 560-280 = 280 Answer: E #### E QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:G 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11 5811 =440 So the remainder will be the remainder of 440/14 which is 6 Ans A #### A QUESTION:John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have? options: A)65 B)68 C)70 D)77 E)80 SOLUTION:Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60. Step 2: Then pencil are distributed in ratio among friends, Rakesh = ( 1 / 2 x 60 ) = 30. Rahul = ( 1 / 3 x 60 ) = 20. Ranjan = ( 1 / 4 x 60 ) = 15. Rohit = ( 1 / 5 x 60 ) = 12. Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x. For minimum number of pencils x = 1 . The person should have atleast 77 pencils. D) #### D QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 10 = 90 ways. E #### E QUESTION:The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is : options: A)1 : 3 : 4 B)1 : 3 : 6 C)1 : 2 : 6 D)1 : 3 : 5 E)1 : 4 : 6 SOLUTION:Ratio of time taken : 1/12 :1/4 : 1/2 = 1 : 3 : 6 ANSWER:B #### B QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 101215/20 = 2420x/32 X=4 Answer: Option A #### A QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B. options: A)16 years B)24 years C)8 years D)12 years E)18 years SOLUTION:let present age of A be A let presennt age of B be B in 6 yrs A+6:B+6=3(B-4):B=6 ie A+6=3(B-4) but given A=B+6 so B+6+6=3(B-4) B=12 ANSWER:D #### D QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king? options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26 SOLUTION:There are 26 black cards and 2 red kings. P(black card or king) = 28/52 = 7/13 The answer is D. #### D QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x 100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:What least number must be added to 1056, so that the sum is completely divisible by 23 ? options: A)2 B)3 C)16 D)18 E)23 SOLUTION:23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2. Answer: Option A #### A QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)100]%=50% Answer A) 50. #### A QUESTION:The ratio between the number of sheep and the number of horses at the Stewart farm is 1 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? options: A)18 B)28 C)32 D)56 E)8 SOLUTION:Let the number of sheeps and horses be 1x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 1x = 18 = 8. Hence E #### E QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. options: A)180 B)181 C)182 D)178 E)168 SOLUTION:add the max weights 52+50+78=180 ANSWER:A #### A QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment? options: A)360 B)420 C)230 D)540 E)610 SOLUTION:Let the value of each installment be Rs.x [x/(1+(20/100))]+[x/(1+(20/100))2]=550 (100x/120)+(10000x/14400)=550 (5x/6)+(25x/36)=550 x=360 Option A #### A QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -225/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph? options: A)32 mph B)34 mph C)36 mph D)35 mph E)31 mph SOLUTION:Explanation : Average speed=Total Distance/Time. Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours. Distance covered in the first 9 hours = 9Ã—40=360 miles Distance covered in the next 6 hours= 6Ã—30=180 miles Therefore, total distance travelled = 360+180=540 miles. The total time taken = 9+6=15hours. Hence, the average speed =540/15= 36 mph. Answer : C #### C QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 45 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 72 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km SOLUTION:M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer: B #### B QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 80 and n is not prime, what is the greatest possible value of f(n)? options: A)75 B)69 C)60 D)55 E)63 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 75 = 355. This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 323. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/41/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/42/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: C. #### C QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is : options: A)700 B)690 C)650 D)698 E)728 SOLUTION:Explanation : Simple Interest (SI) for 1 year = 854-815 = 39 Simple Interest (SI) for 3 years = 39 × 3 = 117 Principal = 815 - 117 = Rs.698 Answer : Option D #### D QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B? options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above SOLUTION:et ratio of A and B be 6x & 7x so net loss = 6x+7x= 7800 x=600 A=6x=6(600)=3600 B= 7x=7(600)=4200 so, B= 4200 ANSWER:A #### A QUESTION:The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1 options: A)(i)0.20(ii)6.31 B)(i)0.21(ii)5.30 C)(i)0.21(ii)6.30 D)(i)1.21(ii)6.50 E)None of these SOLUTION:Explanation : Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10. Without decimal places, these numbers are 63, 105 and 210. Now, H.C.F. of 63, 105 and 210 is 21. H.C.F. of 0.63, 1.05 and 2.1 is 0.21. L.C.M. of 63, 105 and 210 is 630. L.C.M. of 0.63, 1.05 and 2.1 is 6.30. ANSWER IS C #### C QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2 options: A)I only B)I,II only C)II only D)I,III only E)III only SOLUTION:12=223 16=2222 GCF =22=4 Answer : C #### C QUESTION:If y exceeds x by 25%, then x is less than y by? options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3% SOLUTION:X=100 y=125 125------25 100-------? => 20% Answer:A #### A QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi12/4 =12- pi3 ANSWER:B #### B QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6 SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject. B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject. C. Hold. D. since p is a perfect cube, -p will also be a perfect cube. reject. E. (p-q)^6, is a perfect cube, so reject. By elimination C is the answer. Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube. ANSWER:C #### C QUESTION:Which of the following is satisfied with \|x-4\|+\|x-3\|<6? options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4 SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, \|x-4\|+\|x-3\|<6 -> \|x-4+x-3\|<6 -> \|2x-7\|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. #### C QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an odd number II. P is a multiple of 24 III. P is a multiple of 23 options: A)I only B)II only C)III only D)None of the above E)All of the above SOLUTION:The correct answer is B. #### B QUESTION:Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? options: A)$1.08 B)$1.41 C)$1.74 D)$1.98 E)$2.16 SOLUTION:2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E. #### E QUESTION:A bank pays interest to its customers on the last day of the year. The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $5760. What is the average monthly balance maintained by John in his account during the year? options: A) 2840 B) 28800 C) 6840 D) 7540 E) 28400 SOLUTION:bank balance is doubled with accumulation of interest tp 5760.. this means INTEREST is 5760/2=2880 for entire year.. although since interest is 10% of avg MONthly balance, it becomes 28800.. B #### B QUESTION:If x and y are non-zero integers, and 36x^4 – 4y^4 = 6x^2 + 2y^2, which of the following could be the value of x2 in terms of y? options: A)2y^2+1/6 B)2y^2+1/8 C)2y^2+1 D)2y^2 E)2y SOLUTION:36x^4 – 4y^4 = 6x^2 + 2y^2 (6x^2 + 2y^2) (6x^2 - 2y^2) = 6x^2 + 2y^2 6x^2 - 2y^2 = 1 6x^2 = 2y^2+1 x^2 = 2y^2+1/6 Answer : A #### A QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)14.9 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.8 - 19 x 15) kg = 11 kg. Correct Option: C #### C QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 * 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate? options: A)12 Â½ years B)62 Â½ years C)18 Â½ years D)72 Â½ years E)12 Â½ years SOLUTION:100 ---- 200 ---- 5 200 ---- 5 100 ---- 2 1/2 ------------------ 900 ---- 18 Â½ years Answer:C #### C QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed against the current will be options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these SOLUTION:Explanation: Speed with current is 20, speed of the man + It is speed of the current Speed in sƟll water = 20 - 5 = 15 Now speed against the current will be speed of the man - speed of the current = 15 - 5 = 10 kmph Answer: B #### B QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal. options: A)6:7 B)4:5 C)5:8 D)25:64 E)3:5 SOLUTION:The hare takes 3 leaps and the jackal takes 5 leaps. 1 hare leap = 4/3 jackal leaps Thus the hare's 3 leaps = 3(4/3) = 4 jackal leaps. The ratio of their speeds is 4:5. The answer is B. #### B QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 300 E)None of these SOLUTION:Explanation : T = 2 years R = 10% TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120 TD = (PW × TR)/100 ⇒ 120 = (PW × 2 × 10)/100 ⇒ 1200 = PW × 2 PW =1200/2 = Rs. 600 Answer : Option A #### A QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.50.5x = x/4 y%x = 36 (y/100)x = 36 (x/400)x = 36 x^2 = 36400 x = 120 The answer is E. #### E QUESTION:Of the science books in a certain supply room, 40 are on botany, 45 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science? options: A)186 B)225 C)294 D)302 E)314 SOLUTION:The worst case scenario is to remove all the books on botany, zoology, and geology. Also we can remove 79 books each from physics and chemistry. The total is 40 + 45 + 50 + 79 + 79 = 293. The next book removed must either be physics or chemistry, ensuring 80 books in that subject. The answer is C. #### C QUESTION:What is the largest integer n such that 2^n is a factor of 20^8 ? options: A)1 B)2 C)4 D)8 E)16 SOLUTION:20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16. Answer: E. #### E QUESTION:If r and t are positive integers, rt + r + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let rt + t + r = x Add 1 on both sides: rt + t + r + 1 = x + 1 t(r + 1) + r + 1 = x + 1 (r + 1)(t + 1) = x + 1 Minimum value of (r + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> rt + t + r cannot be 6 Answer: B #### B QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is options: A)8/17 B)7/15 C)3/15 D)5/12 E)1/4 SOLUTION:Person ( A ) ( B ) ( A+B ) Time - ( 15 ) ( 20 ) (-) Rate - ( 20 ) ( 15 ) ( 35 ) Work -(300) (300) (300) therefore A+B requires (300/35) days to complete entire work For 1st 5 days they work 35 5 = 175 Remaining work is 300 - 175 = 125 Remaining fraction of work is = 125/300 = 5/12 Answer D #### D QUESTION:By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%? options: A)6.54 B)9.45 C)7.34 D)6.67 E)5.09 SOLUTION:90% --- 8 110% --- ? 90/110 * 8 = 6.54 Answer: A #### A QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:At a recent small town election for mayor a total of 971 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place? options: A)134 B)178 C)197 D)166 E)194 SOLUTION:The number of votes the winning candidate received was 971 + 53 + 79 + 105 /4= 302. The second received 302 – 53 = 249, The fourth place received 302 – 105 = 197. C #### C QUESTION:AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 16.0 grams 4:00 P.M. x grams 7:00 P.M. 20.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.? options: A)12.0 B)18.1 C)12.2 D)12.3 E)18.0 SOLUTION:The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours. Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm: Fractional increase from 1 PM to 4 PM = X / 16.0 Fractional increase from 4 PM to 7 PM = 20.4 / X X \ 16 = 20.4 \ X X^2 = 20.4 * 16 X = 18 answer : E #### E QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(82003))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together. options: A)W8 B)789 C)279 D)277 E)191 SOLUTION:Answer:D #### D QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is? options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15 SOLUTION:100(90/100)(90/100)(95/100) = 76.95 100 - 76.95 = 23.05 Answer: A #### A QUESTION:A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have? options: A)200 B)125 C)180 D)152 E)250 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 45% % of of employees other than secretaries and salespeople = 100 - 60 = 40% But this number is given as 50 so 40% of x = 50 x = 125 Therefore there a total of 125 employees in the company D Correct answer - B #### B QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W? I. 9 II. 15 III. 27 options: A)I only B)II only C)I and II only D)I and III only E)I, II, and III SOLUTION:Ans: C W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)3 means x must contain 3^2 and 5^2 so with these conditions we know that 9=3^2 and 15=35 both have required factors for the divisibility of lowest int for x which is 925 but 27 is not a divisor because it can't divide 925 fully. so Ans : C #### C QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall? options: A)5/7 B)1 C)10/7 D)12/7 E)24/7 SOLUTION:Solution:Let work done by man, women and girl per hour be m,w,g respectively. Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3). No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6. So, n = 1/(7/24) = 24/7 Option, E #### E QUESTION:A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black? options: A)4/7 B)3/5 C)5/8 D)2/3 E)3/4 SOLUTION:Each ball has an equal chance (1/9) of being selected fourth. The probability that a black ball is selected fourth is 6/9 = 2/3. The answer is D. #### D QUESTION:Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103? options: A)2500 m^2 B)2510 m^2 C)2520 m^2 D)2540 m^2 E)2590 m^2 SOLUTION:Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C #### C QUESTION:If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month? options: A)643 B)652 C)660 D)564 E)693 SOLUTION:=560/1.2∗1.21 =564=564 Answer is D #### D QUESTION:12 times a number gives 156. The number is options: A)11 B)12 C)13 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 12×N=156⇒N=13 Correct Option: C #### C QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)299 meters B)278 meters C)500 meters D)276 meters E)299 meters SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: C #### C QUESTION:A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done? options: A)572 B)672 C)472 D)372 E)None SOLUTION:Solution: 10C5: when both are not included. 10C4: when one of them is included. Number of ways = 10C5 +10C4+ 10C4 = 672 Answer: Option B #### B QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x 104.76/100 104.76/100 = 8840 x1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m options: A)II,III only B)I,III only C)I only D)III only E)II only SOLUTION:n > 1. So, option II, III is not possible. So, Option I is correct. Answer : C #### C QUESTION:The ratio, by weight, of coffee to sugar to water in a pot of coffee is 7:3:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:The new ratio of coffee to sugar is 3.5:3 The new ratio of coffee to water is 14:15. The new ratio of coffee to sugar to water is 14:12:15. If there are 12 grams of sugar, then there are (15/12)12=15 grams of water. The answer is D. #### D QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4 and 5). Make the 4 number as large as possible and make the 5 number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6 and 7). Make the 6 number as large as possible and make the 7 number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:8.008/1.001 options: A)0.008 B)8 C)0.8 D)80 E)800 SOLUTION:Answer is 8, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/1001= 8 Answer B #### B QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 804 / 60 = 5 hours 33 mins Answer â€“ B #### B QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 25001.5/1.4= 2478 Answer:- D #### D QUESTION:If 13 = 13w/(1-w) ,then (3w)2 = options: A)1/4 B)1/2 C)1 D)2 E)3 SOLUTION:13-13w=13w 26w=13 w=1/2 3w=3/2 3w2=3/22=3 ANSWER:E #### E QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:The second of two numbers is two less than three times the first. Find the numbers if there sum is 74. options: A)7-19 B)8-20 C)10-16 D)15-9 E)19-55 SOLUTION:We are looking for two numbers. #1 - x #2 - 3x â€“ 2 The sum is 74. #1 + #2 = 74 Substituting x + 3x â€“ 2 = 74 4x â€“ 2 =74 4x = 76 x = 19 The first number is 19, the second number is two less than three times 19 or 55. correct answer E #### E QUESTION:There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than non bird animals at the zoo? options: A)400 B)360 C)270 D)180 E)90 SOLUTION:Total birds = 450 = 5 Other Animals (X) or X = 90. So, Difference in Birds and X = 450-90 = 360. Answer is B. #### B QUESTION:The sum and the product of two numbers are 16 and 15 respectively, the difference of the number is? options: A)14 B)6 C)7 D)8 E)2 SOLUTION:Explanation: x + y = 16 xy = 15 (x- y)2 = (x + y)2 - 4xy (x- y)2 = 256 - 60 => (x - y) = 14 Answer: A #### A QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 960/45 = 94/3 = 12 New time in minutes to cross 9 miles stretch = 960/35 = 912/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/21/5+x/21/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)8 : 9 B)21 : 22 C)17 : 18 D)12 : 20 E)Cannot be determined SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). (120/100 x 7x) and (110/100 x 8x) 42x/5 and 44x/5 The required ratio = (42x/5 : 44x/5)= 21 : 22. ANSWER B #### B QUESTION:There are 20,6 and 9 rupees notes. you have to form 99 rupees with minimum number of notes.At what minimum number of notes you can achieve this? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:203 = 60 62 = 12 92 = 18 91 = 9 9 notes ANSWER:A #### A QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days SOLUTION:B (x â€“ 5)/13 + x/20 = 1 x = 10 10/11 days #### B QUESTION:The sum of two numbers is 45. Their difference is 5. The bigger number is options: A)20 B)25 C)30 D)35 E)45 SOLUTION:X + Y = 45 X - Y = 5 Adding 2X = 50 ==> X = 25 and Y = 45 - 25 = 20 Bigger number is X = 25 Answer B. #### B <<<Examples ends QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? options: A)35 B)20 C)47 D)36 E)30 SOLUTION:1: 2/5 = 5: 2 2/7 * 70 =20 Answer:B #### B QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Ans: 6 Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B #### B QUESTION:Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had? options: A)A)5 B)B)11 C)C)19 D)D)3 E)E)4 SOLUTION:13-10=3. Answer is D #### D QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4side = 4 (3p/5) = 12p/5 Answer is C. #### C QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 * 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:If n is a positive integer, which of the following is a possible value of \|36 - 5n\|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then \|36- 5n\| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then \|36- 5n\| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)16 B)77 C)88 D)55 E)778 SOLUTION:P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. Answer:A #### A QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference D= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x15 x = 6/15=2/5 Answer: B #### B QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:1 weaver can weave 1 mat in 4 days. 10 weavers can weave 10 mats in 4 days. 10 weavers can weave 25 mats in 10 days. The answer is D. #### D QUESTION:Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work. If it takes him exactly 8 minutes more to walk to work than to ride his bicycle, then x equals options: A)4 B)7 C)12 D)15 E)20 SOLUTION:The best way would be... Per km, he takes 40 secs extra if he walks So he will take 8 mins or 860 secs in 860/40 =12 km ANSWER:C #### C QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? options: A)4 min B)8 min C)9 min D)6 min E)1 min SOLUTION:S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min Answer:A #### A QUESTION:In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other? options: A)384 B)396 C)576 D)24 E)696 SOLUTION:Number of total arrangements = 5! Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 22 Total number of arrangements - Number out of restrictions = Result 5! - (4!22) = 120 - (2422) = 24 Answer D #### D QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0 SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4âˆ—6=7.5 The only option ending with a 0.5 in the decimal place is C. ANSWER:C #### C QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following T is a possible value for x + y? I. 18 II. 19 III. 20 options: A)I only B)II only C)T=III only D)II and III only E)None SOLUTION:TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7 i.e. Min Value of x = 8 AND i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11 i.e. Min Value of y = 12 i.e. Minimum Value of x+y = 8+12 = 20 Hence III only can be True Answer: Option C #### C QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there? options: A)2 B)4 C)3 D)5 E)6 SOLUTION:x / 9 – y / 6 = 1/9; 2x – 3y + 2 We can compute that x = 4 and y = 2. Thus, Inlet pipe = x = 4. Answer: B #### B QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:In how many ways a committee of 10 men and 8 women can be made out of total of 15 men and 12 women? options: A)336/987 B)1001/165 C)1245/789 D)3256/789 E)256/85 SOLUTION:Required number of ways = 15C10 * 12C8 = 15C5 * 12C4 = 3003/495 = 1001/165 Answer is B #### B QUESTION:Find the odd man out. 14,35,49,60,70 options: A)14 B)35 C)49 D)60 E)70 SOLUTION:All except 60 are multiples of 7 Answer is D #### D QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell? options: A)111 B)75 C)29 D)128 E)96 SOLUTION:E 96 Joshua sold 90 phones. Rob sold 30 % more phones than Joshua Rob = 90 + 90 × 30% = 90 + 90 × 0.30 = 90 + 27 = 117 Prerna sold 11 more phones than Rob Prerna = 117 + 11 = 128 Declan sold 3/4 of what Prerna sold. Declan= 128 x 3/4 =96 Declan sold 96 phones. The correct answer is E. #### E QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips? options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these SOLUTION:Explanation: Method : 1 If a car covers a certain distance atxkmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph. By using the same formula, we can find out the average speed quickly Speed with which he travels from A to B = x = 40 km/hr Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr average speed = (2×40×60)/(40+60) = 48 km/hr Assume that distance from A to B = x km Speed with which he travels from A to B = x = 40 km/hr Time to travel from A to B = distance/speed = x/40 hr Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr Time to travel from B to A = distance/speed = x/60 Total distance traveled = x+x = 2x Total time taken = x/40 + x/60 Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60) = 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr Answer: Option A #### A QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:Convert 0.30 in to a vulgar fraction ? options: A)18/50 B)16/50 C)3/10 D)19/50 E)None SOLUTION:Answer 0.30 = 30/100 = 3/10 Correct Option: C #### C QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2. options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1 SOLUTION:Explanation: No explanation is available for this question! ANSWER: A #### A QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross-section is 344 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)40 E)71 SOLUTION:1/2 * d (12 + 5) = 344 d = 40 Answer: D #### D QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is? options: A)126 B)156 C)190 D)300 E)260 SOLUTION:Sol. Let width = x, Length = (10+x) Perimeter = 2(x+(10+x)) = 2(2x=10) & 2(2x+10)6.5 = 1950 X = 70 Required perimeter = 2(70+80) = 300 D #### D QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:How much is 80% of 60 is greater than 4/5 of 25? options: A)15 B)28 C)16 D)12 E)73 SOLUTION:(80/100) * 60 â€“ (4/5) * 25 48 - 20 = 28 Answer: B #### B QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)3 B)5 C)6 D)4 E)9 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B #### B QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.09 B)1.6 C)1.2 D)1.5 E)1.1 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer: D #### D QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(46 + 86): (412) 72:48 => 3:2 Answer:C #### C QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=520=100 Total price of 3 packet milk=312=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:The class borrowed a total of 402 = 80 books. The 27 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 132 = 38. To maximize the number of books borrowed by 1 student, let's assume that 12 students borrowed 3 books and 1 student borrowed the rest. 80 - 38 - 312 = 6 The maximum number of books borrowed by any student is 6. The answer is D. #### D QUESTION:John has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:Let there be a pennies , b nickels and c dimes so total amount can be 1+5b+10c cents to 4+5b+10c as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4) So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5. so answer is B #### B QUESTION:Shekar scored 76, 65, 82, 47 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? options: A)71 B)69 C)75 D)85 E)90 SOLUTION:Explanation : Average= (76+65+82+47+85)/5 = 355/5 =71 Hence average=71 Answer : A #### A QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1 options: A)I,III only B)III only C)I only D)II only E)II,III only SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+36=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1; I. y<3x --> is not always true. Answer: E #### E QUESTION:At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples? options: A)1/12 B)5/14 C)4/9 D)1/2 E)2/3 SOLUTION:"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind). C23∗C46C49=514C32∗C64C94=514. C23C32 - # of ways to choose which 2 samples will be tasted; C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples3 cups each = 6 cups); C49C94 - total # of ways to choose 4 cups out of 9. Answer: B #### B QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Answer:C #### C QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 * 6 = 720 Answer:C #### C QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased? options: A)7 B)6 C)5 D)2 pineapples E)3 SOLUTION:Explanation: The equation for this problem can be made as: 5x + 7y =38 Where x is the number of watermelons and y is the number of pineapples. Now test for 2, 3 and 4: For y = 2 5x + 14 =38 x is not an integer For y = 3 5x = 17 X not an integer For y =4 X = 2 So 4 pineapples and 2 watermelons can be bought by 38 Rs. ANSWER:D #### D QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone? options: A)6 B)12 C)14 D)15 E)17 SOLUTION:Renuâ€™s one dayâ€™s work = 1/6 Sumaâ€™s one dayâ€™s work = 1/3 - 1/6 = 1/6 Suma can do it alone in 6 days. ANSWER:A #### A QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:6.513/10.02 = options: A) 0.35 B) 0.3505 C) 0.3509 D) 0.65 E) 0.3527 SOLUTION:6.513 / 10.02 6.513 / 1002 = 6.5 move the comma two places to the left as we have 2 decimal places from the divisor: 0.65. Answer: D #### D QUESTION:The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square? options: A)277 B)268 C)287 D)480 E)281 SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D #### D QUESTION:A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction? options: A)8% B)10% C)2% D)5% E)6% SOLUTION:Actual price = 100+10 = $110 Saving = 10/110 100 = 100/11 =10% approximately Answer is B #### B QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? options: A)14/27 B)15/28 C)27/28 D)16/28 E)30/28 SOLUTION:There are 6 consonants and 2 vowels in KYANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : C #### C QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? options: A)7/72 B)1/6 C)7/36 D)5/28 E)21/36 SOLUTION:Probability = No: of desired outcomes / Total No: of outcomes. You are picking two slips out of 8 slips. So Total No: of outcomes = 8C2 = 28 Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there? If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome. (1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome. So No: of desired outcomes = 5 Probability = 5/28 Answer :D #### D QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:How many natural numbers are there which give a remainder of 41 after dividing 1997? options: A)2 B)4 C)6 D)None of these E)Cannot be determined SOLUTION:Solution Let us assume that the quotient is Q and divisor is D. Using the condition given in question, 1997 = QD + 41 ⇒ QD = 1956. Now we will factorize 1956 in two parts such that D (divisor) is more than 41. Answer C #### C QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)877m B)180m C)786m D)165m E)456m SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B #### B QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781 options: A)386 B)187 C)781 D)682 E)564 SOLUTION:Explanation : In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 75% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)18 C)11 D)38 E)0 SOLUTION:Answer: D Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 75%, we can set up the following equation: 75=15+22+x x=38, choiceD. #### D QUESTION:A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years. Total profit is Rs.1000/-. Find the C's share? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 800 E)Rs. 900 SOLUTION:Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6. So C's share = Rs. (1000 * 6/15) = Rs. 400. Answer: Option C #### C QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011 SOLUTION:Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B #### B QUESTION:What is the value of x if (64^2)-(36^2)=20x? options: A)120 B)100 C)140 D)130 E)115 SOLUTION:20x=(64+36)(64-36) 20x=10028 x=(10028)/20 x=528 x=140 Option C #### C QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:The average age of 39 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)54 years E)None of these SOLUTION:Explanation: Age of the teacher = (40 * 15 - 39 * 14) years = 54 years. Answer: D #### D QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now? options: A)24 years B)27 years C)28 years D)30 years E)40 years SOLUTION:Explanation : Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years. Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years. Answer : A #### A QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent? options: A)22 B)77 C)18 D)21.6 E)88 SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900 Profit(%) = (66900 - 55000)/55000 * 100 = 21.6% Answer: D #### D QUESTION:How many such letter-pairs are there in the word SERVANT having the same no. of letters left between them in the word as they have in the series? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:1 pair is S & V 1 pair is N &S total 2 pair ANSWER: A #### A QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him. Options: options: A)1 apple B)2 apple C)3 apple D)4 apple E)5 apple SOLUTION:This is equivalent to finding the first number that is divisible by 7 that occurs before 4267. In order to divide the sum in 7 parts, the amount must be divisible by 7 Divisibility rule of 7: The sum of the digits must be divisible by 7 Sum of digits of 4267 = 19 and 7 is divisible by 7. Hence, we need to remove 5 to this number for it to be divisible by 7 Correct Option:E #### E QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)100]%=50% Answer A) 50. #### A QUESTION:Simplfy b - [b -(a+b) - {b - (b - a+b)} + a] options: A)a B)2a C)4a D)0 E)1 SOLUTION:Explanation: b-[b-(a+b)-{b-(b-a+b)}+a] =b-[b-a-b-{b-(2b-a)}+a] =b-[-a-{b-2b+a}+a] =b-[-a-{-b+a}+a] =b-[-a+b-a+a] =b-[-2a+b+a] =b-b+a =a Option A #### A QUESTION:The population of a bacteria colony doubles every day. If it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? options: A)512 B)768 C)1024 D)2048 E)4096 SOLUTION:2^11(2) = 2^12 = 4096 The answer is E. #### E QUESTION:In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? options: A)112% B)12% C)333% D)150% E)16% SOLUTION:It is given that in a school the number of girls is 30% the number of boys. If boys=10 girls=3 We are asked for the number of boys as a percentage of girls b/g=10/3=10 1/3=3.333=333% Answer is C #### C QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 6km/hr. Total time of travel is 9 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)90km SOLUTION:t=d/s, so 9=x/21/5+x/21/6(because half distance with 5 km/ph, and remaining half with 6km/hr) 9=x(18/120) x=60km ANSWER:C #### C QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Option A #### A QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:Which of the following is NOT a prime number? options: A)21 B)31 C)41 D)11 E)51 SOLUTION:Ans is A A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number #### A QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/6 E)1/9 SOLUTION:Original share of 1 person =1/7 New share of 1 person =1/6 Increase =1/6 - 1/7 =1/42 Required fraction = (1/42)/(1/7)=1/6 Answer is D. #### D QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? options: A)6 B)8 C)6 D)5 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer:B #### B QUESTION:In a family 16 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family? options: A)28 B)26 C)22 D)31 E)21 SOLUTION:Total people eat veg = only veg + both veg and non veg Total= 16+12= 28 Answer = A #### A QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ? options: A)1 B)10 C)30 D)20 E)21 SOLUTION:This is a solution from Beatthegmat: even numbers: (60-2)/2 + 1 = 30 even integers. (60+2)/2 = 31 is the average of the even set. sum = avg(#of elements) = 3130 = 930 = a odd numbers: (59-1)/2 + 1 = 30 odd integers. (59+1)/2 = 30 is the average of the odd set. sum = avg(#of elements) = 3030 = 900 = b a-b = 930 - 900 = 30. Answer : C #### C QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)8 D)5 E)12 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 50 = 20 + 30 + 30 - (20) - 2x x = 5 So, answer will be D #### D QUESTION:In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/2 B)1/3 C)2/5 D)2/7 E)3/7 SOLUTION:P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5 C #### C QUESTION:In the graph below, no axes or origin is shown. If point B's coordinates are (10,4), which of the following coordinates would most likely be A's? options: A)(17, -2) B)(10, 6) C)(6, 8) D)(-10, 3) E)(-2, -17) SOLUTION:wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10. B rules.. #### B QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:When x divided by 288, the remainder is 47. Find the remainder when the same x is divided by 24? options: A)20 B)21 C)23 D)26 E)29 SOLUTION:23 Option C #### C QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B QUESTION:In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by options: A)64 B)8 C)4 D)64 E)1/64 SOLUTION:Say r=2 => V1 = 1/64 when r=1; V2 = 1/16 V2 = 4V1. Answer=C=4 #### C QUESTION:Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/21/5+x/21/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x50 = 200040 x=1600 2000 ------- 400 Answer: A #### A QUESTION:Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:Two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have ALL even (being multiple of 8) Probability of number selected being odd = Total Odd Numbers / Total available numbers Probability = 100/500 = 0.2 = 20% Answer: Option A #### A QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.1540 + 0.380 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is: options: A)600 B)450 C)350 D)500 E)620 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 40 Ã— 30) Cm(power)2 = 40 Ã— 15 = 600 Cm(power)2 Answer is A. #### A QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C <<<Examples ends QUESTION:The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area? options: A)10% B)11.1% C)25% D)30% E)35% SOLUTION:Sol. Required change = (10100)/(100-10)=11.1% B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:8^100 is divisible by 17. Find the remainder? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later? options: A) $8,000 B) $5,600 C) $3,200 D) $2,400 E) $4,800 SOLUTION:E. Market value in 1982= $ 8000 Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400 Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800 #### E QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup? options: A)1.5 B)1.75 C)2.14 D)2.34 E)2.64 SOLUTION:Let the total solution is 150 L with 80 L water70 L syrup. To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup. Therefore we are taking 55 L of syrup from initial solution and replacing with water. using urinary method: 70 L syrup in 150 L solution 55 L syrup in 117.9 L solution We started by multiplying 10 Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14. Correct option : C #### C QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:How much is 80% of 60 is greater than 4/5 of 25? options: A)15 B)28 C)16 D)12 E)73 SOLUTION:(80/100) * 60 â€“ (4/5) * 25 48 - 20 = 28 Answer: B #### B QUESTION:The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is: options: A)400 B)500 C)600 D)800 E)1000 SOLUTION:Let the sum be $. P. (P(1+10/100)^2-P)=525 P((11/10)^2-1)=2500 SUM = 2500 So SI = 500 ANSWER B #### B QUESTION:A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface. options: A)142 m sqaure B)122 m sqaure C)135 m sqaure D)188 m sqaure E)None of these SOLUTION:Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(62.25+92.25)]+96 = 122 m square Option B #### B QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K? options: A)1 B)3 C)4 D)2 E)6 SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b) So k is 2 Option D #### D QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D QUESTION:The G.C.D. of 1.08, 0.36 and 0.8 is: options: A)0.04 B)0.9 C)0.18 D)0.108 E)0.118 SOLUTION:Given numbers are 1.08, 0.36 and 0.80. H.C.F. of 108, 36 and 80 is 18, H.C.F. of given numbers = 0.04. Answer: Option A #### A QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)54 m B)64 m C)74 m D)84 m E)94 m SOLUTION:Let breadth = x metres. Then, length = (x + 28) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 28) + x] = 200 2x + 28 = 100 2x = 72 x = 36. Hence, length = x + 28 = 64 m B #### B QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 33=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? options: A)10000 B)18999 C)16990 D)16007 E)16991 SOLUTION:100 100 = 10000 125 * 80 = 10000 Answer:A #### A QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C24C1+4C14C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(150âˆ’90)=4/5âˆ—60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150âˆ’138=12 ANSWER:D #### D QUESTION:Find the value of y from the given equation. 9^y = 3^12, what is y? options: A)3 B)5 C)7 D)8 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)46 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 9) years. (x+9+10)=2(x�10) hence x=39. Present age of B = 39 years Answer: Option C #### C QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book? options: A)20 B)18 C)16 D)15 E)15.39 SOLUTION:Actually u can set up 2 equation P--stands for the pages D--stands for the days 1) PD=480 (we want to find the Days, soP=480/D) 2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000 as the 1) stated u can put 1) into 2) => 1000-5P+15D-75=1000 => 15D-5P=75 put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16) => D^2-5D-160=0 so D=15.39days. Ans: (E) #### E QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be? options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1 SOLUTION:Quantity of milk in 30 liters if mix = 302/3 =20 liters Quantity of milk in 35 liters of new mix = 20+5 = 25 liters Quantity of water in it = 35-25 = 10 liters Ratio of milk and water in new mix = 25:10 = 5:2 Answer is D #### D QUESTION:8 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The number of hours required to complete the work is 8818 = 1152 12 × 12 × (x) = 1152 x = 8 The answer is C. #### C QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 12 days. How many days more will P take to finish the work? options: A)12 B)15 C)18 D)20 E)22 SOLUTION:Let work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = 3/4 Remaining work = 1 = 3/4 = 1/4 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (1/4) / (1/48) = 12 Option A #### A QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)150 +x85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (10080)/(8001) = 10% Answer: E #### E QUESTION:A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)? options: A)1250 B)1280 C)1320 D)1340 E)1450 SOLUTION:Explanation: Speed = 5 km/hr Time = 15 minutes = 1/4 hour Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km = 5 × 1/4 × 1000 metre=1250 metre Answer: Option A #### A QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:(a/2)/(b/c) In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6 SOLUTION:(a/2)/(b/c) = (ac)/2b The expression will have the largest value when numerator (ac) is the largest. = (24)/21 =8/2 Answer A #### A QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: options: A)42 B)43 C)46 D)47 E)49 SOLUTION:A 42 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) 125 : 150 :: 35 : x 125 x x = 150 x 35 x = (150 x 35)/125 x = 42 #### A QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The product of 2 integers is negative Thus an odd number of integers need to be negative to have a negative product We are asked at most how many are required. So, the highest odd integer before 6,i.e. 1 Correct Option : A #### A QUESTION:In the x-y plane, the area of the region bounded by the graph of \|x+y\| + \|x-y\| = 10 is options: A)8 B)625 C)16 D)20 E)24 SOLUTION:I've never seen such kind of question in GMAT before. OK there can be 4 cases: \|x+y\| + \|x-y\| = 10 A. x+y+x-y = 10 --> x=5 B. x+y-x+y = 10 --> y=5 C. -x-y +x-y= 10 --> y=-5 D. -x-y-x+y=10 --> x=-5 The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be2525=625 Answer: B #### B QUESTION:9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90% B)85% C)80% D)75% E)70% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1sd; mean+1sd} = {10-10.25; 10+0.25} = {9.75; 10.25}. From the 8 listed numbers, 5 are within this range so 5/8=75%. Answer: D. #### D QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a * 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:The value of (34.50.4731.567)/(0.067323.257.57) is close to options: A)2 B)1.15 C)2.05 D)2.16 E)2.35 SOLUTION:(34.50.4731.567)/(0.067323.257.57) = 25.5710895/11.845 = 2.16 ANSWER:D #### D QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 393 A=3G P=2.5G 3G+2.5G+G= 393 G=393/6.5= 18 A= 63=54 Difference = 36 'D' is the answer #### D QUESTION:The area of a triangle is with base 18m and height 6m? options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2 SOLUTION:1/2 * 18 * 6 = 54 m2 Answer: D #### D QUESTION:Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1 options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8 SOLUTION:[log10a + log10b = log10 ab] and also 1 can be written as log10 10, so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)), this can be solved to get 12x+3=10x+10, that gives x=7/2=3.5 ANSWER:B #### B QUESTION:A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? options: A)2ft. 7 inches B)4ft. 7 inches C)1ft. 7 inches D)3ft. 7 inches E)None of them SOLUTION:Length of board=7ft. 9 inches=(712+9)inches=93 inches. Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches Answer is A. #### A QUESTION:110 is increased by 50%. Find the final number. options: A)100 B)110 C)150 D)155 E)165 SOLUTION:Final number = Initial number + 50%(original number) = 110 + 50%(110) = 110 + 55 = 165. Answer E #### E QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 15 = 45 => x = 60 km/hr. Answer:A #### A QUESTION:The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9.33% B)9.44% C)9.45% D)9.56% E)9.67% SOLUTION:69(90/100)((100-x)/100) = 56.16 x = 9.56% ANSWER:D #### D QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $140 B) $160 C) $220 D) $240 E) $264 SOLUTION:12$ per week! An year has 52 weeks. Annual charges per year = 52* 12 = 624$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 30 = 360$ 624 - 360 = 264 Ans E #### E QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 20x = 80 x = 4. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. Answer: B #### B QUESTION:we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight options: A)19 B)18 C)24 D)21 E)32 SOLUTION:select 5 weight out of 7, 7C5=21 ANSWER:D #### D QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:Light glows for every 16 seconds . How many times did it between 1:57:58 and 3:20:47 am options: A)311 B)322 C)313 D)314 E)385 SOLUTION:the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/16 = 310. so total 311 times light ll glow ANSWER:A #### A QUESTION:In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k? options: A)y = -7/3x + 3m B)y = 3/7x - 7m C)y = 7/3x + 3m D)y = 3/7x + 3m E)y = -3/7x - 7m SOLUTION:The slope of the line is 3m/7m=3/7. The y-intercept is 3m. the equation of the line is: y = 3/7x +3m The answer is D. #### D QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k * 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? options: A)16 B)24 C)26 D)30 E)160 SOLUTION:One of the approaches: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20. But each of these 3 couples can send two persons (husband or wife): 222=2^3=8. Total # of ways: 6C32^3=160. Answer: E. #### E QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students? options: A)17 years B)16 years C)15 years D)14 years E)13 years SOLUTION:Sum of the ages of 14 students = (18 35) - (20 * 25) = 630 - 500 = 130 Required average = (130/10) = 13 years. Answer:E #### E QUESTION:If ab-a-b=265 bc-b-c=155 ac-c-a=150 then find a? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:(A-1)(B-1)=AB-A-B+1=265+1=266..(1) (B-1)(C-1)=BC-B-C+1=155+1=156..(2) (C-1)(A-1)=CA-C-A+1=150+1=151..(3) (1)/(2) gives..(A-1)/(C-1)=266/156..(4) (3)(4) gives..(A-1)^2=257.47...A=17.04 Solving other equations..B=17.58 and C=10.4 ANSWER:B #### B QUESTION:Each student at a certain university is given a four-character identification code, the rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? options: A)135,200 B)67,600 C)64,000 D)60,840 E)58,500 SOLUTION:First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B #### B QUESTION:If 5^29 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 210^p 5^(29) 2 ^ (30) = 2 * (25)^p 5^(29) 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score R for the exam? options: A)74 B)76 C)78 D)80 E)82 SOLUTION:A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d Solving above for Mean R= 74. Answer: A. #### A QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5a1 + 7b1 = t 5a2 + 7b2 = t 5(a1 - a2) = 7(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7q and b2 - b1 = 5q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 512 + 72 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 57 + 75 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:Which of the statements is true for 3111 & 1714 options: A)11 B)88 C)66 D)17 E)16 SOLUTION:Answer:B #### B QUESTION:A scooter costs 30,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years? options: A)10,000 B)12,500 C)12,800 D)12,000 E)15,360 SOLUTION:After first year, the value of the scooter = 24,000 After second year, the value of scooter = 19,200 After third year, the value of scooter = 15,360 Answer E #### E QUESTION:Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range? options: A)3 B)4 C)cannot be determined D)6 E)8 SOLUTION:Yes, the correct answer is C #### C QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream? options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these SOLUTION:Explanation : Speed downstream = 96⁄8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12-4 = 8 kmph Speed upstream = 8-4 = 4 kmph Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B QUESTION:If w,x,y,z are consecutive positive integers ; then which of the following is always odd? [1] wx+(y+2)^2z [2] w^x + z^y [3] 13x^2 options: A)1 B)2 C)3 D)1 and 2 E)2 and 3 SOLUTION:Plug in some numbers w = 1 x = 2 y = 3 z = 4 Check the options - [1] wx+(y+2)^2z = 12 + (3+2)^2 4 => 2 + 254 = 102{ Not an odd Number } [2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number } [3] 13x^2 = 134 =52 even [2] B #### B QUESTION:If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a prime number D)It is a multiple of 5 E)It is a multiple of 2 SOLUTION:n+12 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 12, n + 13, n + 14, n + 15 Sum = 4n + 54 This sum will always be even. Option E #### E QUESTION:22.085 Ã— 0.001 = ? options: A)0.22085 B)2.2085 C)0.022085 D)0.0022085 E)None of these SOLUTION:22.085 Ã— 0.001 = ? or,? = 0.022085 Answer C #### C QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)14% B)23% C)30% D)50% E)100% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.410 = 14 Wage of Charles = 1.6 10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100% = 2/14 * 100% =14% Answer A #### A QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x options: A)14 B)15 C)16 D)17 E)18 SOLUTION:There are two series here 1, 12, 23, 34, ... (Increase by 11) 2, 7, 12, ... (Increase by 5) Hence, next term is 12 + 5 = 17 Correct Answer Choice is D #### D QUESTION:A man sells a horse for Rs.920 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? options: A)287 B)279 C)267 D)860 E)940 SOLUTION:CP = SP + 1CP = SP - g 920 + x = 980 - 2x 3x = 60 => x =20 CP = 920 + 20 = 940 Answer:E #### E QUESTION:What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum? options: A)288 B)266 C)120 D)277 E)6123 SOLUTION:Let the present worth be Rs. x. Then, S.I. = (132 - x) (x * 5 * 2) / 100 = (132 - x) 10x = 13200 - 100x 110x = 13200 => x = 120. Answer: C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 * 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)22772 B)24000 C)23877 D)23789 E)28222 SOLUTION:Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer: B #### B QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9) SOLUTION:The number of possible 4-digit codes is 36^4. The number of possible 5-digit codes is 36^5. The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4) The answer is A. #### A QUESTION:The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers options: A)9 B)10 C)15 D)18 E)17 SOLUTION:The only possible sum for 4 different squares of an integer with total sum number is 95 are : 49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17) or 81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15) hence the answer is (E) #### E QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0-10 inclusive to find one smallest other two should be highest so, lets assume three var are a,b,c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 E #### E QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2â„5 Ã— 300 - 3â„5 Ã— 125 = 120 - 75 = 45 Answer D #### D QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 3 5 b Therefore (3 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 b Therefore, b = 3^3 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 57 = 35 Correct answer A. #### A QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed? options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days SOLUTION:Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work. => In one day A came complete 1/9th of the task(x/9) => In one day B can complete 1/12th of the job.(x/12) First day x/9th work will be done next day x/12th and so on: Together A and B can do x/9 + x/12 work. =>(x/9) + (x/12) = 7/36th work done In 10 days 35/36th of the work will be done. On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work. So, 1/36th work will be done in 1/4 days. =>10.25 days ANSWER: D #### D QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528(80/100)(90/100) = 380 Answer: C #### C QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is options: A)Rs. 150 B)Rs. 170 C)Rs. 180 D)Rs. 190 E)None of these SOLUTION:Explanation: Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2 = 24 : 24 : 12 = 2 : 2 : 1 Money earned by children = 950 x (1/5) = Rs. 190 Answer: Option D #### D QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)$2,750 B)$5,500 C)$11,000 D)$22,000 E)$44,000 SOLUTION:SI for 1st year = 550/2=275 275+275+SI on (275)=605==> SI on 275=55==> SI on 275 = 275R1/100=55 R=20% Now using SI for 2 years on T/2 of the money (T/2)202/100=550 T=5505= 2750 ANSWER:A #### A QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways SOLUTION:6 people can be prized with distinct prizes in 6^6 ways ANSWER:A #### A QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each for the dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total money spent by them? options: A)Rs1628.40 B)Rs1536 C)Rs1492 D)Rs1498 E)none of these SOLUTION:(1379)+(6(x+4)) = 19x 1027 + 6x + 24 = 19x 1051 = 13x x = 1051/13 total money = 19x = 1536 ANSWER:B #### B QUESTION:What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1200 B)1256 C)1349 D)1456 E)1590 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 6 = 18. Hence the number is 1349 C #### C QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability. options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53 SOLUTION:Explanation : There are total 4 letters. The probability that P gets the first position is 1/4. The probability that O is in the second position is 1/3. Likewise, probability for C and Y are 1/2 and 1/1. Hence, the required probability is:- => (1/4) x (1/3) x (1/2) x 1. => 1/24. Answer : C #### C QUESTION:How many minutes does the minute hand gain in every one hour? options: A)55 B)60 C)65 D)No gain E)None of these SOLUTION:55 ANSWER:A #### A QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector? options: A)1/120 B)1/100 C)1/80 D)1/60 E)1/40 SOLUTION:The largest angle is 87. Let d be the difference between any two angles in the progression. The sum of all the angles will be: 87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d The sum of all the central angles in a circle = 360 696 - 28d = 360 d = 336/28 = 12 The smallest sector is (87-7d) = 87-712 = 3 3/360 = 1/120 The answer is A. #### A QUESTION:A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group? options: A)5.55% B)16.67% C)15.75% D)20.45% E)25% SOLUTION:The question basically asks about the probability that Bob and Lisa sit at the ends. The total # of sitting arrangements is 4!. Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 22!. P=(favorable)/(total)=(22!)/4!=1/6. Answer: B. #### B QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x 104.76/100 * 104.76/100 = 8840 x1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B <<<Examples ends QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph SOLUTION:US = 20 DS = 35 M = (35 - 20)/2 = 7.5 Answer:B #### B QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive? options: A)$444 B)$445 C)$446 D)$447 E)$448 SOLUTION:A+B+C = 1200 Given ratio 10:12:13 Let us say the shares of A,B,C deducting 10,20,15 be a,b,c a+b+c = 1200-45= 1155 = 35K c share = (1155X13)/35 = 429 C = chandran share = 429+15 = 444 Option A #### A QUESTION:Find the odd man out 2, 5, 14, 41, 122, 365, 1125 options: A)2 B)14 C)41 D)365 E)1125 SOLUTION:13-1 = 2 23-1 = 5 53-1 = 14 143-1 = 41 413-1 = 122 1223-1= 365 3653-1= 1094 ANSWER:E #### E QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is: options: A)364724 B)365387 C)365737 D)366757 E)366767 SOLUTION:Required number= 999366+103 = (1000-1)366+103 = 366000-366+103 = 365737. ANSWER:C #### C QUESTION:Calculate the number of bricks, each measuring 25 cm 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)23 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Answer: Option B #### B QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y: options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180. Answer C #### C QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer: Option D #### D QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 64 litres of milk = (1⁄4 × 64) litres = 16 litres. Answer A #### A QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|a\| = -a \|b - 4\| + \|ab + b\| = ? options: A)a) ab - 4 B)b) 2b - ab - 4 C)c) ab + 4 D)d) ab - 2b + 4 E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab + b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab + b =ab + 4 Answer: Option C #### C QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? options: A)$8 B)$14 C)$5 D)$15 E)$0 SOLUTION:1/5 x $60 = $12 for sandwich 1/6 x $60 = $10 for museum 1/2 x $60 = $30 for book $12 + $10 + $30 = $52 spent $60 - $52 = $8 left over correct answer A #### A QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|a\| = -a, \|b-3\| + \|ab-b\| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: \|ab\| = ab and \|a\| = -a Question: \|b-3\| + \|ab-b\| = ? ** Looking at \|ab\| = ab tells us that a and b are either both positive or negative Looking at \|a\| = -a tells us that a must be negative ** Combine two observations: a and b are both negative values Let a=-1 and b=-1 \|b-4\| + \|ab-b\| = \|-1-3\| + \|1-(-1)\| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)56 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 5 hours 00 minutes = 300 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (300 â€“ 20)/5 = 56 minutes ANSWER A #### A QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)500 B)350 C)828 D)277 E)122 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/489 = 50/3 3x + 900 = 2400 => x = 500 m. Answer: A #### A QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is? options: A)10 B)20 C)50 D)30 E)40 SOLUTION:Man's speed with the current = 15 km/hr => speed of the man + speed of the current = 15 km/hr speed of the current is 2.5 km/hr Hence, speed of the man = 15 - 2.5 = 12.5 km/hr man's speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km/hr Answer is A. #### A QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)22 seconds B)77 seconds C)40 seconds D)57 seconds E)57 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 (2/25) = 40 seconds Answer:C #### C QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning. options: A)36 B)39 C)42 D)45 E)None of the above SOLUTION:Let the average after 17th inning = x. Then, average after 16th inning = (x – 2). ∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55. Answer E #### E QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? options: A)662 B)678 C)652 D)642 E)721 SOLUTION:8 * 86 = 688 – 10 = 678 ANSWER:B #### B QUESTION:A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. options: A)1/7 B)1/12 C)1/14 D)1/18 E)1/21 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 2 bottles of apple juice is 6C24C4 = 151 = 15 P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14 The answer is C. #### C QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/510000=2000 Answer is A #### A QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)11 B)77 C)36 D)47 E)99 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:The area of a triangle is with base 4m and height 6m? options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 4 * 6 = 12 m2 Answer: E #### E QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony? options: A)182kmph B)192kmph C)193kmph D)196kmph E)190kmph SOLUTION:pony take 20 hours and horse take 12 hours...then Distance chased by them is 32012.so speed of pony is (32012)/20=192kmph. ANSWER IS B #### B QUESTION:20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)7/30 B)3/14 C)9/38 D)4/21 E)5/26 SOLUTION:P(1st ball is even) = 10/20 P(2nd ball is also even) = 9/19 P(both balls are even) = 10/20 * 9/19 = 9/38 The answer is C. #### C QUESTION:For what value of â€œkâ€ will the equation (2kx2 + 5kx +1)=0 have equal roots? options: A)2/7 B)9/4 C)8/25 D)7/1 E)7/2 SOLUTION:for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0 in the given equation (5k)^2-42k1=0 by solving this equation we get k=0, k=8/25 ANSWER:C #### C QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A QUESTION:An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? options: A)4.04 B)4.02 C)4.01 D)4.05 E)4.06 SOLUTION:Formula for Calculation of Percentage error is: =(x−y−(xy)/100)% =(2+2+(2×2)/100)%=4.04% Answer is A. #### A QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7% SOLUTION:Explanation: SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)299 meter C)666 meter D)155 meter E)144 meter SOLUTION:Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State? options: A)7000 B)7200 C)7400 D)7600 E)8000 SOLUTION:State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 E) #### E QUESTION:A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? options: A)A)$200 B)B)$1000 C)C)$819 D)D)$1200 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 55X+44X+1X=8600 25X+16X+X=8600 42X=8600, X=204.76. Daughter receives four times of nephew so 4 204.76= 819. So Each Daughter receives $800. answer is option C) $819. #### C QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)1178 B)144 C)66 D)8 E)55 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways. Hence the total ways are 24 * 6 = 144. Answer: B #### B QUESTION:By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? options: A)9 B)4 C)8 D)7 E)65 SOLUTION:80% --- 12 120% --- ? 80/120 * 12 = 8 Answer: A #### A QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 * price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes SOLUTION:A method has been discussed here to nullify the calculations though. All I can input here is, speed of a crew in still water = 1/2 ( speed upstream + speed downstream) approximating this for time, t = 1/2(84+ (t-7)) giving t = 77 C #### C QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class? options: A)40 B)50 C)28 D)38 E)48 SOLUTION:As half the circle shape consist of 33-8=25 boys, So total number of boys in full circle=225=50 ANSWER: B #### B QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)? options: A)8 B)22 C)10 D)14 E)12 SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2 = 12 Answer: E #### E QUESTION:The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m. correct answer A)50 #### A QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate? options: A)134 B)178 C)195 D)166 E)194 SOLUTION:C 195 The number of votes the winning candidate received was 963 + 53 + 79 + 105 /4= 300. The second received 300 – 53 = 247, The third received 300 – 105 = 195. #### C QUESTION:On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price Q per glass on the second day? options: A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45 SOLUTION:On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade; On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade; So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3. We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day. Say the price of the glass of the orangeade on the second day was $x then 20.6=3x --> x=$0.4. Answer: D. #### D QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway? options: A)1 min B)2 min C)3 min D)4 min E)5 min SOLUTION:C 3 min d = 24 1/4 m + 54 m = 60 m T = 60 meters / 20 meters/min = 3 min #### C QUESTION:If n is an integer, which of the following must be an even integer? options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10 SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 ) A: n^2-n-1 = -1 { If n = 1 } B: n^2-4n+6 = 3 { If n = 1 } C: n^2-5n+5 = 1 { If n = 1 } D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 } E: n^2+2n+10 = 13 { If n = 1 } Thus the only possible answer is (D) #### D QUESTION:What is the are of an equilateral triangle of side 8 cm? options: A)64√5 B)64√9 C)16√3 D)64√3 E)64√2 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2; Answer: C #### C QUESTION:What is the sum of the different positive prime factors of 1092? options: A)5 B)12 C)20 D)25 E)27 SOLUTION:First, we make a prime factorization by dividing 1096 by 2 then 3, etc. 1096=2^23713 22+3+7+13=27 Answer (E) #### E QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled? options: A)px/B B)px/(B(B - P)) C)x/(B - P) D)p/(B - Px) E)p/(B(B - p)) SOLUTION:No of cakes each parent has to bake : x/B No of parents did not bake cake = p No of cakes that were not baked by p parents = px/B No of parents has to bake additional cakes = B-p additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - P)) Answer B #### B QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)22 B)28 C)27 D)80 E)21 SOLUTION:1/2 d (10 + 6) = 640 d = 80 Answer:D #### D QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:Ayesha's father was 31 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)1 years SOLUTION:Explanation: Mother's age when Ayesha's brother was born = 34 years. Father's age when Ayesha's brother was born = (31 + 4) years = 35 years. Required difference = (35 - 34) years = 1 years. Answer: E #### E QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ? options: A)9:6 B)3:2 C)118:126 D)193:122 E)201:132 SOLUTION:m=portion of milk in solution m=(4/7+2/3+3/5)/3➡193/315 315-193=122 122/315=portion of water in solution ratio of milk to water=193/122 ANSWER:D #### D QUESTION:A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount? options: A)30% B)125% C)25% D)20% E)16.66% SOLUTION:Explanatory Answer The easiest way to solve these kinds of problems is to assume a value for the merchant's cost price. To make calculations easy, it is best to assume the cost price to be $100. The merchant marks his goods up by 50%. Therefore, his marked price (quoted price) = cost price + mark up. Marked price = $100 + 50% of $100 = 100 + 50 = $150. The merchant offers a discount of 20% on his marked price. Discount offered = 20% of 150 = $30. Therefore, he finally sold his goods for $150 - $30 = $ 120. We assumed his cost to be $100 and he sold it finally for $120. Therefore, his profit = $20 on his cost of $ 100. Hence, his % profit = profit/cost price * 100 = 20/100 * 100 = 20%. Choice D #### D QUESTION:Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids? options: A)8 B)9 C)3 D)7 E)10 SOLUTION:cost of each apple = 4 dollars Apples that Benny can buy with the amount she has=360/4 = 90. Apples that each kid gets evenly = 90/9 =10 Apples. So the answer is E=10 #### E QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 * 5/6 = 5 #### C QUESTION:Set A: {1, 3, 4, 6, 9, 12, 15} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3? options: A)3/14 B)2/7 C)9/14 D)5/7 E)11/14 SOLUTION:Probability of an event = (# of favorable outcomes) / (total # of outcomes). There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so P=C35C37=27P=C53C73=27. Answer: B. #### B QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=66 = 36 (6^3)= 366 = .16 (6^4)= .166 = ..96 (6^5) = ..966 = ..76 (6^6) = ..766 = ...56 (6^7) = ....566 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is? options: A)4km/h B)3km/h C)2km/h D)(1/2) km/h E)E)None SOLUTION:100 --- 10 DS = 10 ? ---- 1 80 ---- 20 US = 4 ? ----- 1 S = (10 - 4)/2 = 3 kmph ANSWER:B #### B QUESTION:John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour? options: A)30 B)40 C)50 D)55 E)70 SOLUTION:HiBunuel THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55. The question is correct. Here's the explanation: Let distance be D. We can find the total timeequate it, which comes as: 0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D). #### D QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)135 m B)786 m C)566 m D)546 m E)445 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec Length of the train = speed * time = 15 * 9 = 135 m Answer: A #### A QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? options: A)65 sec B)88 sec C)25 sec D)88 sec E)55 sec SOLUTION:D = 100 + 150 = 250 S = 36 * 5/18 = 10 mps T = 250/10 = 25 sec Answer: C #### C QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N * 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:(((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a then what is the units digit for a/((13!)^4)= options: A)7 B)8 C)9 D)6 E)5 SOLUTION:(((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a solving it , we get a/((13!)^4)= ((13!)^4-1) last digit of (13!)^4 will be 0. so last digit of ((13!)^4-1) will be 9. ANSWER:C #### C QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100100=10,000. Now, the area obtained with wrong measurements would be 11695=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C QUESTION:The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − 2)...3.2.1 is not divisible by n is options: A)5 B)7 C)13 D)14 E)16 SOLUTION:Explanation : (n-1)! is always divisible by n unless and untill n is a prime number e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number Therefore, find all prime numbers in the range of 12 to 40 i.e 13, 17, 19, 23, 29, 31 and 37 Hence, the number of positive integers n is 7. Answer : B #### B QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? options: A)25/42 B)25/46 C)25/41 D)25/49 E)25/23 SOLUTION:Total fruits = 9 Since there must be at least two apples, (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer:A #### A QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? options: A)25 B)30 C)45 D)20 E)50 SOLUTION:6p2 = 6 x 5 = 30 B) #### B QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 162 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B QUESTION:The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)11:00 am B)12:00 noon C)1:00 pm D)2:00 pm E)3:00 pm SOLUTION:In ninety minutes, the first train travels 90 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train in 4.5 hours. The second train will catch the first train at 1:00 pm. The answer is C. #### C QUESTION:By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)20% B)30% C)40% D)50% E)60% SOLUTION:(SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)100]%=50% ANSWER D #### D QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 140.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is: options: A)720 B)900 C)1200 D)1800 E)1900 SOLUTION:2(15 + 12) x h = 2(15 x 12) h = 180/27m =20/3 m. Volume = 15 x 12 x20 m3= 1200 m3. ANSWER:C #### C QUESTION:Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 8 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? options: A)24 B)30 C)40 D)50 E)60 SOLUTION:One way to do this would be weighted average method.. 1) let the average of 5 mocks be x... so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67... By alligation/weighted average.. the difference in 760 and 726.67 is 5/6 of difference of 760 and x.. 760-726.67 = 5/6 (760-x) 760-x= 33.336/5=40... so x = 720.. the last of mock test will be 720+8+8=736... so ans = 760-736=24 A #### A QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -3 < x < 7 - true because x can be between -3 < x < 7 E. none of the above. Answer: D #### D QUESTION:If b does not equal zero, and ab = b/2, what is the value of a? options: A)A)1/8 B)B)1/4 C)C)1/3 D)D)1/2 E)of the above SOLUTION:Explanation: To solve for a, divide both sides of the equation by b: ab = b/2 (ab)/b = (b/2)/b a = (b/2)1/b a = 1/2 Answer: (D). #### D QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit? options: A) 50/349 B) 1/313 C) 1/49 D) 1/100 E) 1/50 SOLUTION:Hundreds digit has to be 3 . So units digit needs to 3 as well And both Hundreds and Units digit needs to be 2 more than ten's digit The number is 313 Total numbers between 300 and 349 = (349-300)+1 = 50 Probability = 1/50 Answer E #### E QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? options: A)287 B)27 C)28 D)25 E)28 SOLUTION:[50/x + 50/(x/2)] – 100/x = 2 x = 25 Answer: D #### D QUESTION:Which of the following is closer to √0.8+√0.05? options: A)0.5 B)0.7 C)0.9 D)1.1 E)1.2 SOLUTION:√0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D. #### D QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) * 15 = 45 Answer is C #### C QUESTION:P and Q are the only two applicants qualified for a short-term research project that pays 300 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? options: A)$5 B)$10 C)$15 D)$20 E)$25 SOLUTION:Let Q's hourly wage be x, then P's hourly wage is 1.5x Let T be the number of hours that Q needs, then P needs T-10 hours to do the job. Since they both are paid an equal total amount of $300: xT=1.5x(T-10) T = 30 hours and Q's hourly wage is 300/30 = $10 P's hourly wage is 300/(T-10) = $15 which is $5 per hour more. The answer is A. #### A QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)5 kmph B)1 kmph C)6 kmph D)2 kmph E)3 kmph SOLUTION:The current of a stream = 1 The speed of the motor boat in still water= x Speed downstream = x + 1 Speed upstream = x - 1 since distance = speed Ã— time, we have 35/(x + 1) + 35/(x - 1) = 12 kmph=6 kmph Answer : Option C #### C QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)None of these SOLUTION:Explanation : Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer : Option C #### C QUESTION:There are 5 physics books and 1 chemistry book on shelf P and 3 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student? options: A)1/42 B)1/36 C)1/30 D)1/24 E)1/18 SOLUTION:P(a chemistry book is moved to shelf Q) = 1/6 P(a chemistry book is then chosen from shelf Q) = 1/4 P(the student takes a chemistry book) = 1/6 1/4 = 1/24 The answer is D. #### D QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally? options: A)10 men B)30 men C)40 men D)20 men E)none of these SOLUTION:Let x be the number of men originally Thus, 10x=(10+10)(x-10) 10x=20(x-10) x=2(x-10) x = 20 ANSWER:D #### D QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)ab D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 259x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:If shares of two persons in profits are Rs.600 and Rs.1000 then ratio of their capitals is options: A)3:5 B)2:3 C)4:3 D)1:3 E)1:2 SOLUTION:profit=timecapital so 600:1000=3:5 ANSWER:A #### A QUESTION:If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days? options: A)65mtr. B)52mtr C)70mtr. D)112mtr. E)17mtr. SOLUTION:20 men is 6 days can build 112 metres 25 men in 3 days can build = 112(40/20)x(3/6) = 112 meters Answer: D. #### D QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X. options: A)16.8% B)17.4% C)17.9% D)18.5% E)19.1% SOLUTION:Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20 Selling price of an orange = 10 --> Cost price = 10/1.25 = 8 A > O 23(A) + 10(O) = 653 653 - 23(A) has to be divisible by 10 --> Units digit has to be 0 Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value Between 11 and 21, If A = 11, O = 30 --> Not possible If A = 21, O = 17 --> Possible Cost price = 2021 + 817 = 420 + 136 = 556 Profit = 653 - 556 = 97 Profit% X= (97/556)100 = 17.4% Answer: B #### B QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18(K+(K+1)+...+(K+N-1)) = 18(N(2K+N-1)/2). So the average is 153=[18(N(2K+N-1)/2)]/N = 18(2K+N-1)/2 = 9 (2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---). By ), *) we have K=2, N=14. Since 153/18 = 8.5, 188<153<189. So the number of terms R which are smaller than the average is 182, 183, ..... ,188 ---> 7. The answer is C. #### C QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:A shop owner sells 40 Pencils and gains SP of 15 pencils. Find the gain %? options: A)55% B)40% C)50% D)60% E)78% SOLUTION:Gain=15 oranges Total 40 oranges CP 40-15=25 (15/25)100 =60% Ans D #### D QUESTION:In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number? options: A)24 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=2x Therefore x + 2x = 6 ‹=›3x = 6 ‹=›x= 2. So, ten's digit = 2, unit's digit = 4. Hence, the required number is 24. Answer A #### A QUESTION:Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? options: A)2777 B)2888 C)8400 D)2882 E)2781 SOLUTION:Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 13800 14/23 = Rs. 8400. Answer: C #### C QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) 3600/1000 = 54 km/h The answer is D. #### D QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr? options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 160 * 5/18 = 44 m/sec Time taken = 120/44 = 2.7 sec. Answer: C #### C QUESTION:For any integer p, p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between 4 + 3 and 4 + 4, inclusive? options: A) None B) One C) Two D) Three E) Four SOLUTION:Generally p or p! will be divisible by ALL numbers from 1 to p. Therefore, 4 would be divisible by all numbers from 1 to 4. => 4+3 would give me a number which is a multiple of 3 and therefore divisible (since 4 is divisible by 3) In fact adding anyprimenumber between 1 to 4 to 4 will definitely be divisible. So the answer is none (A)! Supposing if the question had asked for prime numbers between 4 + 3 and 4 + 11 then the answer would be 1. For 4 +3 and 4 + 13, it is 2 and so on... A #### A QUESTION:A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? options: A)2% B)6% C)14% D)28% E)63% SOLUTION:case 1: (7/90)=x/100 x=8% case 2: (9/63)=y/100 y=14% So percent increase is =(y-x)=(14-8)%=6% Answer is B #### B QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y? options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5 SOLUTION:Explanation: 30 x = 50 y x: y = 30: 50 = 3 : 5 Answer:B #### B <<<Examples ends QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these SOLUTION:Explanation : 100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/- Answer : D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781 options: A)386 B)187 C)781 D)682 E)564 SOLUTION:Explanation : In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A QUESTION:What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ? options: A)17/36 B)36/17 C)17/6 D)85/2 E)51/4 SOLUTION:2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12 1/5 - 1/6 = (6-5)/30 = 1/30 So 17/12/1/30 = 17/12 * 30 = 85/2 Answer - D #### D QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5/18 = 10/3 m/s Hence time taken to cover 60 m = 603/10 = 18 seconds. Answer: D #### D QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:The product of all the prime numbers less than 25 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^8 E)10^5 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19,23 =2.2 10^8 D #### D QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77 SOLUTION:Solution P( None is defective) = 18C2 / 22C2 = 51/77 P( at least one is defective) = (1- 51/77) = 26/77. Answer E #### E QUESTION:The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x? options: A)2/5 B)3/4 C)4/5 D)5/4 E)2/7 SOLUTION:a/b = 4/5 m/x = (2/5)5 / (7/4)4 = 2/7 The answer is E. #### E QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)120 E)200 SOLUTION:6C34C2 =120=D #### D QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse? options: A)A)5 B)B)8 C)C)10 D)D)15 E)E)30 SOLUTION:Total number of ways to choose 6 chairs from 5= 6C2=15 Total number of combination=150 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C3=10..... 1015=150 Answer is 5... A #### A QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is options: A)not an even B)an even C)a perfect square D)an odd E)a prime SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1 y = x^2 - x - 2 y = (x-2)(x+1) (Note that one factor is even and one factor is odd.) Then y must be even. The answer is B. #### B QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone. options: A)6 Â½ days B)1 Â½ days C)8 Â½ days D)5 Â½ days E)2 Â½ days SOLUTION:Explanation: 3/20 2 + (2 + x)/5 = 1 x = 1 Â½ days Answer:B #### B QUESTION:One card is drawn from a pack of 52 cards. What is the probability that the card drawn is not a face card? options: A)4/15 B)5/17 C)9/13 D)3/13 E)7/15 SOLUTION:Out of 52 cards there will be 16 face cards are there. probability of getting not a face card = 36/52 = 9/13 Answer is C #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)8 B)15 C)16 D)18 E)None SOLUTION:Solution Capacity of the tank = (12×13.5) litres = 162 litres. Capacity of each bucket = 9 litres. Number of buckets needed = (162/9) ‹=› 18. Answer D #### D QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd. options: A)8/16 B)9/16 C)10/16 D)11/16 E)7/16 SOLUTION:since, p(odd)=3p(even) and p(odd)+p(even)=1 hence p(odd)=3/4 now only oddodd=odd hence two odd i s p(odd)=3/43/4=9/16 ANSWER:B #### B QUESTION:Find the remainder of the division (3^33)/7. options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Find the pattern of the remainders after each power: (3^1)/7 remainder 3 (3^2)/7 remainder 2 (3^3)/7 remainder 6 (3^4)/7 remainder 4 (3^5)/7 remainder 5 (3^6)/7 remainder 1 -->this is where the cycle ends (3^7)/7 remainder 3 -->this is where the cycle begins again (3^8)/7 remainder 2 Continuing the pattern to (3^33)/7 gives us a remainder of 6 Final Answer: E) 6 #### E QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is options: A)25% B)35% C)20% D)23% E)30% SOLUTION:Suppose S.P of 50 mangoes = Rs 50 Therefore, Gain = Rs 10 => C.P = Rs 40 Gain % = 10/40 x 100 = 25% Gain = 25% ANSWER:A #### A QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 2006 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:. The average of first ten prime numbers which are odd is? options: A)22.9 B)28.1 C)12.9 D)15.8 E)11.2 SOLUTION:Explanation: Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x? options: A)13 B)14 C)15 D)16 E)17 SOLUTION:134-132=2 46-44=2 x-12=2 x=14 ANSWER:B #### B QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train? options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes SOLUTION:we don't need to assume here the direction.we need to find which will take less time so there are 2 cases 1)both moving in same direction...then time would be 2 minutes 2)both moving in opp direction then time would be 0.8 minutes as we need the shortest time it would be the second case Answer:E #### E QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers? I. LCM : 24; HCF : 6 II. LCM : 18; HCF : 8 III. LCM : 16; HCF : 9 options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III SOLUTION:We need to keep two things in mind here: 1. Product of two numbers = LCMHCF 2. LCM should be a multiple of HCF Only Statement I follows these two rules. Correct Option A #### A QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:1 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work? options: A)12/9 days B)15/4 days C)82/8 days D)22/76 days E)3/2 days SOLUTION:1M = 6W ---- 20 days 12M + 8W -----? 72W + 8 W = 80W ---? 6W ---- 20 80 -----? 6 * 20 = 80 * x => x = 3/2 days Answer:E #### E QUESTION:Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? options: A)24/64 B)32/64 C)36/64 D)40/64 E)42/64 SOLUTION:Expected value of one die is 1/6(1+2+3+4+5+6)=3.5. Expected value of three dice is 33.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64. That's because the probability distribution is symmetrical for this case: The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum); The probability of getting the sum of 4 = the probability of getting the sum of 17; The probability of getting the sum of 5 = the probability of getting the sum of 16; ... The probability of getting the sum of 10 = the probability of getting the sum of 11; Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2. Answer: B. #### B QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married? options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70 SOLUTION:--------------------M------W--------Total Marrried----------20-----20---------40 Not married-----10-----50---------60 Total-------------30-----70--------100 need married woman/total woman, so 20/70=2/7 C #### C QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? options: A)x/4 B)x/5 C)x/9 D)x/20 E)4x/9 SOLUTION:If 5 people share the rent, each person would pay x/5. If 4 people share the rent, each person will pay x/4. The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20 The answer is D. #### D QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life? options: A)17% B)16% C)15% D)14% E)13% SOLUTION:Average = 7.6 SD = 2.6 7.6 - 2.6 < 72% of distribution < 7.6 + 2.6 5.0 < 72% of distribution < 10.2 28% is outside this range. Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2. Answer: D #### D QUESTION:What percent of 7.2 kg is 18 gms ? options: A)25 B)66 C)288 D)19 E)17 SOLUTION:Explanation: Required percentage = (18/7200 * 100)% = 1/4% = 0.25% Answer: A) .25% #### A QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is: options: A)$153 B)$848 C)$398 D)$549 E)$675 SOLUTION:B $848 S.I. for 1 year = $(1024 - 980) = $44. S.I. for 3 years = $(44 x 3) = $132. Principal = $(980 - 132) = $848. #### B QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these SOLUTION:The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer : B #### B QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have. options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5 SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs Given x + (20+x)= 21 => 2x= 1 or x= 0.5 So Christine and Siri has 20.5 and 0.5 Rs respectively. ANSWER:E #### E QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? options: A)-1f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2f(x) SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x)) = ((1/x^2) - 1) / (1/x) = ((1-x^2)/(x^2)) / (1/x = (1-x^2)/(x^2) = - ( (x^4) -1) / (x) = -1* f(x) Answer is A. #### A QUESTION:A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long? options: A)2.5 B)3 C)5 D)7 E)9 SOLUTION:D = 25 * 60 + 1000 = 2500 m T = 2500/60 * 18/5 = 150 sec = 2.5 mins Answer: A #### A QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)52% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16 so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52% ANSWER:D #### D QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs? options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5% SOLUTION:Fathers without full-time jobs are 1/42/5 = 2/20 of all the parents surveyed. Mothers without full-time jobs are 1/83/5 = 3/40 of all the parents surveyed. The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5% The answer is C. #### C QUESTION:Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam. options: A)2088 B)2000 C)3087 D)None of these E)Cannot be determined SOLUTION:Solution: Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11 Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400 Therefore Shyam's share = (441/841) * 5887 = 3087. Answer C #### C QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/21/21/21/21/21/21/2= 1/128 case 2 .all girls. 1/21/21/21/21/21/21/2=1/128 We will add the cases to get 1/64 #### A QUESTION:What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”? options: A)5 B)10 C)16 D)20 E)9 SOLUTION:The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum). E #### E QUESTION:If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/13 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 4/5 . 2/5 P (A n B) = 8/25. C #### C QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate? options: A)358000 B)368000 C)357000 D)358000 E)367000 SOLUTION:Total number of invalid votes = 15 % of 560000 = 15/100 × 560000 = 8400000/100 = 84000 Total number of valid votes 560000 – 84000 = 476000 Percentage of votes polled in favour of candidate A = 75 % Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000 = 75/100 × 476000 = 35700000/100 = 357000 Answer:C #### C QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)165 B)771 C)245 D)177 E)121 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer: C #### C QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options? Your approach: total 10 options, 5c3. Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together. This gives us 10-3-3=4 as the answer. Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE. D #### D QUESTION:What is the sum of the first 22 natural numbers (starting from 1)? options: A)223 B)233 C)243 D)253 E)263 SOLUTION:The sum of n natural numbers = n(n+1) / 2 = 2223/2 = 253 The answer is D. #### D QUESTION:Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 7 hours? options: A)675 B)750 C)1,800 D)5,900 E)1,575 SOLUTION:8 machines/ 360 cans = 5 machines/ x cans 8x= 1800 x=225 (225)(7 hours)= 1575 cans. The answer is E. #### E QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:If N = 2^0.15 and N^b = 8, b must equal options: A)3/80 B)3/5 C)20 D)5/3 E)80/3 SOLUTION:15/100 = 3/20 N = 2 ^ 3/20 N^b = 2^3 (2^3/20)^b = 2^3 b = 20 Answer: C #### C QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 9 meters, width is 8 meters, and depth is 5 meters? options: A)152 m2 B)162 m2 C)180 m2 D)300 m2 E)314 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(98+85+95)=2(72+40+45)=2157=314 m2 Answer : E #### E QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C55C3 = 42 * 5 = 210 ANS:C #### C QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered? options: A)60 B)72 C)84 D)90 E)216 SOLUTION:E is the answer.... D = TS where D=distance, T=Time and S=Speed To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes Difference, 216 minutes E #### E QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2357 ~ 10^ 2 Answer : C #### C QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)5:4 B)4:5 C)2:5 D)5:2 E)None of them SOLUTION:Let the third number be x. Then, first number = 120% of x = 120x/100 = 6x/5 Second number = 150% of x = 150x/100 = 3x/2 Therefore, Ratio of first two numbers = (6x/5 : 3x/2) = 12x : 15x = 4 : 5. Answer is B. #### B QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:If x=-2, which of the following is(are) true? I. x^2=-\|x\| II \|x\|=-x III x/-3 = -2/3 options: A)II only B)I only C)III only D)I,II only E)II, III only SOLUTION:I. x^2=-\|x\| -2^2 = - \|-2\| Not true II \|x\|=-x \|-2\| =-( -2 ) true III x/-3 = -2/3 Not true Answer : A #### A QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 14 kilometers by car. What is the distance, in kilometers, from the dormitory to the city? options: A)30 B)45 C)60 D)90 E)105 SOLUTION:Whole trip = distance by foot + distance by bus + distance by car x = 1/5x + 2/3x + 14 x - 13/15x = 14 2/15x = 14 => so x = (15/2)14 = 105Km Answer E #### E QUESTION:A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls options: A)8B, 5G B)5B, 8G C)4B, 9G D)9B, 4G E)6B, 7G SOLUTION:120B+100G=1420-----i B+G=13-------ii from i 100B+20B+100G=1420 100(B+G)+20B=1420 100(13)+20B=1420 By simplifing we get B=6;G=7 ANSWER:E #### E QUESTION:A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction? options: A)8% B)10% C)2% D)5% E)6% SOLUTION:Actual price = 100+10 = $110 Saving = 10/110 * 100 = 100/11 =10% approximately Answer is B #### B QUESTION:The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is: options: A)1677 B)2523 C)1683 D)3363 E)3567 SOLUTION:L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683. Answer: Option 'C' #### C QUESTION:Shekar scored 76, 65, 82, 47 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? options: A)71 B)69 C)75 D)85 E)90 SOLUTION:Explanation : Average= (76+65+82+47+85)/5 = 355/5 =71 Hence average=71 Answer : A #### A QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(34)+x/(35)=84/60 x=6 km ANSWER:C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:Compute all real solutions to 16x + 4x+1 - 96 = 0 options: A)3/2 B)3/3 C)2/4 D)4/4 E)4/5 SOLUTION:If we substitute y = 4x, we have y2 +4y-96 = 0, so y = -4 or y = 8. The first does not map to a real solution, while the second maps to x =3/2 correct answer A #### A QUESTION:The number 0.650 is how much greater than 1/8 ? options: A)½ B)21/40 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .65-1/8=x 65/100-1/8=x x=21/40 ans B #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Three coworkers P , W , R meet for Dinner. P had 5 sandwiches, W had 3 and R had none. Both PW share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PW, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. options: A)a) 5$ B)b) 3 $ C)c) 7 $ D)d) 4 $ E)e) 5.5 $ SOLUTION:we got total 8 sandwiches ....we are dividing equally in 3 people. per person: 8/3 initially p:8 W:3 r:0 now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches. now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r ok we have 8 dollars for 8/3 sandwich therefore for 7/3 sandwich we will get 7 dollars. hence p should get 7 dollars. hence C #### C QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/9 B)3/10 C)4/11 D)5/12 E)6/13 SOLUTION:# defective pens = 3 # good pens = 6 Probability of the 1st pen being good = 6/9 Probability of the 2nd pen being good = 5/8 Total probability = 6/9 * 5/8 = 5/12 The answer is D. #### D QUESTION:Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket? options: A)5min. 50sec. B)5min. 30 sec. C)6 min 36 sec. D)6mins. 32 sec. E)6 min. 15 sec. SOLUTION:Explanation: Part filled in 3 minutes = 3∗(1/12+1/15)=3∗9/60=9/20 Remaining part =1−9/20=11/20 =>1/12:11/20=1:X =>X=6.6 mins. =>X=6.6 mins. So it will take further 6 mins 36 seconds to fill the bucket. Option C #### C QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3% Answer B #### B QUESTION:161?85?65?89=100 then use + or - in place of ? and take + as m,- as n then find value of m-n options: A)3 B)-1 C)1 D)-3 E)2 SOLUTION:161-85-65+89=100 so m=1, n=2 => (m-n)=-1 ANSWER:B #### B QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)30 C)99 D)77 E)62 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B #### B QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is? options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15 SOLUTION:100(90/100)(90/100)(95/100) = 76.95 100 - 76.95 = 23.05 Answer: A #### A QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:A cab driver 5 days income was $200, $150, $750, $400 , $500. Then his average income is? options: A)$420 B)$410 C)$400 D)$390 E)$380 SOLUTION:avg = sum of observations/number of observations avg income=(200+150+750+400+500)/5 = 400 Answer is C #### C QUESTION:The expression (5x+2)/(x+3) is equivalent to which of the following? options: A)(5-2)/3 B)5 – (2/3) C)5 – (x)/(x+3) D)5 – (13)/(x+3) E)5 + (17)/(x+3) SOLUTION:Easiest way is to pick any number and put in (5x+2)/(x+3). Then check the options with the same number. I took x=1 and got D as the answer. #### D QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 245= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 245 + 2y =124 then y=2 244 + 2y = 124 then y=14 243 +2y = 124 then y= 26 242 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? options: A)72 B)78 C)80 D)82 E)84 SOLUTION:Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 268 - (A + D) = 268 - 132 = 136. B + B -28 = 136 B = (136 + 28)/2 = 82 ANSWER:D #### D QUESTION:Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings? options: A)(10!)^3 / 2^10 B)(10!)^3 / 3^10 C)30! / 2^10 D)30! / 3^10 E)30! / 6^10 SOLUTION:By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts. 30! / 6^10 ANSWER:E #### E QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100100 = 132 10% discount Then price = 132 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 Ã— 9 Ã— 9 Ã— 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n? I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true. Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D QUESTION:If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 6 other contributions made before john's, what is the size of his donation? options: A)$225 B)$150 C)$200 D)$250 E)$450 SOLUTION:Cavg = average contribution before John Cavg1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by $25, he must put in $25 for each of the 6 people. so $150. But, he also has to put in the average for himself (the seventh person), so add $75. So $225 is your answer. Answer A #### A QUESTION:The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places? options: A)18 B)20 C)40 D)12 E)14 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways. Hence the total ways are 2 6 = 12. Answer:D #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%? options: A)20% B)29% C)10% D)35% E)90% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 90 2/3 SP1 = 90 SP1 = 135 100 --- 35 => 35% Answer: D #### D QUESTION:Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues? One digit is divisible by 1. Two digits are divisible by 2. Three digits are divisible by 3. Four digits are divisible by 4. Five digits are divisible by 5. Six digits are divisible by 6. Seven digits are divisible by 7. Eight digits are divisible by 8. Nine digits are divisible by 9. Ten digits are divisible by 10. options: A)3816547290 B)3816557290 C)3816547280 D)3813547290 E)3816147290 SOLUTION:A 3816547290 #### A QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 * 75 = 20.93 ANSWER:D #### D QUESTION:What is the area of a square with perimeter 12P ? options: A) 16p^2 B) 4P C) 9P^2 D) P/16 E) P^2/16 SOLUTION:Each side is 3p A = (3p)^2 = 9p^2 Answer C #### C QUESTION:At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years. options: A)10% B)15% C)20% D)12% E)23% SOLUTION:Explanation: principal P = 2400/- Rate of interest R = ? Time T = 5 years Accumulated Amount A = Rs.10400/- A = P + I A = P + PTR/100 A = P(1+ TR/100) 2400[ 1 + (5 x R)/100] = 3600 2[(20 + R)/20] = 3 20 + R = 30 R = 10% Answer: Option A #### A QUESTION:A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 12 hours of the journey. options: A)342 km B)352 km C)642 km D)742 km E)492 km SOLUTION:The total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 +50 +52 = sum of 12 terms in AP whose first term is 30 and last term is 52 = 12/2 [30 + 52] = 492 km. ANSWER:E #### E QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? options: A)125 B)772 C)821 D)912 E)121 SOLUTION:Sum of the 35 numbers = 35 * 25 = 875 If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5. Thus, the new average = 25 * 5 = 125. Answer:A #### A QUESTION:A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.9 km C)3.4 km D)1.9 km E)5.6 km SOLUTION:Explanation: Speed in still water = 4 kmph Speed of the current = 1 kmph Speed downstream = (4+1) = 5 kmph Speed upstream = (4-1) = 3 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/5+x/3=1 â‡’3x+5x=15 â‡’8x=15 â‡’x=1.9 km Answer: Option D #### D QUESTION:A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)45 B)35 C)55 D)60 E)66 SOLUTION:Explanation : A : B: C = 107 : 125 : 153 = 27 : 121 : 33 = 14 : 12 : 9 amount that C should pay = 175 * (9/35) = 59 = 45. Answer : Option A #### A QUESTION:A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)37 B)38 C)60 D)90 E)28 SOLUTION:Let number of notes of each denomination be x. Then, x + 5x + 10x = 320 16x = 320 x = 20. Hence, total number of notes = 3x = 60. Answer:C #### C QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A? options: A)1 B)3 C)4 D)6 E)14 SOLUTION:6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 70 = 6K+4k =>k=7 Total Red's in bag A will be 2K = 14 E #### E QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B <<<Examples ends QUESTION:If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)331/8% B)26.67% C)28.5% D)332/3% E)131/3% SOLUTION:100 140 ------ 140-------40 100-------? => 28.5% Answer:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? options: A)30 B)39 C)87 D)27 E)91 SOLUTION:Let the side of the square(ABCD) be x meters. Then, AB + BC = 2x metres. AC = = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = = 30% (approx) Answer:A #### A QUESTION:How many numbers between 11 and 90 are divisible by 7 ? options: A)23 B)11 C)22 D)32 E)15 SOLUTION:The required numbers are 14, 21, 28, 35, .... 77, 84. This is an A.P. with a = 14 and d = (21 - 14) = 7. Let it contain n terms. Then, Tn = 84 => a + (n - 1) d = 84 => 14 + (n - 1) x 7 = 84 or n = 11. Required number of terms = 11 ANSWER B 11 #### B QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers? options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9 SOLUTION:Let two numbers be x and y. Equation (i): x + y = 18 Equation (ii): x - y = 4 Solve system of equations: 2x=22 x=11 y=7 Answer C is correct. #### C QUESTION:For what value of â€œkâ€ will the equation (2kx2 + 5kx +1)=0 have equal roots? options: A)2/7 B)9/4 C)8/25 D)7/1 E)7/2 SOLUTION:for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0 in the given equation (5k)^2-42k1=0 by solving this equation we get k=0, k=8/25 ANSWER:C #### C QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 50 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:Annie earned 40x + 10(2x) = 60x Let H be the number of hours that Harry worked. Harry earned 30x + 1.5x(H-30) = 60x (1.5x)(H) = 75x H = 50 hours The answer is C. #### C QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9 SOLUTION:Speed of Peter = x/9 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x Option D The values 100m and 200m have no role to play here and are just given to confuse you. #### D QUESTION:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours? options: A) $180,000 B) $185,000 C) $180,000 D) $200,000 E) $192,500 SOLUTION:30% of 1000 = 300 worked for 20 hours Payment @ 5/hr Total Payment = 300255 = 37500 50 % of 1000 = 500 worked for 40 hours Payment @ 5/hr Total payment = 500405 = 100000 Remaining 200 worked for 50 Hours Payment for first 40 Hours @ 5 /hr Payment = 200405 = 40000 Payment for next 10 hr @ 7.5/hr Payment = 200 * 10 * 7.5 = 15000 Total Payment = 37500+100000 + 40000 +15000 = 192500 Hence , answer is E #### E QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1996 has to be the ring finger Answer is (D) #### D QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)1/2 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 4 = 4C2 Total possible outcomes - 2^4 (each child can be either a girl or a boy) Probability=2C14C2/2^4= 24/2222=8/16=1/2 Ans=D #### D QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ? options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 19 x 13 ) / (19 +13 ) km/hr. = 15 km/hr. Correct Option: A #### A QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers? options: A)10 B)12 C)14 D)15 E)16 SOLUTION:Solution Let the number be x and (28 - x) = Then, x (28 - x) = 192 ‹=›x2 - 28x + 192 = 0. ‹=›(x - 16) (x - 12) = 0 ‹=›x = 16 or x = 12. Answer B #### B QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:A rectangular block 15cm by 30cm by 75cm is cut into an exact number of equal cubes. Find the least possible number of cubes? options: A)6 B)40 C)15 D)10 E)22 SOLUTION:Volume of the block = 153075 = 33750 cm^3 Side of the largest cube = H.C.F of 15,30,75 = 15cm Volume of the cube = 151515 = 3375 cm^3 Number of cubes = 33750/3375 = 10 Answer is D #### D QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4% ANSWER:B #### B QUESTION:Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last? options: A)6 B)7 C)8 D)8 1/9 E)10 SOLUTION:Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job. Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15 3/20 (t) = 7/15 ---> t = 3 1/9 Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days Answer: D #### D QUESTION:A man spends Rs. 1900 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)2075 B)2175 C)2275 D)2375 E)2475 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 Ã— 1900 = 5700 Total expenditure for 4 months = 4 Ã— 1550 = 6200 Total expenditure for 5 months = 5 Ã— 1800 = 9000 Total expenditure and saving (which is income for one year) = 5700 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 26100/12 = Rs. 2175 Answer B #### B QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train? options: A)200 metres B)180 metres C)324 metres D)228 metres E)150 metres SOLUTION:Speed= 60 x 5/18 m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9 m = 200 m. Option A #### A QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2 SOLUTION:39/360 22/7 * 12 * 12 = 49m2 Answer:C #### C QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers){(n-1)!(111...........n times)-(n-2)!(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!(11111)-(5-2)!1111} = 10{(4!11111)-(3!1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11 inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing may help you with this one.) options: A)100 B)130 C)120 D)110 E)101 SOLUTION:3 x 11 = 33 V = 33 x missing measure V is 330 330 ÷ 33 = 10 which is the missing measure of the side of the box top 10 x 11 = 110 sq. ft. which is area of the top of the box. correct answer D #### D QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet? options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area height = 6(sqrt(3)/4)(200^2)(70) Volume of the center bull's eye that is similar in shape of a hexagon but side 25 = 6 (sqrt(3)/4)(25^2)70 Volume of the building = 6(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)70=7,160,947 Answer is D #### D QUESTION:What is the remainder when 1014104710501053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24242730 break them into pairs 2424/33 gives remainder 15 and 2730/33 gives remainder 18 so 1518/33 gives remainder 6. B #### B QUESTION:If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house? options: A)5 B)30 C)10 D)12 E)15 SOLUTION:Speed = 4.5 * 5/18 = 1.25 m/sec Time taken = 750/1.25 = 600 sec ie. 10 mins. Answer:C #### C QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)205 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 * 8 * 4) = 160. Therefore, 160 * 2.40 + x * 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER:B #### B QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock options: A)47 B)76 C)28 D)66 E)99 SOLUTION:Explanation: For ticking 6 times, there are 5 intervals. Each interval has time duration of 45/5 = 9 secs At 12 o'clock, there are 11 intervals, So total time for 11 intervals = 11 × 9 = 99 secs. Answer: E #### E QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? options: A)40 B)45 C)35 D)50 E)55 SOLUTION:A is one third of the sum of B and C.. or A=1/3(B+C)... But A+B+C=60 so 1/3(B+C)+B+C=60 4(B+C)/3= 60 B+C =603/4 = 45 A=60-45=15 2)B is one fifth of the sum of A and C or B=1/5(A+C)... But A+B+C=60 so 1/5(A+C)+A+C=60 A+C=605/6=50 but A=15, so C=50-15=35 Answer :C #### C QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4. 6000 /4 = 1500 toys correct answer B #### B QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:6x + 2y = -4 4x + y = 1 In the system of equations above, what is the value of x? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:6x + 2y = -4 can be written as 3x + y = -2 Let's subtract the second equation from this equation. -x = -3 x = 3 The answer is C. #### C QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product? options: A)12.5% B)13% C)13.15% D)14% E)15% SOLUTION:Quantity X Rate = Price 1 x 1 = 1 0.7 x 1.25 = 0.875 Decrease in price = (0.125/1) × 100 = 12.5% A) #### A QUESTION:If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)A)60% B)B)85.7% C)C)65% D)D)75% E)of these SOLUTION:A's marks = 70 ; B's marks = 60. Let x% of A = B => x/100 70 = 60 => x = (60 100)/80 = 85.7 B's marks is 85.7% of A's marks. ANSWER:B #### B QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women? options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10 SOLUTION:w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: A #### A QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown? options: A)26 B)19 C)11 D)8 E)6 SOLUTION:No of dogs=45 Long fur=36 Brown=27 Neither long fur nor brown=8 Therefore, either long fur or brown=45-8=37 37=36+27-Both Both=26 Answer A #### A QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 80 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)70 miles B)80 miles C)90 miles D)100 miles E)110 miles SOLUTION:Every hour, Nil gets ahead of Ethan 80 - 20 = 60 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 80 × 1 = 80 miles. correct answer B #### B QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)100 / Initial Value % Reduction= (Reduction in Price)100 / Initial Value i.e. % Reduction= (350)100 / 500 = 70% Answer: Option A #### A QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-2575)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing? options: A)2 B)4 C)12 D)0 E)13 SOLUTION:E 13 This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next. #### E QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks : options: A)300 B)350 C)400 D)450 E)550 SOLUTION:total marks:1500 for three exams 70% of 1500=1050 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =1050 X=550 ANSWER:E #### E QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r? options: A)2 B)3 C)4 D)5 E)Cannot be determined SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y (15^r . 4^2 ) / 4^y = 15^y. 4^0 15^r . 4^(2-y) = 15^y. 4^0 Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete? options: A)ab/(a+b) B)(a-b)/(a+b) C)b/(b+a) D)a/(a+b) E)b/(a-b) SOLUTION:Randy can do the job in a hrs, Alvin can do the job in b hrs. When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin. Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b) So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work. Answer (C). #### C QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 150001/6 = 2500.Answer: C #### C QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)(1+1)=2^3 2^3+2^3=(2^3)(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B QUESTION:A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)3.3 B)3.4 C)3.5 D)3.6 E)3.7 SOLUTION:M = 7 S = 1.2 DS = 7 + 1.2 = 8.2 US = 7 - 1.2 = 5.8 x/8.2 + x/5.8 = 1 x = 3.40.Answer: B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ? options: A)6000 B)5400 C)6200 D)7200 E)8200 SOLUTION:Investment Ratio = Profit Sharing Ratio. Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6. Giri share = 13200 × 6 / 11 = Rs.7200 Hari share = 13200 × 5 / 11 = Rs.6000 Option A #### A QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000100/120000 = 40% Answer: option D #### D QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1x5)/100 + (1600-x)6/100 = 16005.67/100 Simplifying we get x= 528 B #### B QUESTION:What is the sum of all the numbers which divides 100 ? options: A)408 B)102 C)816 D)916 E)416 SOLUTION:You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408. Final Answer: A #### A QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1500. What is their H.C.F.? options: A)5 B)15 C)25 D)35 E)45 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 1500 x = 25 The numbers are (3 x 25), (4 x 25) and (5 x 25). The H.C.F. is 25. The answer is C. #### C QUESTION:In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? options: A)120 B)130 C)110 D)150 E)180 SOLUTION:let x be the correct answer and y be the wrong answer so the total number of questions is (x+y)=150 =>4x-2y=480 =>6x=780 hence x=130 ANSWER:B #### B QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes? options: A)100000 B)85236 C)89562 D)90083 E)95842 SOLUTION:winners votes = 100-45 = 55% invalid votes = 83 polled votes = [(1009000)/(255-100)]+83 = 90083 Answer is D #### D QUESTION:If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women? options: A)10 days B)11 days C)13 days D)15 days E)24 days SOLUTION:8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =1240= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E #### E QUESTION:The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area? options: A)298 B)148 C)289 D)987 E)282 SOLUTION:2(45 + 56 + 46) = 148 Answer:B #### B QUESTION:Find the odd man out. 12, 24, 36, 48, 61, 72, 84 options: A)15 B)25 C)61 D)90 E)115 SOLUTION:Explanation : All except 61 are multiples of 7 Answer : Option C #### C QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:Five kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates? options: A)12312 B)22536 C)4320 D)11268 E)45072 SOLUTION:Since, one child cannot have more than two brands of chocolates, therefore, one child can get a maximum of six chocolates. When there are four winners, the winners can have the chocolates in the following possible way Case I One of them gets six chocolates and the other three get one each. The one who gets six chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways. The three chocolates of the same brand will be distributed among the other three in 3! ways. Hence, the total number of ways = 4 × 3 × 6 = 72 Case II One of them gets 5 chocolates, one of them gets 2 chocolates and the other two get 1 each. Kid with 5 chocolates: The one who gets five chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways. After choosing the two brands (say AB), he can get all three chocolates of one brand in 2 ways (i.e. either A or B). The other two chocolates can be chosen from the second brand in 3 ways. Thus, there are 4 × 3 × 2 × 3 = 36 ways Kid with 2 chocolates: This person can be chosen in 3 ways. Now, he can either get two chocolates from the same brand or from two different brands. Thus, there are 6 × 3 = 18 ways Kids with 1 chocolate each The remaining chocolates can be distributed between the two remaining winners in 2 ways. Therefore, total number of ways = 36 × 18 × 2 = 1296 ways. Case III Similarly for four chocolates the following combinations are possible: a) 4 3 1 1 The number of ways = 4 × 3 × [{6 × 3(1 + ( 6 + 3))} + {1 × 9 × 3 (1 + 6)}] × 2 = 8856 b) 4 2 2 1 The number of ways = 4 × 3 × [{6 × 3(2 × 6 × 3 + (3 + 9))} + {9 × (9 + 9)}] = 12312 Since, the best of them can’t have less than 4 chocolates the above are the only cases applicable. Hence, the total number of ways = 72 + 1296 + (8856 + 12312) = 22536. Option B #### B QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 100 = 18% Answer:C #### C QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches? options: A)31 B)46 C)88 D)13 E)12 SOLUTION:Total score of the batsman in 20 matches = 800. Total score of the batsman in the next 10 matches = 130. Total score of the batsman in the 30 matches = 930. Average score of the batsman = 930/30 = 31. Answer:A #### A QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers The answer is D. #### D QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 12 = 15552 Answer: E #### E QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 301.5 more revolutions is 601.5 = 90 seconds. The answer is C. #### C QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. âˆ´ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 181? options: A)3820 B)5740 C)6580 D)7360 E)9200 SOLUTION:100 + 102 + ... + 180 = 10041 + (2+4+...+80) = 10041 + 2(1+2+...+40) = 10041 + 2(40)(41)/2 = 10041 + 4041 = 140(41) = 5740 The answer is B. #### B QUESTION:Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (660y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:Find the largest 4 digit number which isexactly divisible by 88? options: A)8560 B)8950 C)9944 D)10000 E)10200 SOLUTION:Largest 4 digit number is 9999 After doing 9999 ÷ 88 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 C #### C QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 235^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets options: A)40% B)50% C)65% D)71.4% E)75% SOLUTION:Number of runs made by running = 210 - (3 x 4 + 8 x 6) = 210 - (60) = 150 Now, we need to calculate 60 is what percent of 120. => 150/210 * 100 = 71.4 % D #### D QUESTION:How many positive integers will divide evenly into 440? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:520 = 10134 = 8513 = 2^3513 We need to positive integers will divide evenly into 520 or simply the factors of 520 If a number is of the form 2^a3^b5^c, Total factors = (a+1)(b+1)(c+1) Therefore, number of factors of 520 = (3+1)(1+1)(1+1) = 422 = 18 Option D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)22 B)350 C)268 D)277 E)198 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer:B #### B QUESTION:If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)7/3 E)9/7 SOLUTION:70 Workers = 3 hours then, 1 Worker = 370 Hours 30 Workers = (370) /(30) = 7 ANSWER:C #### C QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:A beats B by 50m in a race of 500m ,then B beats by C by 25m in a race of 500m.Find the distance by which A beats C in a race of 400? options: A)55m B)56m C)57m D)58m E)59m SOLUTION:A beats B in 500m race by 50m so,for every 10 m race A beat B by 1m.. So,in 400 m race A beat B by 40m In a case of B & C, B beats C by 25m in 500m race.. So,B beats C by 1m in 20 m race Now,in a 400m race B beats C by 18m.. In a 400m race, A beats B by 40m & B beats C by 18m.. So,A beats C by 58m ANSWER:D #### D QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle. options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110° SOLUTION:Solution If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence x + 3x + 8x = 180 Solve for x 12x = 180 x = 15 The measures of the three angles are x = 15° 3x = 3 × 15 = 45° 8x = 8 × 15 = 120° ANSWER IS C #### C QUESTION:One day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at which point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each subsequent turn, Connie wins 1 6 of the amount she would have won the previous turn. What is Connie's expected earnings from the game? options: A)32/31 B)33/31 C)34/31 D)36/31 E)0/31 SOLUTION:Connie has a 1 6 chance of winning 6 dollars her first turn. She has a 5/6 1/6 chance of winning 1 dollar her second turn. Next, she has a 25 36 1/6 chance of winning 1/6 dollars her third turn. Generalizing, Connie's expected earnings form a geometric series with initial term 1/6 6 = 1 and common ratio 5/6 1/6 = 5/36 . Hence, Connie's expected earnings are 1/1- 5/36 = 36/31 correct answer D #### D QUESTION:A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:60% is 20%-points above 40% and 20%-points below 80%. Thus the ratio of "the first 30 games" to "remaining games" is 1:1. So the team played a total of 30+30 = 60 games. The answer is B. #### B QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:If 20% of a number = 1000, then 120% of that number will be? options: A)20 B)120 C)360 D)6000 E)820 SOLUTION:Let the number x. Then, 20% of x = 1000 x = (1000 * 100)/20 = 5000 120% of x = (120/100 * 5000) = 6000. ANSWER:D #### D QUESTION:Of the 100 athletes at a soccer club, 40 play defense and 62 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between options: A)10 to 20 B)10 to 40 C)22 to 40 D)30 to 70 E)40 to 70 SOLUTION:First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E. {Total} = {defense} + {midfield} - {both} + {neither} 100 = 40 + 62 - {both} + {neither} {both} = {neither} + 2. Since the least value of {neither} is given to be 20, then the least value of {both} is 20+2=22.Eliminate A and B. Answer: C. #### C QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:The forth proportional to 6,8,15 is? options: A)15 B)12 C)18 D)20 E)24 SOLUTION:Let the fourth proportional to 6,8,15 be x then 6:8::15:x 6x = 815 x = 20 Answer is D #### D QUESTION:When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time. options: A)2 PM B)9 PM C)4 PM D)8 PM E)6 PM SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=4/8x⇒x=20 Time is 4 PM Answer:C #### C QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2(44 + 124) = 2(16+48) = 128 Then, Finally Length (L) = 212 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2(22 + 242) = 2(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)100 /Initial Area i.e. % change in Area of four walls = (104-128)100 /128=- 18.75% (Decrease) Answer: Option D #### D QUESTION:Which of the following is equal to 1(4/5)%? options: A)0.012/100 B)0.12/100 C)1.2/100 D)1.8/100 E)12/10 SOLUTION:This notation may be confusing for some, since it looks like we're multiplying 1 and 4/5 How about adding a space:Which of the following is equal to (1 4/5)% (1 4/5)% = 1.8% = 1.8/100 Answer: D #### D QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ? options: A)240 B)140 C)230 D)130 E)105 SOLUTION:Let the number be x. Then, 4x/5 â€“(60% of x) = 21 4x/5 â€“ 60x/100 = 21 x = 105. Answer E. #### E QUESTION:A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in? options: A)days B)days C)days D)1/2 days E)days SOLUTION:Explanation: 10/40 + 10/30 + 10/x = 1 x = 24 days Answer: A #### A QUESTION:Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? options: A)1/8 B)1/4 C)2/4 D)1/4 E)3/4 SOLUTION:3/12 + x/13 = 1 x= 7 3/4 Answer: E #### E QUESTION:The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers. options: A)16,8 B)10,2 C)17,6 D)14,10 E)12,4 SOLUTION:Let numbers be x and y. Equation (i): x - y = 8 Equation (ii): (x + y)/4 = 6 Solve system of equations: x=16, y=8 A is the correct answer. #### A QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is: options: A)260 B)262 C)270 D)272 E)None of these SOLUTION:Explanation: Volume will be length breadth * height, but in this case two heights are given so we will take average, Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3 Option C #### C QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)296 m B)267 m C)297 m D)150 m E)255 m SOLUTION:Speed = 60 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer:D #### D QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (7506+ 770 20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? options: A)1 B)2 C)3 D)5 E)4 SOLUTION:Assume initial amount is x Annual Interest is 34.1% so after 1 year the amount will become x (100+33.34)/100 => x4/3 now we need to find n for x (4/3)^n = 3x or in other words n = 4 E #### E QUESTION:The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number? options: A)40 B)45 C)55 D)45 E)50 SOLUTION:a1 = 120/3 = 40 a2 = a1 -5 = 35 sum of second list = 353 = 105 therefore the number = 105 -60 = 45 D #### D QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E <<<Examples ends QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres? options: A)20 B)200 C)300 D)400 E)100 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] 26.50 = 9540 [4L - 40] = 9540 / 26.50 = 360 4L = 400 L = 400/4= 100 meters. Answer: E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!22= 480 The answer is C. #### C QUESTION:A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)5 B)6 C)21 D)8 E)9 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [385 * 3/55] sec = 21 sec Answer: C #### C QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? (A) The median of S is prime. Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime. (B) The median of T is prime. Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number. (C) The median of S is equal to the median of T. Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true. (D) The sum of the terms in S is prime. Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime. (E) The sum of the terms in T is prime. Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime. C #### C QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:70,76, 74,85,90,105,105,130,130,130 The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD. We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74. Answer: C. #### C QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses? options: A)1/8 B)1/3 C)1/4 D)1/2 E)1 SOLUTION:P(THH) = 1/21/21/2=1/8 The answer is A. #### A QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 (2/25) = 40 seconds Answer:C #### C QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap? options: A)90 seconds B)54.44 seconds C)110 seconds D)63 seconds E)77 seconds SOLUTION:A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point). A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 704.5 = 315 seconds. In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs Answer (A) #### A QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required? options: A)34 B)40 C)68 D)88 E)26 SOLUTION:We have: l = 20 ft and lb = 60 sq. ft. So, b = 3 ft. Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft. ANSWER:E #### E QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None SOLUTION:Solution Perimeter of the rhombus = 56 m Each side of the rhombus = 56 / 4 m = 14 m. Height of the rhombus = 5 m Area = (14 x 5) m² = 70 m² Answer B #### B QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 1110^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:There are different 10 circles. What is the number of the greatest possible points with which the circles intersect? options: A)90 B)100 C)110 D)180 E)200 SOLUTION:Maximum points of intersection between n different circles = n(n - 1) = 109 = 90 Answer: A #### A QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6? options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720 SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6 Seeing the Options After Dividing an Finding the Reminder of 2 My Answer was A #### A QUESTION:P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 12 days. How many days more will P take to finish the work? options: A)12 B)15 C)18 D)20 E)22 SOLUTION:Let work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = 3/4 Remaining work = 1 = 3/4 = 1/4 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (1/4) / (1/48) = 12 Option A #### A QUESTION:A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work? options: A)4 days B)8 days C)12 days D)9 days E)3 days SOLUTION:2/5 + (2 + x)/10 = 1 => x = 4 days Answer: A #### A QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%x = 20%y y/x = 1/5 = 20% The answer is A. #### A QUESTION:A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race? options: A)10 meters B)25 meters C)45 meters D)15 meters E)35 meters SOLUTION:Answer A runs 25% as fast as B. i.e., if B runs 100 m in a given time, A will run 125 m in the same time. In other words, if A runs 5 m in a given time, then B will run 4 m in the same time. Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat. Ratio of length of start given : length of race :: 1 : 5 In this question, we know that the start given is 7 m. Hence, the length of the race will be 7 5 = 35 m. Choice E #### E QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 130 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 2 = 5.76 \Answer:C #### C QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 11 = (5,6)(6,5)= 2 ways Total ways of getting outcome on two dice =66=36 Probability of getting sum as 11 in any attempt =2/36=1/18 Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18 Probability of losing game =(17/18)(17/18)(17/18)=139/165 I.e. Probability of wining game = 1-(139/165) =26/165 Answer : Option C #### C QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green? options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220 SOLUTION:Prob of selecting one blue and two green is (487/121110) one blue and two green can be arranged in 3!/2! ways hence the prob becomes 3487/121110=28/55 Correct answer is B #### B QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46 options: A)16 B)46 C)24 D)11 E)7 SOLUTION:Explanation : 7 is the only odd number in the given series Answer : Option E #### E QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. options: A)276 B)552 C)414 D)1104 E)2202 SOLUTION:Let x be the divisor. N1 = xa + 238 N2 = xb + 362 N1 + N2 = x(a+b) + 600 = xc + 68 x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1. The answer is B. #### B QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is? options: A)1 B)22 1/7 C)2 D)22 1/2 E)3 SOLUTION:100 --- 10 DS = 10 ? ---- 1 200 ---- 30 US = 8 ? ----- 1 S = (10 - 8)/2 = 1 kmph. Answer:A #### A QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. âˆ´ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)x = 240 => x = (240 100)/60 = 400 Answer B #### B QUESTION:A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)24/78 B)24/709 C)24/76 D)24/71 E)24/72 SOLUTION:Explanation: Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random. Therefore, n(S) = 13C2 = 78 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 24/78 ANSWER:A #### A QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? options: A)2.04% B)6.12% C)8% D)8.25% E)10% SOLUTION:Per quarter, interest = 2% So for a year, interest = 8% Due to quarter cumulation, effective yield (YTM) would be slight higher than 8% Answer = 8.25% =ANSWER:D #### D QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Asha=25 Nisha =n Usha =3n Asha=2a Nisha =a Usha =34 The difference of all ages must be same 25-2a=n-a=3n-34 We will get two equation 2n+a=34 n+a=25 From the equation we will get n=9 and a=16 The ages are Asha=2a=32 Nisha =16 and Usha =34 Sum of the ages =100 (32+x)+(16+x)+(34+x)=100 82+3x=100 3x=18 x=6 Age of Usha =34+6=40 ANSWER:D #### D QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3Ã—7/36 = 7/12 Remaining work = 1 â€“ 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)11 days B)16 days C)13 days D)15 days E)19 days SOLUTION:B 16 days P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)7 B)9 C)8 D)4 E)5 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 8 Answer:C #### C QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr. SOLUTION:Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=24 or x=12. Rate upstream=12 km/hr,rate downstream=36 km/hr. Hence,rate of stream=1/2(36-12)km/hr=12 km/hr. Answer is B. #### B QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? options: A)100 B)72 C)110 D)135 E)145 SOLUTION:Explanation : Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x. .'. 60% of x = 36 +5/6 36 =>60/100 x = 66 =>x = 110 Answer : C #### C QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C #### C QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have. options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5 SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs Given x + (20+x)= 21 => 2x= 1 or x= 0.5 So Christine and Siri has 20.5 and 0.5 Rs respectively. ANSWER:E #### E QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents SOLUTION:Solution: 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. Answer: A #### A QUESTION:What is the value of âˆš36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>âˆš16% =âˆš36/âˆš100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is options: A)11 B)13 C)15 D)17 E)18 SOLUTION:Sequence is contain prime numbers. Final sequence : 2,3,5,7,11,13,17,19 ANSWER:B #### B QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers? options: A)121 B)133 C)145 D)150 E)165 SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by x + (x + 4) 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131 "The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131 Solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 As an exercise, check that the sum of the first and third is 131 less than three times B #### B QUESTION:Find the least number must be subtracted from 11070 so that remaining number is divisible by 22. options: A)2 B)3 C)4 D)7 E)8 SOLUTION:On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A. #### A QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution? options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30 SOLUTION:Water:soap = 3:4 Soap:Salt=15:20 => For 15 soap, salt = 20 => For 4 Soap, salt = (20/15)4 = 80/15=16/3 So, water:soap:salt = 3:4:16/3= 9:12:16 After open container, water:soap:salt =4.5:12:16 So, water:salt = 4.5:16 = 9:32 ANSWER:A #### A QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.9 B)1.5 C)1.2 D)1.6 E)1.1 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer:B #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation? options: A)Doesn't Change B)Decreases by Factor 20 C)Can't be determined D)Increases by 20 E)Increases by Factor 20 SOLUTION:Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E #### E QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible? options: A)100 B)90 C)80 D)70 E)60 SOLUTION:Secretary can sit in 2C2 ways = 1 Near the gate we can have 6C2 combinations (2 secretaries are already having a place) In the center we can have 4 C2 employees as 4 already have a place Near coffee machine we can have 2C2 employees as all other place are taken Number of selection = 2C2 6C2 * 4C2 * 2C2 = 90 Ans: B #### B QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 80 percent of the drive from the center, what percent of the round-trip has the technician completed? options: A)5% B)75% C)25% D)40% E)50% SOLUTION:The complete round trip consists of driving to the service center and then back home again. So, once the technician drives to the service center he/she has already competed 50% of the entire trip. Since the technician completes a portion of the trip back home,the correct answer must be greater than 50% Only one answer choice works. Answer: B #### B QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)23 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Answer: Option B #### B QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:2^23^32^23^6 = options: A)3^52^5 B)2^93^4 C)2^43^9 D)5^8 E)6^10 SOLUTION:2^23^32^23^6 = A) 3^52^5 B) 2^93^4 C) 2^43^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^43^9. Hence the answer is C #### C QUESTION:Find the option to replace the question mark in the series below 5 ? 15 75 525 4725 options: A)2 B)6 C)7 D)5 E)8 SOLUTION:ol: 5 x 1 = 5 5 x 3 = 15 15 x 5 = 75 75 x 7 = 525 525 x 9 = 4725 So ? = 5 Answer:D #### D QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:The ratio 15:25 expressed as percent equals to options: A)70 % B)60 % C)30 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 15 is what percent of 25, which can be calculated as, (15/25)100 = 15 * 4 = 60 Answer: Option B #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)22 B)98 C)60 D)88 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:A bowl of fruit contains 14 apples and 23 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples? options: A)3 B)6 C)14 D)17 E)20 SOLUTION:Number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x Total number of fruits after x oranges are removed = 14+(23-x) = 37-x 14/(37-x) = 7/10 =>20 = 37-x =>x= 17 Answer D #### D QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D QUESTION:When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item? options: A)$1,600 B)$1,850 C)$2,250 D)$2,400 E)$2,750 SOLUTION:Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250. Answer: C. #### C QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ? options: A)75 kg B)55 kg C)80 kg D)85 kg E)25 kg SOLUTION:Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (60 + 20) kg = 80 kg. Answer: C #### C QUESTION:Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? options: A)3, 8, 24 B)7, 9, 17 C)6, 9, 12 D)5, 15, 18 E)9, 10, 13 SOLUTION:I didnt get your point on eliminating A. The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps. I choose this and marked A. #### A QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=5015/85=8.82 ANSWER:E #### E QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x x = 162 => x= 9 Answer: B #### B QUESTION:A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? options: A)299m B)287m C)279m D)100m E)277m SOLUTION:A can give B (5 min - 4 1/2 min) = 30 sec start. The distance covered by B in 5 min = 1000 m. Distance covered in 30 sec = (1000 * 30)/300 = 100 m. A can give B 100m start. Answer:D #### D QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3% SOLUTION:675 ---- 225 100 ---- ? => =33 1/3% Answer:C #### C QUESTION:If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) options: A)18 B)24 C)30 D)36 E)40 SOLUTION:Speed = 54 Km/hr => 54,000 m/hr In one minute => 54000/60 = 900 meters In one sec => 900/60 = 15 meters Time = Total distance need to be covered / Avg. speed => 600/ 15 =40 and hence the Answer : E #### E QUESTION:Two trains of length 120 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? options: A)100/7 sec B)80/7 sec C)57/7 sec D)120/7 sec E)104/7 sec SOLUTION:Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (120 + 100 + 300)/35 = 520/35 = 104/7 sec. ANSWER:E #### E QUESTION:Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop? options: A)128 B)64 C)32 D)16 E)8 SOLUTION:Before stop 3, there were 2 passengers on the bus. Before stop 2, there were 4 passengers on the bus. Before stop 1, there were 8 passengers on the bus. The answer is E. #### E QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-xy C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:Which of the following is NOT the sum of the squares of two integers? options: A)36 B)37 C)65 D)146 E)147 SOLUTION:List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. (A) 36 - 9+25. NO. (B) 37 - 1+36. NO. (C) 65 - 1+64. NO. (D) 146 - 25+121. NO. (E) - must be the answer. ANSWER:E #### E QUESTION:Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? options: A)4hrs B)6hrs C)8hrs D)10hrs E)16hrs SOLUTION:machine A will do 6/8 in 6 hrs, so A does 3/4 of the work .. Therefore, B will do the remaining 1/4 th work alone.. As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job... ans 8 C #### C QUESTION:Ayesha's father was 31 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)1 years SOLUTION:Explanation: Mother's age when Ayesha's brother was born = 34 years. Father's age when Ayesha's brother was born = (31 + 4) years = 35 years. Required difference = (35 - 34) years = 1 years. Answer: E #### E QUESTION:A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)100 = 68.75% Answer:- C #### C QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 46 x = 12 Answer is B #### B QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7. options: A)150 B)152 C)154 D)158 E)160 SOLUTION:D = d Q + R D = 17 * 9 + 7 D = 153 + 7 D = 160 ANSWER E #### E QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C 100 =50% Answer A #### A QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:Which of the statements can be dispensed with while answering the above question? options: A)A only B)B only C)A or C only D)B or C only E)C or D only SOLUTION:Explanation: Justification: We can find the code for 'home' from the second and third statements. For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data. Clearly, statement A is not necessary. Answer: A #### A QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages. options: A)30% B)32.50% C)33 1/3% D)40% E)50% SOLUTION:Explanation: The gain is 4 out of 12 articles. Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3% Answer: Option C #### C QUESTION:What is the probability of flipping a fair coin five times and the coin landing on heads on at least two flips? options: A)5/8 B)7/8 C)11/16 D)13/16 E)27/32 SOLUTION:The number of possible outcomes is 2^5=32. 0 heads: There is 1 way to have all tails. 1 head: There are 5 ways to have one head. P(0 or 1 head)=6/32=3/16 P(at least 2 heads)=1 - 3/16 = 13/16 The answer is D. #### D QUESTION:Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)60% B)50% C)25% D)20% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 55 - {both} + 40 {both} = 20%. Answer: D. #### D QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time W it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week? options: A) 0.8(80 – y) B) 0.8 + 0.0025y C) 80/y – 1.25 D) 80/1.25y E) 80 – 0.25y SOLUTION:This may be a case of bad numberpicking but it worked for me. 80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 401/10 = 4 houses per week will be painted at this rate. 80-y = 80-40 = 40 houses are to be painted at the faster rate. X1,25=12,5 houses per week <=> 1/12,5 weeks per house 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks. Which means finishing all houses at normal rate W=> 24 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks. 7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9. #### B QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished. options: A)10 days B)12 days C)14 days D)5 days E)6 days SOLUTION:Explanation: A & B completes the work in 1224/12+24 = 1224/36 = 8 days 2 days work = 2+1/8 = ¼ work Remaining work = 1-1/4 = ¾ A completes ¾ work in ¾16 = 12 days Answer: Option B #### B QUESTION:If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ? options: A)40 kms B)30 kms C)46 kms D)32 kms E)36 kms SOLUTION:Explanation: Let the actual distance travelled be x km. Then x/8=(x+20)/12 => 12x = 8x + 160 => 4x = 160 => x = 40 km. ANSWER IS A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is options: A)276 B)299 C)312 D)322 E)None SOLUTION:Solution Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. Answer D #### D QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3. We need to add 5 more to these 12 because of 9, 18, 27, and 36. The greatest integer of k is 17. The answer is C. #### C QUESTION:(x —1)(x + 3) > 0 (x +5)(x—4) < 0 Which of the following values of x satisfy both inequalities shown? I. -6 II. -4 III. 2 IV. 3 options: A)I and II only B)I and III only C)II and III only D)II and IV only E)II, III, and IV SOLUTION:(x - 1)(x + 3) > 0 --> x<-3 or x>1. (x + 5)(x - 4) < 0 --> -5<x<4. Among choices only -4 and 2 satisfy both inequalities. Answer: E. #### E QUESTION:How many digits are in (8×10^10)(10×10^5)? options: A)17 B)25 C)26 D)27 E)28 SOLUTION:The question simplfies to (8×10^10)(10^6) => 810^16 => Will contain 16 zeros +1 digit 8 =>17 Ans A #### A QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 40007 = 28000. Answer : Option A #### A QUESTION:Amal borrowed a sum of money with simple interest as per the following rate structure: (a) 6 p.c. p.a. for the first three years (b) 8 p.c. p.a. for the next five years (c) 12 p.c. p.a. for the next eight years If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow? options: A)8,000 B)10,000 C)12,000 D)6,000 E)None of these SOLUTION:Let x be the amount Amal borrowed. ∴ 18% of x + 40% of x + 48% of x = 5040 or, 106% of x = 5040 ∴ x = 5040⁄106 × 100 = 4754.71 Answer E #### E QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: Q=2550+(10050)=7550.B #### B QUESTION:What percent of 7.2 kg is 18 gms ? options: A)25 B)66 C)288 D)19 E)17 SOLUTION:Explanation: Required percentage = (18/7200 * 100)% = 1/4% = 0.25% Answer: A) .25% #### A QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 98 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 76 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5 SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) #### B QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:Tough and Tricky questions: Absolute Values. If \|a\| = 1/5 and \|b\| = 2/3, which of the following CANNOT be the result of a + b? options: A)13/15 B)-13/15 C)-7/15 D)7/15 E)7/5 SOLUTION:\|a\| = 1/5 Absolute value of 'a' can have two values = 1/5 and -(1/5) \|b\| = 2/3 Absolute value of 'b' can have two values = 2/3 and -(2/3) Now different combinations of a + b are as follows: a + b = (1/5) + (2/3) = 13/15 - a - b = -(1/5) - (2/3) = -13/15 a - b = (1/5) - (2/3) = -(7/15) -a + b = -(1/5) + (2/3) = 7/15 Cross verifying with the given options, left over option is E. #### E <<<Examples ends QUESTION:A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)22 days B)12 days C)67 days D)17 days E)18 days SOLUTION:C = 1/2 - 1/6 - 1/4 = 1/12 => 12 days Answer:B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)11.3 C)13 D)14 E)15 SOLUTION:Speed of the first train = 120/9 = 13.3 m/sec. Speed of the second train = 120/15 = 8 m/sec. Relative speed = 13.3 + 8 = 21.3 m/sec. Required time = (120 + 120)/21.3 = 11.3 sec. Answer: Option B #### B QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? options: A)338 B)2767 C)1023 D)1877 E)1722 SOLUTION:Explanation: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted. Hence, the required number of ways = 45 - 1. = 210 - 1 = 1024 - 1 = 1023 Answer:C #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)140km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5 or, x/40 + (250 - x)/60 = 5 or, (3x + 500 - 2x)//120 = 5 or 500 + x = 600 x=100 ANSWER:C #### C QUESTION:If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage? options: A)50% B)100% C)45% D)55% E)65% SOLUTION:Let the C.P of each book be Re 1. Then, S.P of 5 books= C.P of 10 books= Rs. 10 Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10 Gain = Rs ( 10 -5 ) = Rs 5. Gain% = ( 5/5× 100 ) % = 100% Answer : B #### B QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000? options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000 SOLUTION:Saving = (45-30)% of 48000 = 7200. Answer:D #### D QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520 SOLUTION:P - 340 = (P48)/100 P = 500 Answer:D #### D QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:In how many ways can 7 boys be seated in a circular order? options: A)110 B)230 C)720 D)420 E)680 SOLUTION:Number of arrangements possible =(7−1)!=6!=6x5x4x3x2x1=720 Answer: C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:By selling an article at Rs.600, a profit of 30% is made. Find its cost price? options: A)400 B)267 C)287 D)480 E)811 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+50)] = 600 * [100/150] = Rs.400 Answer: A #### A QUESTION:A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? options: A)288 m B)256 m C)400 m D)278 m E)287 m SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (900 + x)/60 = 65/3 x = 400 m. Answer:C #### C QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/161/a^2100)=56.25% Answer is(B) #### B QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: options: A)48759 B)51236 C)47619 D)6974 E)1235 SOLUTION:Explanation: By hit and trial, we find that 47619 x 7 = 333333. ANSWER:C #### C QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum? options: A)337 B)268 C)198 D)697 E)168 SOLUTION:1200 = P [1 + (126)/100] P = 697' Answer:D #### D QUESTION:The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number? options: A)40 B)45 C)55 D)45 E)50 SOLUTION:a1 = 120/3 = 40 a2 = a1 -5 = 35 sum of second list = 353 = 105 therefore the number = 105 -60 = 45 D #### D QUESTION:If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil? options: A)5 B)3 C)1 D)4 E)2 SOLUTION:Blue is 1/2 but can also be written as 4/8 Red is 1/8 White is 3/8 4/8+1/8+3/8= 8/8=1 Answer is C) 1 #### C QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water? options: A)6 B)24 C)8 D)12 E)44 SOLUTION:40 --- 8 DS = 5 ? ---- 1 56 ---- 8 US = 7 ? ---- 1 M = ? M = (5 + 7)/2 = 6 Answer: A #### A QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h? options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these SOLUTION:Explanation: Let the length of the train be L. Then, => (450 + L)/42 = (650+L)/50. => L= 600 m. Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25(18/5) = 90 Km /hr. ANSWER IS A #### A QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (54 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? options: A)11 B)44 C)24 D)25 E)22 SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, A=236 and B=25 Ans - D #### D QUESTION:According to a survey, at least 60% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? options: A)15% B)20% C)25% D)0% E)35% SOLUTION:It seems that something is wrong with your answer options. 1) minimum applesbananas: [XXXXXXXXXXXXXX------] - apples [-----XXXXXXXXXXXXXXX] - bananas mimimum ab = 60 - (100-75) = 35% 2) minimum (applesbananas)cherries: [XXXXXXXXX-----------] - applesbananas [----XXXXXXXXXXXXXXXX] - cherries mimimum ab = 35 - (100-80) =15% A #### A QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3 SOLUTION:Others equal 80 whereas (c) equals 80.8. Answer C #### C QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B? options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above SOLUTION:et ratio of A and B be 6x & 7x so net loss = 6x+7x= 7800 x=600 A=6x=6(600)=3600 B= 7x=7(600)=4200 so, B= 4200 ANSWER:A #### A QUESTION:Of the 50 researchers in a workgroup, 30 percent will be assigned to Team A and the remaining 80 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 20 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 30 will be in team A 70 will be in team B The larger diff is 70 want team A so diff is 70-30=40. At least 40 people will NOT get their wish, so for 50 researchers the same number is 20. Answer choice C #### C QUESTION:The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of present committee is; options: A)39 years B)38 years C)36 years D)35 years E)37 years SOLUTION:Total age of the committee = 408 = 320, Total age when a member is retired and a new one was joined = 320-55 +39, =304 Average age of present committee = 304/8 = 38. ANSWER:B #### B QUESTION:Evaluate: \|7 - 8(3 - 12)\| - \|5 - 11\| = ? options: A)40 B)50 C)73 D)70 E)80 SOLUTION:According to order of operations, inner brackets first. Hence \|7 - 8(3 - 12)\| - \|5 - 11\| = \|7 - 8(-9)\| - \|5 - 11\| According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence = \|7 + 72\| - \|5 - 11\| = \|79\| - \|-6\| = 79 - 6 = 73 correct answer C)73 #### C QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (2010.5 + 3012) = 0 Answer : A #### A QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:16.02 Ã— 0.1 = ? options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these SOLUTION:16.02 Ã— 0.1 = 1.602 The answer is C. #### C QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ? options: A)15 : 8 : 2 B)19 : 7 : 9 C)7 : 15 : 10 D)12 : 9 : 17 E)None of these SOLUTION:Explanation: Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively. Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y) Now, 6x – 5y = 1/4(6x) 24x – 20y = 6x 18x = 20y x/y = 20/18 = 10 / 9 Savings of P / Savings of Q = 6x – 5y / 8x – 8y = [6(x/y) – 5] / [8(x/y) – 8] = [(6 * 10/9) – 5] / [(8 * 10/9) – 8] = 15/8 Savings of Q / Savings of R = 8x – 8y / 11x – 12y = [8(x/y) – 8] / [11(x/y) – 12] = (8 * 10/9) – 8 / (11* 10/9) – 12 = 8/2 Ratio of savings of P : Q : R = 15 : 8 : 2 ANSWER: A #### A QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:The difference between a two-digit number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? options: A)4 B)9 C)3 D)Cannot be determined E)None of theses SOLUTION:Let the two-digit number be 10x + y. Then, (10x + y) – (10y + x) = 36 or x – y = 4 Answer A #### A QUESTION:Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder options: A)1235 B)1456 C)1567 D)1678 E)1631 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 35 5x = 1330 x = 266 Large number = 266+1365 = 1631 E #### E QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Sol. By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6. Answer C #### C QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ? options: A)1 B)10 C)30 D)20 E)21 SOLUTION:This is a solution from Beatthegmat: even numbers: (60-2)/2 + 1 = 30 even integers. (60+2)/2 = 31 is the average of the even set. sum = avg(#of elements) = 3130 = 930 = a odd numbers: (59-1)/2 + 1 = 30 odd integers. (59+1)/2 = 30 is the average of the odd set. sum = avg(#of elements) = 3030 = 900 = b a-b = 930 - 900 = 30. Answer : C #### C QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37 options: A)13 B)18 C)40 D)37 E)25 SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong. Answer : D #### D QUESTION:A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent? options: A)18 1/9 % B)18 9/3 % C)18 1/3 % D)14 2/7 % E)18 7/3 % SOLUTION:C.P. of 1 kg = 595/85 = Rs. 7 S.P. of 1 kg = Rs. 8 Gain % = 1/7 100 = 100/7 = 14 2/7 % Answer: D #### D QUESTION:John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 69 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let number of mangoes be x, number of oranges be 12-x 0.80x +(20-x)0.60/20 = 0.69 solving for x, we get x = 9 --> Mangoes 9, Oranges 11 Now, number of oranges to be returned be y 0.809 + (11-y)0.60/20-y = 0.72 solving for y, y = 5 Ans: B #### B QUESTION:A cube of edge 7 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to: options: A)1:25 B)1:49 C)1:52 D)1:522 E)None SOLUTION:Sol. Required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1/49 = 1:49. Answer B #### B QUESTION:A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? options: A)4:7 B)4:0 C)4:3 D)4:1 E)4:2 SOLUTION:12:9 = 4:3 Answer: C #### C QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ? options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 19 x 13 ) / (19 +13 ) km/hr. = 15 km/hr. Correct Option: A #### A QUESTION:The area of a triangle is with base 4m and height 5m? options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2 SOLUTION:1/2 * 4 * 5 = 10 m2 Answer:B #### B QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3% SOLUTION:675 ---- 225 100 ---- ? => =33 1/3% Answer:C #### C QUESTION:For which of the following values of s is (40+s)/s an integer? options: A)3 B)4 C)9 D)11 E)40 SOLUTION:This problem has to be solved by checking the options (40 + s)/s For this entity to be an integer, 50 + s should be divisible by s Option A: 43/3 - Not an Integer Option B:44/4 - Not an Integer Option C: 49/9 - Not an integer Option D: 51/11 - Not an integer Option E - 80/40- Integer Correct Option: E #### E QUESTION:By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price options: A)s. 700/- B)s. 800/- C)s. 880/- D)s. 900/- E)s. 990/- SOLUTION:80 % ------> 560 (80 * 7 = 560) 100 % ------>700 (100 * 7 = 700) Cost price = Rs. 700/- A #### A QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%? options: A)600 B)887 C)256 D)654 E)675 SOLUTION:Cost price = Rs.500 profit = 35% of 500 = Rs.175 Selling price = Cost price + Profit = 500 + 175 = 675 Answer: E #### E QUESTION:The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output? options: A)20% B)27% C)30% D)32% E)79% SOLUTION:The original output increases by 15% and then 20%. Total % change = a + b + ab/100 Total % change = 15 + 20 + 1520/100 = 38% Now, you want to change it to 0, so, 0 = 38 + x + 38x/100 x = -38(100)/138 = 27% approximately Answer is B #### B QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((910)/2) = 910 = 90. ANSWER:A #### A QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12 SOLUTION:Let the two numbers be x and y. 60/100 * x + y = 5/4y => 3/5 x = 1/4 y => x/y = 5/12 E) #### E QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:A man purchased 3 blankets @ Rs.100 each, 2 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)278 B)900 C)278 D)450 E)772 SOLUTION:10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 – 600= 900 Answer:B #### B QUESTION:Of the 100 athletes at a soccer club, 40 play defense and 62 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between options: A)10 to 20 B)10 to 40 C)22 to 40 D)30 to 70 E)40 to 70 SOLUTION:First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E. {Total} = {defense} + {midfield} - {both} + {neither} 100 = 40 + 62 - {both} + {neither} {both} = {neither} + 2. Since the least value of {neither} is given to be 20, then the least value of {both} is 20+2=22.Eliminate A and B. Answer: C. #### C QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed? options: A)5 B)4 C)3 D)2 E)0 SOLUTION:= 147,000 = 147 x 1000 = (3) x (7 x 7) x (2x2x2) x (5x5x5) = 2^3 x 3^1 x 5^3 x 7^2 red = 7^2 = 49 ANSWER:D #### D QUESTION:A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? options: A)76 sec B)89 sec C)87 sec D)95 sec E)16 sec SOLUTION:Speed = 360/30 = 12 m/sec. Required time = (360 + 780)/12 = 95 sec. Answer:D #### D QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is options: A)9800000 B)2000000 C)7500000 D)1200000 E)None of these SOLUTION:Explanation: Number = (400200400)/422 = 2000000 Answer: B #### B QUESTION:The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area? options: A)1:1 B)1:9 C)1:3 D)1:4 E)1:3 SOLUTION:1:4 Answer: D #### D QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 17. D #### D QUESTION:A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 4016=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)9 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. answer has to be 1 in the units digit.. only 11 fits in.. 2) BA=10B+A, and AB=10A+B.. it is given that BA+AB=121.. or 10B+A +10A+B=121.. 11(A+B)=121.. so A+B=11.. ANSWER:D #### D QUESTION:If an average hard drive had a capacity of 0.1 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)1536 SOLUTION:0.12^10=0.11024=102.4 The answer is D. #### D QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 23 x = 6 Answer is E #### E QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4side = 4 (3p/5) = 12p/5 Answer is C. #### C QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-xy C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least? options: A)18 hours B)22 hours C)25 hours D)26 hours E)20 hours SOLUTION:Let the persons be A, B, C. Hours worked: A = 290/9 = 20 hours B = 390/9 = 30 hours C = 490/9 = 40 hours C is the hardest worker and A worked for the least number of hours. So the difference is 40-20 = 20 hours. Answer : E #### E QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)$2,750 B)$5,500 C)$11,000 D)$22,000 E)$44,000 SOLUTION:SI for 1st year = 550/2=275 275+275+SI on (275)=605==> SI on 275=55==> SI on 275 = 275R1/100=55 R=20% Now using SI for 2 years on T/2 of the money (T/2)202/100=550 T=5505= 2750 ANSWER:A #### A QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A. options: A)240 B)388 C)288 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 756 = 288 Answer: C #### C QUESTION:Today Joelle opened an interest-bearing savings account and deposited $10,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$12025 B)$11075 C)$11025 D)$11095 E)$11015 SOLUTION:Interest for 1st year =100005/100 = 500 Interest for 2nd year = 10500 5/100 = 525 Total =10000+500+525 = 11025 Answer : C #### C QUESTION:How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? options: A)03 B)4 C)5 D)1 E)7 SOLUTION:You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines. AB , AC BA , BC CA , CB There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB. The lines are: AB, BC and AC ; 3 lines only. So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important. Answer:A #### A QUESTION:In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ? options: A)22 B)27 C)75 D)29 E)271 SOLUTION:Explanation: Let the number of students in the class be 100 and let this required average be x. Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80) => 70x = 8000 - (950 + 1800) = 5250 => x = 75. Answer: C) 75 #### C QUESTION:If â€œâ€ is called â€œ+â€, â€œ/â€ is called â€œâ€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 24080 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 24080 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.6 kmph B)17.5 kmph C)12.8 kmph D)12.5 kmph E)14.5 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. options: A)5113 B)5117 C)5120 D)8119 E)10115 SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year. If x = initial number of trees = 5120 Year 1 = 5/4x Year 2 = (5/4)(5/4)x Year 3 = (5/4)(5/4)(5/4)x Year 4 = (5/4)(5/4)(5/4)(5/4)x Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500 Hence, correct answer = C #### C QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W? I. 9 II. 15 III. 27 options: A)I only B)II only C)I and II only D)I and III only E)I, II, and III SOLUTION:Ans: C W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)3 means x must contain 3^2 and 5^2 so with these conditions we know that 9=3^2 and 15=35 both have required factors for the divisibility of lowest int for x which is 925 but 27 is not a divisor because it can't divide 925 fully. so Ans : C #### C QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? options: A)30 B)39 C)87 D)27 E)91 SOLUTION:Let the side of the square(ABCD) be x meters. Then, AB + BC = 2x metres. AC = = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = = 30% (approx) Answer:A #### A QUESTION:9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90% B)85% C)80% D)75% E)70% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1sd; mean+1sd} = {10-10.25; 10+0.25} = {9.75; 10.25}. From the 8 listed numbers, 5 are within this range so 5/8=75%. Answer: D. #### D QUESTION:By investing in 1623% stock at 64, one earns Rs. 1600. The investment made is options: A)s. 9600 B)s. 7500 C)s. 5640 D)s. 6144 E)s. 6760 SOLUTION:Explanation : Market Value = Rs.64 Face Value is not given and hence take it as Rs.100 16 2/3% of the face value = 50/3 ie, to earn 50/3, investment = Rs.64 Hence, to earn Rs.1600, investment needed = 64×3×1600/50=6144 Answer : Option D #### D QUESTION:A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later? options: A)2(10^5) B)9(10^5) C)(2^9)(10^5) D)(10^9)(10^5) E)(10^5)^9 SOLUTION:Every 10 minutes, the population is double the previous population. In 90 minutes, the population doubles 9 times. The population then is 2^910^5. The answer is C. #### C QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(8400047/2)/100 = i i = 11760 Answer: D #### D QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)300 B)368 C)375 D)337 E)639 SOLUTION:A+B+C = 1200 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1200 => 300 Answer:A #### A QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 1000.70.60.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792? options: A)1600 B)2777 C)2889 D)27670 E)2771 SOLUTION:1792 = P [1 + (512/5)/100] P= 1600.Answer:A #### A QUESTION:How many 0's are there in the binary form of 61024 + 464 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:61024 + 464 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! A #### A QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score? options: A)662 B)672 C)652 D)646 E)721 SOLUTION:8 * 82 = 656 – 10 = 646 ANSWER:D #### D QUESTION:A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 305 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day? options: A)400 B)440 C)550 D)625 E)700 SOLUTION:Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour. 7A+11B=305 ---(1) 8A+22C=600 ---(2) Dividing (2) by 2 4A+11C=300.....(3) Adding (1)(3) 11A+11B+11C = 605 A+B+C=55 per hour So for eight hrs = 558 = 440 = Answer = B #### B QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers){(n-1)!(111...........n times)-(n-2)!(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!(11111)-(5-2)!1111} = 10{(4!11111)-(3!1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 160 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start? options: A)5.0 B)5.5 C)6.0 D)6.5 E)7.0 SOLUTION:In 2 hours, A travels 60 km. B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts. So A and B both travel a distance of 240 km. C needs 1.5 hours to travel 240 km, so C leaves 6.5 hours after A. The answer is D. #### D QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled? options: A)1200 B)1400 C)1600 D)1500 E)1540 SOLUTION:Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %) 20 % = 60 % - 40 % 20% -----> 280 (20×14 = 280 ) 100% -----> 1400 (100×14 = 1400) Option 'B' #### B QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4 SOLUTION:P1 takes 12 hrs Rate for P2P3 together = 1/16 + 1/18 = 17/144 Therefore they take 144/17 Ratio = 144/17 = D #### D QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")(Number of ways the vocalist can sing "new songs")= 1510=150 Answer: C #### C QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5) Answer - C #### C QUESTION:Convert the following into a fraction: 0.3% options: A)1/3 B)2/3 C)3/10 D)1/6 E)None of the Above SOLUTION:0.3 =3/10 Answer is C. #### C QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 x = 9 6 * 1000 or x = 961000/ 410 = 1350 Answer : B #### B QUESTION:The perimeter of one face of a cube is 40 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)1000cm3 E)None of these SOLUTION:Explanation: Edge of cude = 40/4 = 10 cm Volume = aaa = 101010 = 1000 cm cube Option D #### D QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=2726^2 The answer is C. #### C QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice. options: A)25 B)34 C)50 D)67 E)100 SOLUTION:A =25 1 oz concentrate + 3 oz ofwater = 4 oz jucie 300 oz concentrate +900 oz of waer = 1200 oz juice no of cans==300/12=25 Ratio of juice to water ===> 1:3 total 2006 ounces 12 ounce juice cans ==> 1200/12 == 1001/4 (ratio of jiuce to total) == 25 #### A QUESTION:A walks at 10 kmph and 5 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A? options: A)100km B)150km C)50km D)120km E)200km SOLUTION:Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 5 hours. x/10 - x/20 = 5 x = 100 km Answer is A #### A QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 310 , 410 , 510 Hence required H.C.F. = 10 Answer is A #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:Solve : 42 : 56 :: 110 : ? options: A)121 B)111 C)132 D)143 E)158 SOLUTION:67=42 78=56 1011=110 11*12=132 ans 42:56::110:132 ANSWER:C #### C QUESTION:If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))? options: A)81 B)16 C)300 D)256 E)625 SOLUTION:f(c)=c^2 f(f(c)) = (c^2)^2 = c^4 Therefore f(f(c)) will be numbers that are 4th power of other numbers. Checking the options: 81 = 3^4 16 = 2^4 300. This cannot be written as the 4th power of any number 256 = 4^4 625 = 5^4 Answer: C #### C QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C <<<Examples ends QUESTION:Find 30 % of 240 options: A)72 B)94 C)86 D)74 E)110 SOLUTION:We know that R % of m is equal to R/100 × m. So, we have 30 % of 240 30/100 × 240 = 72 Answer:A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately). options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48% SOLUTION:Let the total money=300 A's part=100 B's part=200 After 2 years A's part=73.46 (As it depreciates by 14.29% per annum) After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where P=200,r=0.2,n=1,t=2) So, After 2 years total amount=361.46 Therefore % increase in money=(361.46-300)100/300=20.48% ANSWER:B #### B QUESTION:The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is options: A)Rs. 7000 B)Rs. 8000 C)Rs. 8500 D)Rs. 9000 E)None SOLUTION:Answer Average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = Rs. 9000 Correct Option: D #### D QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games? options: A) 7 B) 6 C) 5 D) 4 E) 3 SOLUTION:18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most. Answer (C) #### C QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 5002/25 =40sec ANSWER:A #### A QUESTION:If n is the product of three consecutive integers, and n is divisible by 6, which of the following is not necessarily a divisor of n ? options: A)242 B)4 C)6.8 D)5 E)0. SOLUTION:IF ONE NO. IS 6 THEN OTHER CONSEQUTIVE NO. ARE 456 =120 , 567=210 , 678 =336 NO NUMBER WILL NO BE DIVISOR OF N E #### E QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5 SOLUTION:Note that we have 5positivetemperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits. Answer: B. #### B QUESTION:The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is options: A)1/8 B)1/4 C)2/3 D)3/4 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4 Ans.(B) #### B QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? options: A)1500 B)1600 C)1750 D)1900 E)2000 SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. #### C QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make? options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss SOLUTION:81 ---- 17 100 ----- ? è 20.98%loss Answer: B #### B QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? options: A)229 B)270 C)877 D)266 E)281 SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages. Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left. 23⋅x−13⋅x=9023⋅x−13⋅x=90 13⋅x=9013⋅x=90 x=270x=270 So the book is 270 pages long. Answer:B #### B QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform? options: A)45 B)47 C)49 D)51 E)53 SOLUTION:Let the length of the train be x meters. When a train crosses an electric pole, the distance covered is its own length x. speed = 36 km/h = 36000 m / 3600 s = 10 m/s x = 14 * 10 = 140 m. The time taken to pass the platform = (140 +370)/ 10 = 51 seconds The answer is D. #### D QUESTION:here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? options: A)2100 B)1800 C)1245 D)3210 E)4521 SOLUTION:5 subjects can be arranged in 6 periods in 6P5 ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements = 6P5× 5C1 /2!=1800 Ans: B #### B QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters? options: A)50 B)51 C)52 D)53 E)54 SOLUTION:50000 ->1 41000 ->5 31100 ->10 32000 ->10 21110 ->10 22100 ->15 11111 ->1 1+5+10+10+10+30+1=52 ANSWER:C #### C QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)6 Answer: B #### B QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C22C2=151=15 B. 1 kind of cheese and 1 kind of fruit --> 6C12C1=62=12 A+B=15+12=27 Answer: E. #### E QUESTION:Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance? options: A)$2.40 B)$3.00 C)$3.20 D)$3.60 E)$4.80 SOLUTION:Total allowance=X Amount spent at the arcade=3/5X Amount Remaining=2/5X Amount Spent at the toy store=2/51/3X=2/15X Amount Remaining=2/5X-2/15X=4/15X Now, 4/15X=$0.96 Therefore, X=$3.60. Answer D #### D QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:Which of the following is equal to 3.14 x 10^6) ? options: A)3.14 B)3140000 C)31400 D)314 E)314000 SOLUTION:= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is B. #### B QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively options: A)19 B)17 C)13 D)22 E)21 SOLUTION:Explanation: Answer will be HCF of (48-4, 210-12, 136-4) HCF of (44, 198, 132) = 22 Option D #### D QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3 SOLUTION:total 10 from take one. 10c1=10 red 6 from one 6c1=6 6/10= 3/5 ANSWER:C #### C QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream? options: A)15 B)17 C)19 D)18 E)16 SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 57/3 = 19 kmph. Answer:C #### C QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:Two pipe A and B fill a tank in 6 hours and 8 hours respectively.and C empty that tank in 12 hour.if all three pipe open together in empty tank then how much time it take to fill the tank? options: A)19/3 B)23/2 C)24/5 D)18 E)16 SOLUTION:all three pipe resultant fill tank in 1 hour=[1/6+1/8-1/12]=5/24 total time taken to fill tank=24/5 hour answer C #### C QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speedâˆ—Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier so actual day to return home is Friday. Rohit returned after days so Tuesday. ANSWER:C #### C QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)58 B)70 C)63 D)65 E)72 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-2=2a+6 2a=8 . a=4 Therefore, A(0,0); B(0,14); C(9,14) 1/2914=63 Answer: C #### C QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue? options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17 SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/189/17 = 12/17. Answer: E. #### E QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar? options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9) SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg Actual price of sugar = 10100/((100-10 )4) = Rs. 2(7/9) B #### B QUESTION:The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ? options: A)148 B)134 C)156 D)144 E)None SOLUTION:Solution: Ratio of Ducks and Frogs in Pond, = 37 : 39. Average of Ducks and Frogs in Pond, = 132. So, total number of Ducks and Frogs in the Pond, = 2 132 = 262. Therefore, Number of Frogs, = (26239)/76 = 134. Answer: Option B #### B QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+1664=0 (x-32)^2=0 x=32 A #### A QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years? options: A)6.9% B)2.9% C)9.9% D)5.9% E)4.9% SOLUTION:220.50 = (15003R)/100 R = 4.9% Answer: E #### E QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is: options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in one years is: 5,870,000,000,000 = 587 * 10 ^10 The distance of the light travels in 1000 years is: = 587 * 10^10 x 10 ^3 = 587 x 10^13 miles Answer :A #### A QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:0.[u]225[/u = 0.225225225..... Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5. Answer E #### E QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)150 B)152 C)154 D)158 E)144 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:What is the sum of all the numbers which divides 100 ? options: A)408 B)102 C)816 D)916 E)416 SOLUTION:You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408. Final Answer: A #### A QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)787 C)178 D)179 E)172 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)Rs.10528 B)Rs.10521 C)Rs.10511 D)Rs.10411 E)Rs.10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs.10500 Answer: E #### E QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is: options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons SOLUTION:Explanation: Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying] Volume of {\color{Black} \frac{1}{40}} part = 3 gallons Volume of whole = (3 x 40) gallons = 120 gallons. Answer: C #### C QUESTION:The greatest common factor of positive integers m and n is 9. What is the greatest common factor of (2m^2, 2n^2)? options: A)9 B)81 C)162 D)324 E)405 SOLUTION:m = 9j and n = 9k, where the greatest common factor of j and k is 1. 2m^2 = 299j^2 and 2n^2 = 299k^2 The greatest common factor of 2m^2 and 2n^2 is 299 = 162 The answer is C. #### C QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:In how many different number of ways 5 boys and 4 girls can sit on a bench? options: A)700 B)710 C)720 D)362880 E)740 SOLUTION:npn = n! 9p9 = 9 X 8 X 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 362880 D #### D QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 * 6 = 6. Answer:C #### C QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)(9C2) =736= 252 Answer : B #### B QUESTION:A company spends an average of $500 for its 20 employees's salaries and an average of $100 for its 5 drivers' salaries. What is the average expenditure of the company? options: A)$360 B)$290 C)$420 D)$600 E)$240 SOLUTION:Number of employees is 20 Their average salary is $500 Number of drivers is 5 Their average salary is $100 Total salary of the employees is 20500=$10,000 Total salary of the drivers is 5100=$500 Total expenditure for company is 10,000+500=$10,500 Average expenditure is 10,500/20+5=$420 Answer is C #### C QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is: options: A)6 hours B)10 hours C)15 hours D)30 hours E)35 hours SOLUTION:suppose first pipe filled the tank in x hour so second in x-5 and third in x-9 1/x+1/(x-5)=1/(x-9) by solving it we get x=15 ANSWER:C #### C QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:1398 x 1398 = ? options: A)1624404 B)1851404 C)1951404 D)1954404 E)None of these SOLUTION:Explanation : 1398 x 1398 = (1398)2 = (1400 - 2)2 = 14002 - (2 × 1400 × 2) + 22 = 1960000 - 5600 + 4 = 1954404. Answer : Option D #### D QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(2916-2915) =29 years. ANSWER:C #### C QUESTION:The average of four consecutive odd numbers is 24. Find the largest number. options: A)25 B)27 C)29 D)31 E)32 SOLUTION:Explanation: Let the numbers are x, x+2, x+4, x+6, then =>x+(x+2)+(x+4)+(x+6)4=24 =>4x+12)4=24 =>x+3=24=>x=21 So largest number is 21 + 6 = 27 Answer: Option B #### B QUESTION:Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){18, 20} B){8, 10} C){28, 38} D){6, 10} E){5, 10} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others. Hence Answer : B #### B QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons? options: A)200 B)210 C)230 D)250 E)270 SOLUTION:7p3 = 7 × 6 × 5 = 210 B) #### B QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 21=2. Answer: C. #### C QUESTION:David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? options: A)75 B)27.6 C)66.6 D)16.5 E)11 SOLUTION:Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C #### C QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose? options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0 SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x' The problem boils down to: Rose to Poppy: s+3=x/6 ------- 1 Daisy to Rose: s=(x+18)/10------ 2 so from 1 we can re write x as x=6s+18 substitute the value of x in 2 gives us s=1.8 m/s D #### D QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame? options: A)10 B)20 C)30 D)40 E)54 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so Area of frame = (1/3) a^2 Area of Frame + Painting = a^2 + (1/3)a^2 = (4/3)a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to bsqrt2 so, b sqrt2 = 12 so, b = 6 * sqrt2 b^2 = 72 we know that b^2 = (4/3)a^2 so, a^2 = (3/4)b^2 = (3/4)72 = 54 And area of painting = a^2 = 54 So, answer will be E. #### E QUESTION:If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4 Median = 4 Difference = 4-4 = 0 Option A #### A QUESTION:A man can do a job in 5 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.3 B)6.9 C)3.5 D)6.1 E)6.2 SOLUTION:1 day work of the three persons = (1/5 + 1/20 + 1/25) = 29/100 So, all three together will complete the work in 100/29 = 3.5 days. Answer:C #### C QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A QUESTION:A jar contains 12 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed? options: A)1/495 B)1/165 C)1/81 D)11/31 E)3/220 SOLUTION:Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue. Sample space = 12C3 = 220. Probability of choosing 3 red = 3C3/12C3 = 1/220. Probability of choosing 3 green = 3C3/12C3 = 1/220. Probability of choosing 3 blue = 3C3/12C3 = 1/220. Required probability = 1+1+1/220 = 3/220 Ans (E). #### E QUESTION:On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between options: A)10 and 20 B)20 and 30 C)30 and 40 D)40 and 50 E)50 and 60 SOLUTION:Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.) Here are the starting values: L = $3000 M = $3000 S = $4000 Apply the first year’s changes, so that you have these numbers on 1/1/2012: Newer L = $3000 + 10% = $3300 Newer M = $3000 + 20% = $3600 Newer S = $4000 + 15% = $4600 Now apply the second year’s changes to L and M: Newest L = $3300– 20% = $3300– $660 = $2640 Newest M = $3600– 10% = $3600– $360 = $3240 Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120 The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks: 10% of $4600 = $460. So 20% is just double that, or $920. And so on. From this $480 lies between $460 and $920 The correct answer is A. #### A QUESTION:Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year? options: A)1:2:1 B)2:3:6 C)3:2:1 D)1:2:3 E)1:4:3 SOLUTION:Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively. 3b = 2b = c. a = c/3. b = c/2. Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments = 2:3:6. ANSWER:B #### B QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges? options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2 SOLUTION:The cost of one orange=5/12=0.416 The cost of ten oranges= 0.416x10= $ 4.16 Answer: B #### B QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:6C15C2 = 610 = 60 The answer is C. #### C QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20100)/36) %=120% Answer E)120 #### E QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P105)/100 P = 6200 Answer: A #### A QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:In case O is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)P and Q E)T and U SOLUTION:P and Q should serve on A ANSWER:D #### D QUESTION:Peter's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Peter makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0? options: A) 15 B) 24 C) 25 D) 26 E) 13 SOLUTION:day 0- payment of $7 is made in the morning (after 12 am midnight) day 1 onwards(after 12 am midnight) internet service will begin and will run for 72=14 days i.e. at the end of day 15 balance will be zero. now Peter can still use the internet till her debt reaches $5 which means total of 52=10 days. now the question states for how many days, including today, will she be connected to the internet without any additional paymentsi.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C #### C QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod? options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these SOLUTION:Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 7 :: 42.75 : x => 11.25 x x = 7 x 42.75 => x = (7 x 42.75) / 11.25 => x = 26.6 Answer : B #### B QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1â„2 C)17 D)Data inadequate E)None of these SOLUTION:12 M Ã— 18 = 12 W Ã— 18 Ã— 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 Ã— 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12Ã—18/12 2/3=17days Answer C #### C QUESTION:A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? options: A)39:40 B)39:45 C)39:40 D)39:41 E)39:42 SOLUTION:3: 4 A = 3/7210 = 90 390: 400 39:40 Answer: A #### A QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10? options: A)5 B)7 C)4 D)9 E)3 SOLUTION:30,40,50,60,70 total 5 Answer is A #### A QUESTION:1401 x 1401 = ? options: A)1962800 B)1962801 C)1960000 D)1951611 E)1951613 SOLUTION:1401 x 1401 = (1401)2 = (1400+1)2 = (1400)2 + (1)2 + (2 x 1400 x 1) = 1960000 + 1 + 2800 = 1960001+ 2800 = 1962801. B) #### B QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2PD or m - 2PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr? options: A)12 km/hr B)14 km/hr C)10 km/hr D)8 km/hr E)9 km/hr SOLUTION:Explanation: The person needs to cover 6 km in 45 minutes Given that he covers one-half of the distance in two-thirds of the total time => He covers half of 6 km in two-thirds of 45 minutes => He covers 3 km in 30 minutes Hence, now heneed to cover the remaining 3 km in the remaining 15 minutes Distance = 3 km Time = 15 minutes = 1/4 hour Required Speed=Distance/Time = 3/(1/4) = 12 km/hr Answer: Option A #### A QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km. Speed = Distance/Time Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours] Required speed = 3000 x 3/5 km/hr = 1800 km/hr. Answer: Option B #### B QUESTION:A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work? options: A)12/15 B)37 1/2 C)3/7 D)4/9 E)5/2 SOLUTION:Explanation : Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 ½ days ANSWER:B #### B QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/13 B)2/15 C)4/13 D)3/17 E)1/19 SOLUTION:Here, n(S) = 52 There are 13 cards that are diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:The greatest common factor of two positive integers is P. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other? options: A)PY⁄Z B)XZ + YZ C)X⁄Z + Y D)X + Y⁄Z E)X + Z⁄Y SOLUTION:Say other integer is W Formula GCF(WZ)LCM(WZ) = WZ PY = WZ So W= PY/Z Answer A #### A QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers){(n-1)!(111...........n times)-(n-2)!(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!(11111)-(5-2)!1111} = 10{(4!11111)-(3!1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long? options: A)2.5 B)3 C)5 D)7 E)9 SOLUTION:D = 25 60 + 1000 = 2500 m T = 2500/60 * 18/5 = 150 sec = 2.5 mins Answer: A #### A QUESTION:The ratio of the prices of three articles X, Y and Z is 8 : 5 : 3. If the prices of X , Y and Z are increased by 25%, 20% and 33 1/3% respectively, then what would be the ratio of the new prices of X, Y and Z? options: A)5 : 3 : 1 B)5 : 3 : 2 C)10 : 7 : 4 D)10 : 8 : 5 E)None of these SOLUTION:Let the prices of X, Y and Z be 8k, 5k and 3k respectively. After increase Price of X = 8k * 125/100 = 10k Price of Y = 5k * 120/100 = 6k Price of Z = 3k * (133 1/3)/100 = 4k Required ratio = 10k : 6k : 4k = 5 : 3 : 2. ANSWER:B #### B QUESTION:A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 24 on Wednesday, what would be the value of D calculated on the following Saturday? options: A)3450 B)3860 C)4220 D)4670 E)5040 SOLUTION:On Saturday, the value would be 76524 = 5040 The answer is E. #### E QUESTION:Amal borrowed a sum of money with simple interest as per the following rate structure: (a) 6 p.c. p.a. for the first three years (b) 8 p.c. p.a. for the next five years (c) 12 p.c. p.a. for the next eight years If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow? options: A)8,000 B)10,000 C)12,000 D)6,000 E)None of these SOLUTION:Let x be the amount Amal borrowed. ∴ 18% of x + 40% of x + 48% of x = 5040 or, 106% of x = 5040 ∴ x = 5040⁄106 × 100 = 4754.71 Answer E #### E QUESTION:In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant. options: A)250 m B)560 m C)100 m D)320 m E)240 m SOLUTION:Explanation : Abhishek's speed = 100/5=20 m/s. Time taken by Abhishek to cover 500 m =500/20=25 seconds. Dishu's speed = 500/20 or 25 m/s Prashant's speed = 15 m/s Time taken by Dishu to meet Prashant in 500m race in opposite direction: Distance covered by Abhishek: =>500/(15+25). =>12.5 sec. =>12.5(20)= 250 m. Answer : A #### A QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(7206)=4320. Answer is E #### E QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (527) - (425) = 135-100 = 35 Answer: Option A #### A QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E <<<Examples ends QUESTION:A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.) options: A)1/5 B)1/2 C)2/3 D)4/5 E)6/5 SOLUTION:Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B FOR THE FIRST BUCKET ... Red color - 2 Blue color - 2 FOR THE SECOND BUCKET Red color - 3 Blue color -2 In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios : Scenario I - He picks Red color from List A and Blue color from List B Scenario II - He picks Blue color from List A and Red color from List B Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5 Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ... Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ... We get 1/5 + 3/10 = 2/3 (C) #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options? Your approach: total 10 options, 5c3. Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together. This gives us 10-3-3=4 as the answer. Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE. D #### D QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:If x and y are different integers and x^2 = xy, which of the following must be true ? I. y = 0 II. x = 0 III. x = y options: A)I only B)II only C)III only D)I and III only E)II, and III SOLUTION:Answer choice A is correct. The question gives you x^2=xy you can simplify that as x^2-xy=0 x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer. Answer E #### E QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)19 years E)15 years SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38 => x = 19 Son's age 5 years back = (19 - 5) = 14 years. Answer: B #### B QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 13.7 II. 12.3 III. 9.3 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+21.3 = 14.6 2 SD below mean = 12-21.3 = 9.4 12.3 and 13.7 lies in the range of 2SD from mean Answer: Option D #### D QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:which of the following is a prime number ? options: A)17 B)18 C)15 D)20 E)25 SOLUTION:Clearly, 17 is a prime number. Option A #### A QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)15 B)30 C)36 D)72 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 16) = (x + 8) or x = 24. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72. Answer: D #### D QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail? options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8 SOLUTION:Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {HHH,HTH,THH,HHT} P(E) = n(E)/n(S) =4/8 = 1/2 Answer is D #### D QUESTION:In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women? options: A)63 B)67 C)70 D)90 E)80 SOLUTION:We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this = 6C4 × 4C2 90 D) #### D QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent? options: A)22 B)77 C)18 D)21.6 E)88 SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900 Profit(%) = (66900 - 55000)/55000 * 100 = 21.6% Answer: D #### D QUESTION:A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.? options: A)50 kmph B)58 kmph C)62 kmph D)65 kmph E)75 kmph SOLUTION:Relative speed = 280/9 m / sec = ((280/9)(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph. Answer : C. #### C QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter? options: A)15 B)25 C)30 D)45 E)60 SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach... We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats. Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as... 15X/7X When we add the 16 cats and factor in the 'ending ratio', we have an equation.... 15X/(7X+16) = 15/11 Here we have 1 variable and 1 equation, so we can solve for X.... (15X)(11) = (7X+16)(15) (X)(11) = (7X+16)(1) 11X = 7X + 16 4X = 16 X = 4 With this X, we can figure out the initial number of dogs and cats... Initial dogs = 15X = 15(4) = 60 Final Answer: D #### D QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)10987 B)11755 C)17576 D)19775 E)21899 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:1 weaver can weave 1 mat in 4 days. 10 weavers can weave 10 mats in 4 days. 10 weavers can weave 25 mats in 10 days. The answer is D. #### D QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? options: A)52 B)68 C)62 D)67 E)69 SOLUTION:Answer No. of pieces = Total length / Length of each piece = 192/3.2 = 60 Option: D #### D QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? options: A)112 B)77 C)267 D)12 E)99 SOLUTION:Explanation: As the division is by 2, 3, 7 together, the numbers are to be divisible by: 237 = 42 The limits are 100 and 600 The first number divisible is 423 = 126 To find out the last number divisible by 42 within 600: 600/42 = 14.28 Hence, 4214 = 588 is the last number divisible by 42 within 600 Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12 ANSWER: D #### D QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase? options: A)$32 B)$50 C)$320 D)$400 E)$500 SOLUTION:Property tax as a percentage of its assessed value = 8% Increase in assessed value of the property = 24000 - 20000 = 4,000 $ Increase in property tax = (8/100)* 4000 = 320 $ Answer C #### C QUESTION:The difference between the squares of two consecutive odd integers is a square<1000 whose root equals the combined sum of the digits of the two integers. What is the sum of the digits M of the larger integer? options: A)M=2 B)M=5 C)M=8 D)10 E)11 SOLUTION:Really hard. But let's start with few concepts: 1. Square of an odd integer will be odd. 2. Difference of odd and odd will be even. 3. Any odd integer can be expressed as difference of two squares. 4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4. Assume two odd integers to be (2x-1) and (2x+1). Difference of their squares = (2x+1)^2 - (2x-1)^2 = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x) = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x = 8x Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers. 8 = 2^3, so x needs to be such that itcompletesa perfect square. If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits. Let's check the options, starting with c. For sum to be 8, few possibilities are: 17, 35, 53, 71 If we take 17, the pair is 15 and 17, meaning x = 8. 8x = 64 root of 64 = 4 but 4 is not equal to 1+5+1+7. Reject. If we take 35, the pair is 33 and 35, meaning x = 17. 8x = 817 Reject since perfect square is not possible. If we take 53, the pair is 51 and 53, meaning x = 26. 8x = 826 Reject since perfect square is not possible. If we take 71, the pair is 69 and 71, meaning x = 35. 8x = 835 Reject since perfect square is not possible. I tried each option and the possibilities and then got lost. Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits? Starting with option a, only 2-digit odd integer whose sum is 2 is 101. If we take 101, the pair is 99 and 101, meaning x = 50. 8x = 850 = 400 root of 400 = 20 which is indeed equal to 9+9+1+1. Answer (A). #### A QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L? options: A)6 B)-1 C)-2 D)-6 E)-10 SOLUTION:We need to find out the value of p and L to get to the slope. Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving 5 = -p2 +9 p2 = 4 p = + or - 2 simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7. -7 = -t2+9 t = +or - 4 considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1 IMO option B is correct answer. #### B QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20100)/36) %=120% Answer E)120 #### E QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? options: A)125 B)772 C)821 D)912 E)121 SOLUTION:Sum of the 35 numbers = 35 25 = 875 If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5. Thus, the new average = 25 * 5 = 125. Answer:A #### A QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -225/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c11c11c1)/5c3 =3/10 ANSWER:A #### A QUESTION:If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission? options: A)4% B)0.4% C)0.04% D)0.004% E)0.0004% SOLUTION:% of sales amount of commission = (Commission/Total Value) 100 = (0.8/2000) * 100 = 0.04% The answer is C. #### C QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:Evaluate 30!/28! options: A)720 B)600 C)870 D)910 E)650 SOLUTION:we have 30!/28! = 302928!/28! = 3029 = 870 Answer is C #### C QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is options: A)40 B)49 C)80 D)88 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 22 and x2 + y2 = 386. Now, 2xy = (x+y)2 - (x2 + y2) = (22)2 - 386= 484 - 386= 98 xy = 49. Answer B #### B QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 2600 = Rs.1200 Answer: A #### A QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:5216 × 51 = ? options: A)266015 B)266014 C)266016 D)266116 E)266226 SOLUTION:Normal way of multiplication may take time. Here is one alternative. 5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016 Answer is C. #### C QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes. options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20 SOLUTION:Assume the manager bought 100 tomatoes. Cost Price = 80 Given: 10% are damaged --> Available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90x - 80 = 9.6 90x = 89.6 x = 89.6/90 = 0.995 x is slightly under 0.9955 = 0.99 Answer: C #### C QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest? options: A)3.6 B)7 C)18 D)Cannot be determined E)None SOLUTION:Explanation: Let rate = R% and time = R years. Then, (1500 x R x R)/100 = 735 15RÂ² = 735 RÂ² = 49 R = 7. Answer: Option B #### B QUESTION:If a man walks to his office at 5/4 of his usual rate, he reaches office 30 minutes early than usual. What is his usual time to reach office. options: A)2 hrs B)2 1⁄2 hrs C)1 hr 50 min D)2 hrs 15 min E)None of these SOLUTION:usual time × (4⁄5 - 1) = -30⁄60 ⇒ usual time = 1⁄2 × 5 = 21⁄2 hrs Answer B #### B QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket? options: A)5min. 50sec. B)5min. 30 sec. C)6 min 36 sec. D)6mins. 32 sec. E)6 min. 15 sec. SOLUTION:Explanation: Part filled in 3 minutes = 3∗(1/12+1/15)=3∗9/60=9/20 Remaining part =1−9/20=11/20 =>1/12:11/20=1:X =>X=6.6 mins. =>X=6.6 mins. So it will take further 6 mins 36 seconds to fill the bucket. Option C #### C QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? options: A) 1000 B) 625 C) 1,250 D) 2,500 E) 10,000 SOLUTION:total fish = x percentage of second catch = (2/40)100 = 5% so, x 5% = 50 x = 1000 ans.A #### A QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24 options: A)22 B)62 C)28 D)16 E)11 SOLUTION:Answer:B #### B QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:Average age of students of an adult school is 42 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students. options: A)1200 B)120 C)360 D)200 E)None of these SOLUTION:Explanation : Let the original no. of students be x. According to situation, 42x + 12032 = (x + 120)36 ⇒ x = 80 So, Required no. of students after joining the new students = x + 120 = 200. Answer : D #### D QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is: options: A)$153 B)$848 C)$398 D)$549 E)$675 SOLUTION:B $848 S.I. for 1 year = $(1024 - 980) = $44. S.I. for 3 years = $(44 x 3) = $132. Principal = $(980 - 132) = $848. #### B QUESTION:Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)60% B)50% C)25% D)20% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 55 - {both} + 40 {both} = 20%. Answer: D. #### D QUESTION:A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is? options: A)7 B)6 C)8 D)4 E)2 SOLUTION:US = 20 DS = 34 M = (34 - 20)/2 = 7 Answer:A #### A QUESTION:If 2x = 3y = 20, then 12xy = ? options: A) 1,200 B) 800 C) 120 D) 40 E) 20 SOLUTION:2x = 20;x=10 3y = 20;y=20/3 Multiply: 12xy=121020/3=800. Answer: B. #### B QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides? options: A)3 B)6 C)5 D)9 E)1 SOLUTION:S = (1 + 2 + 7)/2 = 5 Answer:C #### C QUESTION:If (5^15)(9^8)=3(15^x), what is the value of x? options: A) 7 B) 9 C) 11 D) 13 E) 15 SOLUTION:(5^15)(9^8)=3(15^x) => 5^15 * 3^16 = 3 * 3^x * 5^x => 5^15 * 3^16 = 3^(x+1) * 5^x Value of x = 15 Answer E #### E QUESTION:The speeds of 3 trains in the ratio 10:15:20. The ratio between time taken by them to travel the same distance is? options: A)6:4:3 B)1:2:3 C)4:8:9 D)6:5:2 E)4:8:7 SOLUTION:Ratio of time taken is = 1/10 : 1/15 : 1/20 = 6:4:3 Answer is A #### A QUESTION:8k8 + k88 -------- 1,6w6 If k and w represent non-zero digits within the integers above, what is w? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16w6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8+7=16 or 8+8=16 (k can not be less than 7 or 9, as the result won't be 16*). After that it's easy to get that k=7 and w=6. Answer: A. #### A QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 210 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ? options: A)40 ml B)70 ml C)20 ml D)20/3 ml E)10 ml SOLUTION:There are 0.3100=30 ml of element X in the initial solution. We need X to be 1/3rd of 210 ml in the resulting solution, so 70 ml. Thus out of 110 ml of solution added, 40 must be X (in order it to become 70 ml) ans the remaining 70 must be Y. Answer: B #### B QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls? options: A)1/12 B)5/36 C)1/9 D)1/3 E)17/36 SOLUTION:no. of possible outcomes = 66 = 36 no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) ) So, the probability = 1/9 (Option C) #### C QUESTION:If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w? options: A)40 B)44 C)45 D)46 E)50 SOLUTION:Answer E = 50 We have (10^w)-74, where the sum of the digits is 440. 100-74 = 26, so we already have 2+6 = 8 from the 440. Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926. So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction. So we have 48 + 2 as an w = 50 #### E QUESTION:A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work? options: A)12/15 B)37 1/2 C)3/7 D)4/9 E)5/2 SOLUTION:Explanation : Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 ½ days ANSWER:B #### B QUESTION:Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank? options: A)IX B)XXIII C)XV D)XI E)None SOLUTION:Explanation: This is a simple addition series; each number is 3 more than the previous number. Answer: D #### D QUESTION:The ratio of two quantities is 2 to 5. If each of the quantities is increased by 5, what is the ratio of these two new quantities? options: A)2/5 B)5/8 C)7/13 D)22/25 E)It cannot be determined from the information given. SOLUTION:Correct Answer: E Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5. For example, if x = 2 and y = 5, then (x+5)/(y+5) = (2+5)/(5+5) = 7/10. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+5)/(y+5) = (4+5)/(10+5) = 9/15. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E). #### E QUESTION:If (x + 1) times (2x + 1) is an odd integer, then x must be options: A)an odd integer B)an even integer C)a prime number D)a composite number E)a negative integer SOLUTION:(x + 1) times (2x + 1) means (x + 1) (2x + 1).. (x + 1)(2x + 1)= 2x^2+3x+1... for 2x^2+3x+1 to be odd, 3x+1 should be odd.. hence 3x should be even, which further leads to x as even.. so x is even integer.. ANSWER:B #### B QUESTION:The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas. options: A)5:25 B)4:25 C)3:15 D)7:15 E)6:15 SOLUTION:Let the diagonals of the squares be 2x and 5x respectively. Ratio of their areas = (1/2)(2x) 2:(1/2)(5x) 2 = 4x2: 25x2 = 4 : 25. ANSWER B 4:25 #### B QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)20 B)99 C)77 D)26 E)12 SOLUTION:10 * 2 = 20 years Answer: A #### A QUESTION:A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue? options: A)no change B)decreases by 6.5% C)increases by 6.5% D)increases by 5.6% E)None of these SOLUTION:Explanation : Reduction of price = (100 -15)% = 85% = 0.85 Increase of sale = (100+15)% = 115% = 1.15 Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5% Answer :B #### B QUESTION:A man buys 1kg of sandalwood and 1kg of teakwood. He sells one for 10% profit and other for 10% loss. What is total profit/loss percentage? options: A)1% loss B)2% loss C)3% loss D)4% loss E)5% loss SOLUTION:if x is both the profit and loss % then it must be loss of x^2/100; so 1010/100=1; 1% loss ANSWER:A #### A QUESTION:A candidate got 30% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast? options: A)7500 B)2028 C)2775 D)10000 E)6851 SOLUTION:30%-----------L 70%-----------W ------------------ 40%----------4000 100%---------? => 10000 Answer:D #### D QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 5x) = 23/30. Hence, A #### A QUESTION:A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent? options: A)9% B)11% C)13% D)15% E)17% SOLUTION:Let P be the original price and let x be the number of items sold originally. The original income is Px. After the changes, the income is 0.9P1.3x = 1.17(Px), an increase of 17%. The answer is E. #### E QUESTION:If 144/0.144 = 14.4/x, then the value of x is: options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144 SOLUTION:=144/0.144 = 14.4/x =144 x 1000/144 =14.4/x =x = 14.4/1000 = 0.0144 Answer is C. #### C QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? options: A)5/6 B)2/7 C)2/8 D)9/2 E)8/9 SOLUTION:P (getting a prize) =10/(10 + 25) = 10/35 = 2/7 . Answer:B #### B QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ? options: A)124 B)144 C)134 D)142 E)143 SOLUTION:The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B #### B QUESTION:A statue is being carved by a sculptor. The original piece of marble weighed 180 kg. In the first week 28 percent is cut away. In the second week 18 percent of the remainder is cut away. In the third week the statue is completed when 20 percent of the remainder is cut away. What is the weight of the final statue? options: A)105 kg B)85 kg C)108 kg D)125 kg E)117 kg SOLUTION:B 85 kg 180 Ã— 0.72Ã— 0.82Ã— 0.8 = 85 kg. #### B QUESTION:One pump drains one-half of a pond in 5 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone? options: A)1 hour B)1.2 hour C)3 hours D)5 hours E)1.1 hours SOLUTION:The tricky part here, I believed is one half hour = 1/2. Then everything would be easy. We have the 1st pump working rate/hour = 1/2 : 5 = 1/10 Working rate of 2 pumps: 1/2 : 1/2 = 1. Working rate of 2nd pump: 1 -1/10 = 9/10 --> Time taken for the 2nd pump to finish: 1 : 9/10 = 10/9 = 1.1 hours. E #### E QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/42/3 = 1/6 of the attendees. Females who did not arrive on time are 1/61/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches? options: A)51 B)52 C)78 D)54 E)55 SOLUTION:Total no. of person = 11 Total no. of glass clinches = n(n-1)/2 =1312/2 = 78 ANSWER:C #### C QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ? options: A)28years B)29years C)30years D)31years E)32years SOLUTION:Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 25) years = 35 years. Ayush's father's present age = (35+ 5) years = 40 years. Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years. Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years. Answer: A) 28 year #### A QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? options: A)Rs.16003 B)Rs.16029 C)Rs.1288 D)Rs.16108 E)Rs.12000 SOLUTION:Explanation: Manager's monthly salary Rs. (2000 21 - 1500 * 20) = Rs.12000. Answer: E #### E QUESTION:Which of the following is closer to √0.8+√0.05? options: A)0.5 B)0.7 C)0.9 D)1.1 E)1.2 SOLUTION:√0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D. #### D QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3Ã—7/36 = 7/12 Remaining work = 1 â€“ 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x 100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? options: A)12500 B)27767 C)16688 D)26678 E)19987 SOLUTION:Let the CP be Rs. x. Had he offered 25% discount, profit = 8% Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500 => 1.08x = 13500 => x = 12500 \Answer: A #### A QUESTION:8 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The number of hours required to complete the work is 8818 = 1152 12 × 12 × (x) = 1152 x = 8 The answer is C. #### C QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:4 E)1:2 SOLUTION:He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33) Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters) Hence the water added would be .1 liter. Therefore the ratio of water to milk is .1/1 = 1/10 ANSWER:B #### B QUESTION:By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.300 D)s.450 E)s.550 SOLUTION:SP = 500 Profit = 25% CP = (SP)[100/(100+P)] = 500 * [100/125] = 400 Loss = 25% = 25% of 400 = Rs.100 SP = CP - Loss = 400 - 100 = Rs.300 ANSWER:C #### C QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers : options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer: B #### B QUESTION:what is the smallest integer that is multiple of 3,7 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 3,7 and 20 which is 420 #### E QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months. options: A)7500 B)6500 C)8125 D)9125 E)None of them SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years. Simple Interest = (PRT)/100 = Rs.(73,000(50/3)(3/4)(1/100))= Rs.9125 Answer is D. #### D QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=? options: A)2515 B)2525 C)2535 D)2545 E)2555 SOLUTION:given,(x+ 1/x) = 5 x^2 + 1/x^2 = (x+ 1/x)^2 - 2x1/x = 5^2 - 2 = 23 -------(1) x^3 + 1/x^3 = (x+ 1/x)^3 - 3x1/x(x+ 1/x) = 5^3 - 35 = 110 -------(2) multiplying (1)& (2), we get =>(x^2+ 1/x^2)(x^3+ 1/x^3) = 23110 => x^5 + 1/x + x + 1/x^5 = 2530 => x^5 + 1/x^5 + (x+ 1/x)= 2530 => x^5 + 1/x^5 + 5 = 2530 => (x^5+ 1/x^5)= 2525 ANSWER:B #### B QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 3001 = revenue (eq -1) if he reduced his price by 20% then , 240(customer) = 125/100revenue customer = 1.25300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:Find the odd man out 4, 10, 22, 40, 84, 94 options: A)22 B)40 C)94 D)84 E)10 SOLUTION:Differnce is multiple of 6 4 and 10 diff is 6 10 and 22 diff is 12 22 and 40 diff is 18 40+24 = 64 but in series it is mentioned as 84 64+30 = 94 ANSWER:D #### D QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 18/5 = 72 kmph Answer: A #### A QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 1304=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? options: A)670 B)710 C)750 D)790 E)830 SOLUTION:total pay = 40$12.50 + $0.16x = 620 x = 120 / 0.16 = 750 The answer is C. #### C QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)77/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-7 = 1/3 (B+7) ----> 3A-21 =B+7 Scenario 2 B-7 = 1/2 (A+7) -----> 2B-14 = A+7 From Scenario 1, B = 3A-28 Substitute B with this information in Stmt 2 2 (3A-28) -14 = A+7 ------> 6A -56-14 = A+7 ------> 6A- A = 70+7 ---> 5A= 77 A= 77/5, Answer choice A #### A QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/21/21/21/21/21/21/2= 1/128 case 2 .all girls. 1/21/21/21/21/21/21/2=1/128 We will add the cases to get 1/64 #### A QUESTION:The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? options: A)4/19 B)1/9 C)2/3 D)1 1/9 E)2 1/9 SOLUTION:Total bought = 4/19+2/13 left part 4/26--->2/13 so used part 4/19+2/13-2/13=4/19 ANSWER:A #### A QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A? options: A)a) 50% B)b) 53% C)c) 54% D)d) 55% E)e) 57% SOLUTION:Let total voters = 100 so D= 60, vote for the mayor 6075%=45 (603/4) R= 40, vote for the mayor 4020%= (401/5) 45+8=53 53/100100=55% D #### D QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(32^25) B)y/(3^225) C)y/(325^2) D)y/(5^32^2) E)y/(532) SOLUTION:Solution: As y and n are both integers so y is of the form of 3522*K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 5 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10 So, 10-5 = 5 Answer A #### A <<<Examples ends QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)35 min B)30 min C)25 min D)20 min E)40 min SOLUTION:Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20 ANSWER IS D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. options: A)220. B)205. C)250 D)105 E)225 SOLUTION:different ways.. 1) EASIEST approach.. lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220... Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15.. total = 220-15 = 205 ANSWER:B #### B QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300 SOLUTION:260-X+X+300-X+GT60 = 400 =>X = GT 620-400 => X = GT 220 => X >= 220 (Here GT means Greater than) So Min value of X is 220 coming to options D/E X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260 ANSWER:D #### D QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg? options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None SOLUTION:Required ratio = 750 : 250 = 3 : 1 Answer A #### A QUESTION:A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? options: A)5% B)10% C)15% D)20% E)It can not be determined SOLUTION:Solution: let the total number of flags be 100(even number) let the total number of 'blue' flags alone be 'a' let the total number of 'red' flags alone be 'b' let the total number of 'both' flags be 'c' We have given, total number of blue flags = 60% = 60 = a+c total number of red flags=55%=55=b+c total number of flags = a+b+c=100 (since all the flags have been utilized) So, substituting for c in the third equation, we have, 60-c+c+60-c=100 c=20 Option D. #### D QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is? options: A)675 B)680 C)685 D)690 E)695 SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec. Length of the train = 75 * 9 = 675 m. Answer: Option A #### A QUESTION:In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ? options: A)3990 B)1540 C)1995 D)3672 E)None of these SOLUTION:In order that two books on French are never together, we must place all books as under X E X E X E X E X E .....X E X where E denotes the position of an English book and X that of a French book. Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways Answer B. #### B QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)106 C)110 D)120 E)130 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:Which of the following is equal to 1(4/5)%? options: A)0.012/100 B)0.12/100 C)1.2/100 D)1.8/100 E)12/10 SOLUTION:This notation may be confusing for some, since it looks like we're multiplying 1 and 4/5 How about adding a space:Which of the following is equal to (1 4/5)% (1 4/5)% = 1.8% = 1.8/100 Answer: D #### D QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is options: A)35.22 B)36.12 C)36.22 D)36.42 E)None SOLUTION:Solution Correct sum = (36x50+44-23) = 1821. âˆ´ Correct mean = 1821 / 50 = 36.42. Answer D #### D QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:7+2+2^2+2^3+2^4+2^5=？ options: A)(2^3-1)(2^3+1) B)2^6+5 C)2^5-1 D)2^5+1 E)2^5-2 SOLUTION:From 7+2+2^2+2^3+2^4+2^5=69, 2^6+5=69 the correct answer is B. #### B QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!10! 1211/21 =66 ANSWER:D #### D QUESTION:A scooter costs 30,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years? options: A)10,000 B)12,500 C)12,800 D)12,000 E)15,360 SOLUTION:After first year, the value of the scooter = 24,000 After second year, the value of scooter = 19,200 After third year, the value of scooter = 15,360 Answer E #### E QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 987656!/2!=5443200. Answer: C. #### C QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)22 B)25 C)66 D)77 E)91 SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office? options: A)38 B)27 C)24 D)19 E)17 SOLUTION:Explanation: Let t be his usual time to reach his office and v be his usual speed. v = d/t ……….(d is the distance Ajay travels while going to his office) vt = d At v1 = 4v/5 ; t1 = t + 6 4v/5 = d/(t + 6) 4v/5* (t + 6) = d 4v/5* (t + 6) = vt On solving we get, t = 24 minutes ANSWER:C #### C QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:70,76, 74,85,90,105,105,130,130,130 The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD. We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74. Answer: C. #### C QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is? options: A)10 B)20 C)50 D)30 E)40 SOLUTION:Man's speed with the current = 15 km/hr => speed of the man + speed of the current = 15 km/hr speed of the current is 2.5 km/hr Hence, speed of the man = 15 - 2.5 = 12.5 km/hr man's speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km/hr Answer is A. #### A QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article? options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2 SOLUTION:Explanation: Let C.P. = Rs. 5x and S.P. = Rs. 7x. Then, Gain = Rs. 2x Required ratio = 2x : 5x = 2:5 Answer: Option B #### B QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? options: A)4 B)16 C)8 D)1 E)2 SOLUTION:Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B #### B QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:The middle number is 40. Let the smallest number be x. Then the largest number is 2x+20. To make x as small as possible, let's make the remaining numbers as large as possible. So the second largest = the largest = 2x+20. The second smallest should be equal to the median. The numbers are x, 40, 40, 2x+20, 2x+20. x + 40 + 40 + 2x + 20 + 2x + 20 = 540 = 200 5x = 80 x = 16 The answer is B. #### B QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe? options: A)15 B)60 C)75 D)90 E)105 SOLUTION:This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one. Teena covers 55 miles in 60 mins. Yoe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +15 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 15 miles in 60 mins So answer 30+60= 90 mins.D #### D QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse? options: A)6 B)8 C)10 D)15 E)30 SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 1510=150 Answer is 6... A #### A QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence. $50, $55, $65, $80, $85, $95, $110, $115, $125, ? How much will she pay back on the tenth month? options: A)$155 B)$140 C)$135 D)$125 E)$130 SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140 Ans B #### B QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 83= 24 tubes A is the answer #### A QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:For any non-zero a and b that satisfy \|ab\| = ab and \|a\| = -a \|b - 4\| + \|ab + b\| = ? options: A)a) ab - 4 B)b) 2b - ab - 4 C)c) ab + 4 D)d) ab - 2b + 4 E)e) 4 - ab SOLUTION:\|a\| = -a Suggests that 'a' is Negative \|ab\| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so \|b - 4\| = -b+4 Since ab is Positive and b is Negative so \|ab - b\| = ab + b i.e. \|b - 4\| + \|ab - b\| = -b+4 + ab + b =ab + 4 Answer: Option C #### C QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3% SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% Answer: A #### A QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5 SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) #### B QUESTION:If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%. options: A)4% B)5% C)6% D)3% E)5.5% SOLUTION:sol. cp=rs490,sp= 465.50. loss=rs(490-465.50)=rs 24.50. loss%=[(24.50/490)100]%=5% Answer is B. #### B QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x1/10 + Nx1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/9 B)3/10 C)4/11 D)5/12 E)6/13 SOLUTION:# defective pens = 3 # good pens = 6 Probability of the 1st pen being good = 6/9 Probability of the 2nd pen being good = 5/8 Total probability = 6/9 * 5/8 = 5/12 The answer is D. #### D QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time W it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week? options: A) 0.8(80 – y) B) 0.8 + 0.0025y C) 80/y – 1.25 D) 80/1.25y E) 80 – 0.25y SOLUTION:This may be a case of bad numberpicking but it worked for me. 80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 401/10 = 4 houses per week will be painted at this rate. 80-y = 80-40 = 40 houses are to be painted at the faster rate. X1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks. Which means finishing all houses at normal rate W=> 24 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks. 7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9. #### B QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have. options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5 SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs Given x + (20+x)= 21 => 2x= 1 or x= 0.5 So Christine and Siri has 20.5 and 0.5 Rs respectively. ANSWER:E #### E QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes. options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20 SOLUTION:Assume the manager bought 100 tomatoes. Cost Price = 80 Given: 10% are damaged --> Available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90x - 80 = 9.6 90x = 89.6 x = 89.6/90 = 0.995 x is slightly under 0.9955 = 0.99 Answer: C #### C QUESTION:Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be options: A)1:3 B)2:3 C)24:25 D)20:22 E)3:4 SOLUTION:=(120004):(100005) =48000:50000 =24:25 ANSWER:C #### C QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6? options: A)35 B)47 C)58 D)26 E)34 SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals) In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16 Number of multiples of 56 i.e. 30 = 100/30 = 3 Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58 Answer is C #### C QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 150= 1200 liters. #### A QUESTION:The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class? options: A)218 B)226 C)234 D)242 E)250 SOLUTION:1/22/5 + 3/43/5 = 4/20 + 9/20 = 13/20 The number of degrees is 13/20 * 360 = 234 degrees The answer is C. #### C QUESTION:If 9^y = 3^14, what is y? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:9^y = 3^2y = 3^14 2y=14 y = 7 The answer is E. #### E QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is: options: A)1677 B)2523 C)1683 D)3363 E)3567 SOLUTION:L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683. Answer: Option 'C' #### C QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? options: A)2 years B)5 years C)9 years D)4 years E)1 years SOLUTION:28 * 2 = 56 20 * 3 = 60 ----------- 4 years Answer:D #### D QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples? options: A)1:7 B)1:5 C)1:4 D)1:2 E)2:5 SOLUTION:To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars. To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these. 45 split in the ratio 1:4 gives 9 and 36. 9 apples split into 3 apples each will give $3. 36 apples split into 6 apples each will give $6. They add up to $9 so we have hit the right answer. Answer (C) #### C QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=2726^2 The answer is C. #### C QUESTION:In a coconut grove, (x + 3) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 3) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. options: A)3 B)4 C)5 D)6 E)None of the above SOLUTION:(x+3)×60+x×120+(x−3)×180/(x+3)+x+(x−3)=100 ⇒ 360x−360/3x = 100 ⇒ 60x = 360 ⇒ x = 6 Answer D #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km SOLUTION:M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer: B #### B QUESTION:Anitha had 80 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 55 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:(17)3.75 x (17)? = 178 options: A)2.29 B)2.75 C)4.25 D)4.5 E)None of these SOLUTION:Solution let (17)3.75 * (17)x = 178. then, (17)3.5 + x = (17)8. ∴ 3.75 + x = 8 ⇔ x = (8 - 3.75) ⇔ x = 4.25 Answer C #### C QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually? options: A)1500 B)1750 C)2000 D)3500 E)2500 SOLUTION:An easy way too attempt this is by approximation: For the first quarter, he pays 8% of 10,000 which is $800. So for the four quarters in the year, he will approximately play 8004=3200 over the entire year. Because of compound interest it will be more than 3200. Approx. option D is correct. Answer :D #### D QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word â€˜POWERâ€™ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 54321 = 120 ANSWER:E #### E QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed) options: A)4443 B)5980 C)5992 D)5990 E)5994 SOLUTION:n = 333 = 27 <x> = (333 + 111) / 2 = 222 Sum = number of integers x average value n <x> = 27 * 222 = 5994 answer = E #### E QUESTION:A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)90 B)70 C)50 D)80 E)60 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. Answer is A. #### A QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (12, 2), (12,-7)? options: A)64 B)68 C)72 D)76 E)80 SOLUTION:By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is: Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides. We can now determine the area of the quadrilateral: Area = 1/2 × (10 + 9) × 8 = 76. The answer is D. #### D QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c11c11c1)/5c3 =3/10 ANSWER:A #### A QUESTION:The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram? options: A)90° B)75° C)60° D)45° E)30° SOLUTION:let smaller be x ,larger becomes x+90... total of all angles=360 so 4x+180=360 and x=45 ANSWER:D #### D QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in. options: A)40 min B)25 min C)54 min D)65 min E)58 min SOLUTION:Distance = Speed * time 320/3= 20km New Speed = 18 kmph Therefore time = 20/18 = 10/9= 54min Answer : C. #### C QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 72 = 48 Answer: B #### B QUESTION:What is the area of a square with perimeter 8P ? options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16 SOLUTION:Each side is 2p A = (2p)^2 = 4(p^2) Answer B #### B QUESTION:What is the next number of the following sequence 7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ? options: A)28 B)29 C)30 D)31 E)32 SOLUTION:7,0,1,8,5,12,9,26,3,2,23,X (7,0,1,8),(5,12,9,26),(3,2,23,X) 7+0+1=8 5+12+9=26 3+2+23=X => X=28 ANSWER:A #### A QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 30, find the number? options: A)11201 B)12102 C)12081 D)12108 E)10126 SOLUTION:D 12108 Let the three digit numbers be 100a + 10b + c a = b + 2 c = b - 2 a + b + c = 3b = 30 => b = 10 So a = 12 and b = 8 Hence the three digit number is: 12108 #### D QUESTION:How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0? options: A)A.66 B)B.57 C)C.31 D)D.32 E)E.58 SOLUTION:Number of subset Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations. 6c1+6c2+6c3+6c4+6c5+6c6=57 And one set is the NULL set having no elements in it so 57+1=58. ANSWER E. #### E QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)754 m B)704 m C)708 m D)706 m E)204 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.915 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.920 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5100 = 107% of 7.5. Answer: B. #### B QUESTION:A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin? options: A)15/2 B)9/4 C)5/9 D)7/5 E)9/7 SOLUTION:Blue tin or red tin: 2/3 (N) Red tin: (1/3)N Blue tin: (1/4)N What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin) # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12 # of cookies in red and green tin = N/3 + 5N/12 = 9N/12 Fraction T= 5N/12 12/9N = 5/9 (C) #### C QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page? options: A)6:26 B)6:56 C)7:26 D)7:56 E)8:26 SOLUTION:Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom. The answer is C. #### C QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is options: A)37 B)36 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2(b-10) => 2b-a = 30 ......(i) a = b+6 =>2b-b-6 = 30 b=36 so the present age of b is 36 years ANSWER:B #### B QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)12 sec B)30 sec C)36 sec D)16 sec E)18 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 5/18 = 50/3 m/sec. Time taken to pass the man = 600 * 3/50 = 36 sec. Answer: C #### C QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = xx is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by: options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800 SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6) = 147 : 189 : 126 = 7 : 9 : 6. Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22 = Rs.3600 ANSWER:C #### C QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? options: A)90 min B)100 min C)110 min D)120 min E)None SOLUTION:Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)(5 choose 2) = 410 = 40 Jaune X = (4 choose 2)(5 choose 1) + (4 choose 3) = 65 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:An oblong piece of ground measures 19m 2.5dm by 12m 5dm. From the centre of each side a path 2m wide goes across to the centre of the opposite side. Find the cost of paving these paths at the rate of rs.1.32 per sq m? options: A)Rs. 43.6 B)Rs. 78.65 C)Rs 54.75 D)Rs. 344 E)Rs. 34.4 SOLUTION:Area of path horizontal=20192.5=3850 dm^2 Area of path vertical=20125=2500 dm^2 Since center path is covered twice so total area=(3850+2500)-(2020)=5950 dm^2 total cost=1.3259.5 m^2=78.54 ANSWER:B #### B QUESTION:A baker filled with a measuring cup with 1/3 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? options: A)1/8 cup B)3/8 cup C)11/24 cup D)1/2 cup E)7/8 cup SOLUTION:1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24. so 50% more than what he started was = 1/3+1/2(1/3)=1/2 Amount of water needed to add = 1/2 - 1/24=11/24 C #### C QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? options: A)1:3 B)9:13 C)5:11 D)11:3 E)15:4 SOLUTION:The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7) = 11/7 : 3/7 = 11:3 Answer is D #### D QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between Bunuel, can you please explain this one? options: A)0 and 0.5 B)0.5 and 1 C)1 and 1.5 D)1.5 and 2 E)2 and 2.5 SOLUTION:Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase). Try x=1 --> LHS=3^5=813=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1. Answer: E. #### E <<<Examples ends QUESTION:If y is an integer, then the least possible value of \|23 - 4y\| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. \|23-4(5)\| \|23-20\| \|3\| = 3 Next, let’s let y equal 5. \|23-4(6)\| \|23-24\| \|-1\| = 1 We see that the smallest possible value of \|23-4y\| is 1. Answer A. #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:6x + 2y = -4 4x + y = 1 In the system of equations above, what is the value of x? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:6x + 2y = -4 can be written as 3x + y = -2 Let's subtract the second equation from this equation. -x = -3 x = 3 The answer is C. #### C QUESTION:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)? options: A)72 B)180 C)70 D)90 E)140 SOLUTION:Length of side 1= 9+1=10 Length of side 2= 8+1= 9 Area of rectangle= 109= 90 D is the answer #### D QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3. options: A)131 B)197 C)207 D)219 E)227 SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3. Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131. ANSWER:A #### A QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(150âˆ’90)=4/5âˆ—60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150âˆ’138=12 ANSWER:D #### D QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer? I. w + t + 2 II. w^2 + 2wt + t^2 III. w^2 + t^2 options: A)None B)I only C)II only D)III only E)I, II, and III SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even. Check all options: I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard; II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard; III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard. Answer: A. #### A QUESTION:the banker's discount on a bill due 4 months hence at 15% is Rs.420. what is the true discount? options: A)41 B)400 C)390 D)380 E)480 SOLUTION:TD= (BD 100)/(100+TR)= (420 * 100)/100+((4/12)15)= (420 100)/100+((1/3)15) =(420 100)/100+5= (84 * 100)/21 = 4100=400 correct answer: (B) #### B QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:Excluding stoppages, the speed of a train is 55 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? options: A)82 B)16 C)12 D)82 E)18 SOLUTION:Explanation: T = 15/55 60 = 16 Answer: Option B #### B QUESTION:The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ? options: A)11 B)13 C)14 D)16 E)10 SOLUTION:Explanation : Let Somu's age be x and that of his father be 3x. So, x - 8 = 3x - 8/5 = x = 16 Answer : Option D #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly? options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20 SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/51/4 = 9/10. Answer: D. #### D QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock? options: A)20029 B)22500 C)20289 D)20027 E)20026 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 450 => x = 22500 Answer: B #### B QUESTION:If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals? options: A)4:3 B)4:0 C)4:5 D)4:7 E)4:2 SOLUTION:Explanation: a1:a2 = 4:3 d1:d2 = 4:3 Answer: Option A #### A QUESTION:A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? options: A)6 B)4 C)8 D)2 E)3 SOLUTION:M = 45 S = 1.5 DS = 6 US = 3 AS = (2 * 6 * 3) /9 = 4 Answer: B #### B QUESTION:Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have. options: A)16.5 B)17.5 C)18.5 D)19.5 E)20.5 SOLUTION:Let Siri has x Rs, then Christine has 20+x Rs Given x + (20+x)= 21 => 2x= 1 or x= 0.5 So Christine and Siri has 20.5 and 0.5 Rs respectively. ANSWER:E #### E QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed? options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days SOLUTION:Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work. => In one day A came complete 1/9th of the task(x/9) => In one day B can complete 1/12th of the job.(x/12) First day x/9th work will be done next day x/12th and so on: Together A and B can do x/9 + x/12 work. =>(x/9) + (x/12) = 7/36th work done In 10 days 35/36th of the work will be done. On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work. So, 1/36th work will be done in 1/4 days. =>10.25 days ANSWER: D #### D QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments? options: A)50% B)40% C)20% D)30% E)10% SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 10) * X percentage of apartments in the building are two-bedroom apartments ----> (1/10) * 100 ---> 10% Answer : E #### E QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters? options: A)132 m2 B)145 m2 C)165 m2 D)152 m2 E)120 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(87+74+84)=2(56+28+32)=2116=132 m2 Answer : A #### A QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)6 B)40 C)50 D)10 E)20 SOLUTION:Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E #### E QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A QUESTION:How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%? options: A)100 ml B)60 ml C)120 ml D)130 ml E)150 ml SOLUTION:we can also go by answer choices Tke 100 ml for eg 400 (old)+100 (new concentr)ml 50026/100 = 130 ml (30ml is de old concentration +100 ml (newly added) Answer D #### D QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)5 B)4 C)6 D)8 E)3 SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4%.Answer:B #### B QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)5 B)6 C)9 D)7 E)3 SOLUTION:7 8 : 9 * x = 8:9 => x= 7 Answer: D #### D QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer:D #### D QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut. options: A)550 B)275 C)50 D)300 E)250 SOLUTION:piece one as p1, and piece two as p2. p2+50=p1 as eq.a p1+p2=600 as eq.b substitute eq. a into eq.b, resulting in (p2+50) + p2=600mm. Group like terms, p2+p2=600-50 (2p2/2)=550/2 solves to p2= 275. Ansewr is B. #### B QUESTION:Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days? options: A)1/8 B)1/3 C)1/6 D)1/2 E)5/3 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/60 (A + B)'s one day's work = 1/30 + 1/60 = 1/20 The part of the work completed in 10 days = 10 (1/20) = 1/2. Answer:D #### D QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph SOLUTION:Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'x' km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 => x = 49 km/hr. ANSWER IS A #### A QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)8 D)5 E)12 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 50 = 20 + 30 + 30 - (20) - 2x x = 5 So, answer will be D #### D QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 3.5) kg = 35 kg. Weight of new person = (65 + 35) kg = 100 kg. Answer: A #### A QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2 SOLUTION:P(at least one graduate) = 1 - P(no graduates) = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 5 * 4)/(10 * 9 * 8) = 5/6 Answer: D #### D QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:What is the are of an equilateral triangle of side 4 cm? options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 4, Area of triangle = √3/4 * 4 * 4 = 4√3 cm2; Answer:D #### D QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper? options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075 SOLUTION:Cost of 8 kg apples= 70 × 8 = 560. Cost of 9 kg of mangoes = 70 × 9 = 630. Total cost he has to pay = 560 + 630 = 1190. D) #### D QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? options: A)$8 B)$14 C)$5 D)$15 E)$0 SOLUTION:1/5 x $60 = $12 for sandwich 1/6 x $60 = $10 for museum 1/2 x $60 = $30 for book $12 + $10 + $30 = $52 spent $60 - $52 = $8 left over correct answer A #### A QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 * 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item? options: A)$1,600 B)$1,850 C)$2,250 D)$2,400 E)$2,750 SOLUTION:Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250. Answer: C. #### C QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250. Answer: D #### D QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr SOLUTION:still in water=1/2(98+10)km/hr =54km/hr correct option is :B #### B QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =441=16/9==> Remainder=7 Answer: E #### E QUESTION:v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z? options: A)30 B)35 C)37 D)38 E)40 SOLUTION:sum=150 mid value = 25 minimize 'z'. So, 25 25 25 37 38 answer: D #### D QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:3640 ÷ 14 × 16 + 340 = ? options: A)0.7 B)3525 C)4480 D)None of these E)Cannot be determined SOLUTION:Solution Given exp. = 260 × 16 + 340 = 4160 + 340 = 4500. Answer D #### D QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die. options: A)1/2 B)1/6 C)0 D)5/6 E)1 SOLUTION:Determine if E and F are independent. P(E\|F) = the probability of event E occurring given that event F has already occurred P(E\|F) ≠ P(E) as P(E) is changed if it is given that F occurs. Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F) We must use the more complex formula for finding the intersection of E and F: P(E∩F) = P(F)P(E\|F) P(F) = the probability of event F occurring The probability of rolling a 1, 2, or 3 is 3/6 = 1/2 P(E\|F) = the probability of event E occurring given that event F has already occurred If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E\|F) = 1/3 P(E∩F) = P(F)P(E\|F) = (1/2) * (1/3) = 1/6 Answer B #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE SOLUTION:Solution: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000. => 3x = 36000. => x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. So A's share = Rs. (35000 x 21/50) = Rs. 14,700. Answer: Option D #### D QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)84 = 36. The answer is E. #### E QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty five paise coins are in the ratio of 3:2:4, add up to Rs 75. Then how many 1 rupee coins he have? options: A)10 B)20 C)45 D)128 E)49 SOLUTION:Explanation : Given ratio = 3:2:4. Let us assume that there are 3 one rupee coins,2 fifty paise coins and 4 twenty-five paise coins in all. Their value=(31)+(2.50)+(4.25)=3+1+1=Rs 5 If the total is Rs 5, number of 1 rupee coins are 3. If the total is Rs 75, number of 1 rupee coins would be 753/5=45. Answer : C #### C QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2. #### B QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)(1/4)S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2? options: A)1 B)3 C)5 D)6 E)14 SOLUTION:For unit digit of a^2 to be 9...unit digit of a has to be 3 or 7... Now for unit digit of (a+1)^2 to be 4..unit digit of a has to be 1 or 7.... From the above two conditions, unit value of a has to be 7, which will satisfy both the conditions... Now id unit digit of a is 7, unit digit of (a+2)^2 hast to be 1. ANSWER:A #### A QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 3016=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)1/10=80.5+7.51/10 80.5+0.75=81.25 E #### E QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2879 C)2700 D)2797 E)2761 SOLUTION:(1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer:A #### A QUESTION:How much interest will $8,000 earn in 9 months at an annual rate of 6%? options: A)$250 B)$350 C)$360 D)$550 E)$650 SOLUTION:Soln:- 9 months = 3/4 of year; 6% = 6/100=3/50; $8,000(principal)3/50(interest rate)3/4(time)=$360. ANSWER:C #### C QUESTION:The ratio, by volume, of bleach to detergent to water in a certain solution is 4 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain? options: A)80 B)70 C)60 D)40 E)50 SOLUTION:B:D:W = 4:40:100 Bnew / Dnew = (1/3)(4/40) = (1/30) Dnew / Wnew = (1/2)(40/100) = (1/5) Wnew = 300 Dnew = Wnew/5 = 300/5 = 60 So, answer will be C #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 11 * 7 = 154 ANSWER:B #### B QUESTION:If 2x = 3y = 20, then 12xy = ? options: A) 1,200 B) 800 C) 120 D) 40 E) 20 SOLUTION:2x = 20;x=10 3y = 20;y=20/3 Multiply: 12xy=121020/3=800. Answer: B. #### B QUESTION:A man spends Rs. 1500 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)2075 B)2100 C)2200 D)2300 E)2400 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 Ã— 1500 = 4500 Total expenditure for 4 months = 4 Ã— 1550 = 6200 Total expenditure for 5 months = 5 Ã— 1800 = 9000 Total expenditure and saving (which is income for one year) = 4500 + 6200 + 9000 + 5200 = Rs. 24900 So, Average monthly income = 24900/12 = Rs. 2075 Answer A #### A QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500(1+(4/100)2] = Rs (7500 (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November? options: A)$466 B)$470 C)$472 D)$484 E)$491 SOLUTION:if its prevoius november (before discount) then price is $470. but if its November of next year then 16% discount on $470=470(1-16/100)=$394.8 again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466 Ans A #### A QUESTION:If e<0, which of the following must be true? options: A)–100 < e < 100 B)e ≤ –1 C)e ≤ 1 D)e^2 ≥ 1/4 E)–100 < e < 0 SOLUTION:e is a negative number. A. –100 < e < 100e can be a negative number less than -100 B. e ≤ –1e can be a fraction, in which case it would be greater than -1 C. e ≤ 1must be true since 1 is positive and e is negative D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5 E. –100 < e < 0e can be a negative number less than -100=C #### C QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)(r+4)/(y+r+6) D)(y+3)/(y+r+7)(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:10 men working 6 hrs per day manufacture 200 shoes in 18 days. How many hours a day must 15 men work to manufacture the same 200 shoes in 12 days? options: A)6 B)10 C)12 D)15 E)18 SOLUTION:Let the required number of hours be x. More men, less hours per day (Indirect proportion) Less days, more working hours per day (Indirect proportion) men 15 : 10 } : : 6 : x days 12 : 18 .'. 1512x = 10186 = x = 10186/(1512) = x = 6 ANSWER : A #### A QUESTION:If n = 30! + 27, then n is divisible by which of the following? I. 25 II. 27 III. 29 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:27 divides 30! so 27 also divides 30! + 27. 25 and 29 divide 30! so they do not divide 30! + 27. The answer is C. #### C QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)(White / Total Coins) = (Blue / Total Coins) í.ẹ. RedWhite = BlueTotal Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a * 3b = 3c3(a+b+c) í.ẹ. ab = c(a+b+c) For smallest values of a, b and c 23 = 1(1+2+3) í.ẹ. Minimum Total Coins = 3(1+2+3) = 15 Answer: Option C #### C QUESTION:An article is bought for Rs.1300 and sold for Rs.1250, find the loss percent? options: A)3 11/13% B)3 2/9% C)3 5/3% D)3 2/3% E)3 7/3% SOLUTION:1300 ---- 50 50 ---- ? => 3 11/13% Answer: A #### A QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 (2/25) = 40 seconds Answer:C #### C QUESTION:A brick measures 20cm10cm7.5cm how many bricks will be required for a wall 25m2m0.75m ? options: A)24000 B)23000 C)22000 D)25000 E)27000 SOLUTION:2520.75=20/10010/1000.75/100X 25=1/100X X=25000 Answer :D #### D QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? options: A)months B)months C)months D)months E)months SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 ANSWER:D #### D QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is : options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 0 SOLUTION:Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 396 99c - 99a = 99(c - a) = 396 396 = 994 = 99(c - a) So c - a = 4 Answer (A #### A QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is: options: A)260 B)262 C)270 D)272 E)None of these SOLUTION:Explanation: Volume will be length breadth * height, but in this case two heights are given so we will take average, Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3 Option C #### C QUESTION:Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996? options: A) $24 million B) $120 million C) $144 million D) $240 million E) $888 million SOLUTION:Convert units to millions as answer is in millions 1996 Imports = $1.44 bill = $1440 mill i.e. 1440/12 = $120 mill/month 1997 Imports = $388 mill/2 month i.e. $194 mill/month Difference/month = 194-120 = 74 Difference/year = $74 mill * 12 = $988 mill ANSWER: E #### E QUESTION:15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours? options: A)360 B)480 C)720 D)960 E)1000 SOLUTION:D 15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour. 5 grams sugar cubes will take less time to move. Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour. More ants, more sugar cubes they can move. 20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams. #### D QUESTION:O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(11.6) + E(–10.4) + o(–9.2) + e(9.5) is: options: A)-3 B)-1 C)0 D)1 E)3 SOLUTION:O(11.6) + E(–10.4) + o(–9.2) + e(9.5) = 13 + (-10) + (-11) + 8 = 0 The answer is C. #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? options: A)112 B)50 C)77 D)14 E)12 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/63/6 = 6/36; P(negative,positive ) = 3/6 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct? options: A)A > 4. B)0 < A <4. C)-4 < A < 0. D)A < -4. E)A < -20. SOLUTION:B is +veC is -ve Eliminate AB For min. value max. numerator and minimize dinominator take B=4.1A=-0.9 A=4.1/-0.9 A<-4 Ans D #### D QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -1 Prob = 1/12 Answer -A #### A QUESTION:David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 600 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 4,800. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.? options: A)2400 B)3600 C)3000 D)2800 E)2500 SOLUTION:let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3) now population at 4pm =4800 thus we have 600(x^3) = 4800 =8 thus x=2 therefore population at 3pm = 600(4) = 2400 Answer : A #### A QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B? options: A)5000 B)2787 C)2679 D)2790 E)2712 SOLUTION:Let x, y and z be the amount invested in schemes A, B and C respectively. Then, (x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200 10x + 12y + 15z = 320000 Now, z = 240% of y = 12/5 y And, z = 150% of x = 3/2 x x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y 16y + 12y + 36y = 320000 y = 5000 Sum invested in scheme B = Rs. 5000.Answer: A #### A QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:A jeep takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? options: A)48 Kmph B)52 Kmph C)6o Kmph D)63 Kmph E)65 Kmph SOLUTION:Time = 6 Distance = 540 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 540/9 = 60 Kmph C) #### C QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E QUESTION:The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? options: A)11.73 B)12 C)13.8 D)14 E)18 SOLUTION:Clearly E is the answer I used POE here Lets consider option (E) 1018= 180 now 180(115/100)=207 => possible ANSWER IMO E #### E QUESTION:The wheel of an engine 30/7 metres in circumference makes seven revolutions in 4seconds. Find the speed of the train in km per hour? options: A)15km/hr B)25km/hr C)32km/hr D)18km/hr E)27km/hr SOLUTION:Distance travelled by the train in 4 seconds = 307/7 = 30 metres speed of the train = 30/4 = 15/2 m/s = 27 km/hr Answer is E #### E QUESTION:A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)Rs. 2000 B)Rs. 2010 C)Rs. 2100 D)Rs. 2200 E)Rs. 2300 SOLUTION:Total expenditure for the first 3 months = 3 × 1600 = 4800 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 4800 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 25200/12 = Rs. 2100 C #### C QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 8:2. If 80% of the Toyota bought and 20% of the Honda bought were SUVâ€™s. How many SUVâ€™s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)69% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 80 and Honda 20, so total number of SUV's bought for Toyota and Honda respectively 80* 80/100=64 and 20* 20/100=4 so total 68 SUV's were bought out of 100 Vehicles bought..so required % is 68% ANSWER:C #### C QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? options: A)66 B)83.5 C)84 D)95 E)76 SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4 = 84 ANSWER:C #### C QUESTION:If k^3 is divisible by 60, what is the least possible value of integer k? options: A)12 B)30 C)60 D)90 E)120 SOLUTION:60 = 2^235 Therefore k must include at least 2 * 3 * 5 = 30. The answer is B. #### B QUESTION:The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%? I will see what is the quickest way to solve it then I will provide the explanation options: A)6 B)7 C)9 D)10 E)11 SOLUTION:The following approach might be the easiest one and less error prone. We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time. Answer: A #### A <<<Examples ends QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r1^2 . h1/r2^2. h2 => 1/15 = (1)^2h1/(2)^2h2 => h1/h2 = 3/5 i.e. h1 : h2 = 3:5 Answer: A #### A QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of? options: A)150 B)339 C)342 D)359 E)362 SOLUTION:Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer W= 19 + 290 + 351 = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out? options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None SOLUTION:Solution Volume = πr2h ‹=› (22 /7 ×3×3×24)m3 ‹=›678.6 m3. Answer A #### A QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ? options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5 SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7 = 2 (2^7) + 3 (3^7) = 2^1 (2^7) + 3^1 (3^7) = 2^(1+7) + 3^(1+7) = 2^8 + 3^8 Ans: A #### A QUESTION:Convert 50miles into yards? options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards SOLUTION:1 mile = 1760 yards 50 miles = 501760 = 88000 yards Answer is C #### C QUESTION:Maddie has 15 apples, if she give 8 to mike, how many does she have left? options: A)1 B)7 C)3 D)4 E)5 SOLUTION:15-8=7 B. 7 #### B QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:Which of the following is equal to 3.14 x 10^6) ? options: A)3.14 B)3140000 C)31400 D)314 E)314000 SOLUTION:= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is B. #### B QUESTION:A beats B by 50m in a race of 500m ,then B beats by C by 25m in a race of 500m.Find the distance by which A beats C in a race of 400? options: A)55m B)56m C)57m D)58m E)59m SOLUTION:A beats B in 500m race by 50m so,for every 10 m race A beat B by 1m.. So,in 400 m race A beat B by 40m In a case of B & C, B beats C by 25m in 500m race.. So,B beats C by 1m in 20 m race Now,in a 400m race B beats C by 18m.. In a 400m race, A beats B by 40m & B beats C by 18m.. So,A beats C by 58m ANSWER:D #### D QUESTION:If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively. 2(60+p+60+q)= 240 + 2(p + q). 2(p+q) can range from 0 up to a maximum value of 36 when p=q=9. Then the tens and ones digits of 2(x+y) can range from 40 up to 76. There can be 4 possibilities for the tens digit. The answer is C. #### C QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:1395 x 1395 options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these SOLUTION:1395 x 1395 = (1398)2 = (1400 - 2)2 = (1400)2 + (5)2 - (5 x 1400 x 5) = 1946025. Answer: Option A #### A QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2781 C)2278 D)2081 E)2721 SOLUTION:Explanation: (1010)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: A #### A QUESTION:Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest? options: A)3.6 B)7 C)18 D)Cannot be determined E)None SOLUTION:Explanation: Let rate = R% and time = R years. Then, (1500 x R x R)/100 = 735 15RÂ² = 735 RÂ² = 49 R = 7. Answer: Option B #### B QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000 SOLUTION:0.7(x-600)=0.6(x-400) 0.1x=420-240 x=1800 The answer is D. #### D QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/99 B)33/91 C)36/91 D)33/97 E)33/33 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 33/91 Answer: B #### B QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:There are 5 boxes in a cargo. The weight of the 1st box is 200 KG, the weight of the 2nd box is 20% higher than the third box, whose weight is 25% higher than the 1st box weight. The 4th box which weighs 350 KG is 30% lighter than the 5th box. Find the difference in average weight of the 4 heaviest boxes and the four lightest boxes. options: A)22 B)75 C)25 D)70 E)11 SOLUTION:weight of 1st box=200 weight of 3rd box=(125/100)200=250 weight of 2nd box=(120/100)250=300 weight of 4th box =350 weight of 5th box=(10/7)350=500 average of 4 highest weighted boxes=(500+350+300+250)/4=350 average of 4 lightest boxes=(350+300+250+200)/4=275 therefore difference=350-275=75 Answer:B #### B QUESTION:if log 5 = 0.69897, the number of digits in 5128 is options: A)90 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46 ie, its characteristic = 89 Hence, number of digits in 2128 = 89+1 = 90 Answer: Option A #### A QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? options: A)6 B)8 C)3 D)4 E)0 SOLUTION:Explanation: Use formula For a work Members Ã— days = constant 8 Ã— 3 = 4 Ã— a a = 6 so answer is 6 days Answer: A #### A QUESTION:What is the units digit of 3333^(333)3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D QUESTION:A customer pays 40 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)50 B)40 C)70 D)60 E)20 SOLUTION:Let x be the original price. x - 20 = 40 x - 20 + 20 = 40 + 20 x + 0 = 60 x = 60 Answer is D #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)2388 B)2380 C)2888 D)2663 E)2922 SOLUTION:Kamal : Sameer = (9000 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs. 2380. Answer: B #### B QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”? options: A)5 B)7 C)49 D)20 E)25 SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). C #### C QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20. options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280 SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83. A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392; C's share = $ (1162 x (20/83))= $ 280. Option C #### C QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. options: A)Rs. 1900 B)Rs. 2660 C)Rs. 2800 D)Rs. 2840 E)Rs. 3000 SOLUTION:Explanation: For managing, A received = 5% of Rs. 7400 = Rs. 370. Balance = Rs. (7400 - 370) = Rs. 7030. Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3) = 39000 : 42000 : 30000 = 13 : 14 : 10 B's share = Rs.(7030 X 14/37)=Rs. 2660. ANSWER IS B #### B QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)891 E)1,001 SOLUTION:James = (0.5/100)2000 = 10 Votes to win = (45/100)Total Votes +1 = (45/100)2000 +1 = 901 Remaining Voted needed to win election = 901 - 10 = 891 Answer: option D #### D QUESTION:The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is? options: A)$1500 B)$4000 C)$2000 D)$2500 E)$3200 SOLUTION:Let the income of A and B be $5x and $4x Let their expenditures be $3y and $2y 5x-3y = 1600-------1) 4x-2y = 1600-------2) From 1) and 2) x = 800 A's income = 5x = 5800 = $4000 Answer is B #### B QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 311. All other products are too big. The answer is B. #### B QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph SOLUTION:US = 45 DS = 55 M = (45 + 55)/2 = 50 Answer:D #### D QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre. options: A)Rs. 15000 B)Rs. 15550 C)Rs. 24750 D)Rs. 16500 E)None of these SOLUTION:Solution Area of the floor = (5.5 × 3.75) m2 = 20.625 m2 ∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C #### C QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 5/18 = 40 m/sec Time taken = 150/40 = 3.75 sec. ANSWER:C #### C QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min SOLUTION:1/20 + 1/40 - 1/80 = 5/80 80/5 = 16 ANSWER:E #### E QUESTION:The sum of two consecutive number is 109. Which is the larger number? options: A)42 B)43 C)44 D)45 E)55 SOLUTION:Let consecutive number be x, x+1 Therefore sum of the consecutive number is x + x+1=109 2x+1=109 2x=108 x=54 Therefore larger number is x+1=55 ANSWER:E #### E QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? options: A)112 B)50 C)77 D)14 E)12 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:If n = 2.0767 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0047 E) 0.0033 SOLUTION:n=2.08 n-n=2.08-2.0767 0.0033 Answer: E #### E QUESTION:The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A options: A)A)11 B)B)12 C)C)13 D)D)14 E)E)15 SOLUTION:Explanation: Given that A+B = 11 + B + C => A – C = 11 + B – B = 11 => C is younger than A by 11 years Answer: Option A #### A QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B QUESTION:A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.4 days B)4.4 days C)5.4 days D)8.4 days E)2.4 days SOLUTION:A 6.4 days 1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300 So, all three together will complete the work in 300/47 = 6.4 days.- #### A QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 66 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)(3/7)(4/6)(3/5) [4!/(2!2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)13 8/3 days B)13 1/3 days C)13 6/3 days D)63 1/3 days E)13 5/3 days SOLUTION:5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B #### B QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train. options: A)a) 45 B)b) 33 C)c) 48 D)d) 55 E)e) 61 SOLUTION:Let y be the balance distance to be covered and x be the former speed. A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late so, y/(3x/4) - y/x = 35/60 4y/3x - y/x = 7/12 y/x(4/3-1)=7/12 y/x1/3=7/12 y/x=7/4 4y-7x=0 ........ 1 Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late so, (y-24)/(3x/4) - (y-24)/x = 25/60 4(y-24)/3x - (y-24)/x = 5/12 (y-24)/x (4/3-1) = 5/12 (y-24)/x 1/3 = 5/12 (y-24)12 = 3x5 (y-24)4 = 5x 4y-5x = 96 ....... 2 eq2 - eq1 2x=96 x=48=T Ans = C #### C QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? options: A)897 B)164,850 C)164,749 D)149,700 E)156,720 SOLUTION:Explanatory Answer Step 1: Identify the series The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101. The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107. The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998. It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2). So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3. Step 2: Compute the sum Sum of an Arithmetic Progression (AP) = [first term + last term/2]n We know the first term: 101 We know the last term: 998. The only unknown is the number of terms, n. In an A.P., the nth term an = a1 + (n - 1)d In this case, therefore, 998 = 101 + (n - 1)* 3 Or 897 = (n - 1) * 3 (n - 1) = 299 or n = 300. Sum of the AP will therefore, be [101+998/2]∗300 = 164,850 Choice B is the correct answer. #### B QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ? options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Expanding we have 6x^2 - 3x + 4x -2 6x^2 + x - 2 Taking coefficients, a = 6, k= 1, n = -2 Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9 The answer is C. #### C QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3Ã—7/36 = 7/12 Remaining work = 1 â€“ 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? options: A)20 B)55/4 C)25 D)14 E)13 SOLUTION:After passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles/hour. In those 5 mins the cyclist travels a distance of 5/4 miles. In those 5 mins the hiker travels a distance of 1/3 miles. So the hiker still has to cover 11/12 miles to meet the waiting cyclist. The hiker will need 55/4 mins to cover the remaining 11/12 miles. So the answer is B. #### B QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 20% slower than the second car's speed. If the distance between the cars is 1125 km, how many hours will it take until the two cars meet? options: A)4 B)4.5 C)4.8 D)5 E)5.5 SOLUTION:The speed of the first car is 100 km/h. The speed of the second car is 100 / 0.8 = 125 km/h. The two cars complete a total of 225 km each hour. The time it takes the cars to meet is 1125 / 225 = 5 hours. The answer is D. #### D QUESTION:If shares of two persons in profits are Rs.600 and Rs.1000 then ratio of their capitals is options: A)3:5 B)2:3 C)4:3 D)1:3 E)1:2 SOLUTION:profit=timecapital so 600:1000=3:5 ANSWER:A #### A QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 5/6 = 5 #### C QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is: options: A)364724 B)365387 C)365737 D)366757 E)366767 SOLUTION:Required number= 999366+103 = (1000-1)366+103 = 366000-366+103 = 365737. ANSWER:C #### C QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes? options: A)6 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 11 - 1 = 10 rounds per hour. Time taken to complete one round at this speed = 1/10 hr = 6 min. A #### A QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A QUESTION:Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 450 or over 650. If the individual ranges of the three people's scores in those 4 practice tests were 30, 80 and 110, what is the difference between the maximum and minimum possible ranges of all their scores put together. options: A)90 B)120 C)50 D)70 E)100 SOLUTION:According to the information in the question the maximum range would be between 450 and 650(200). The minimum range would be the greatest range for any one individual, which is listed in the problem as 110. So the difference between these would be 200-110 or 90. Answer: A #### A QUESTION:What percent of 60 is 90? options: A)133 1⁄3 B)150 C)60 D)33 1⁄3 E)25 SOLUTION:% of 60 is 90? = 90/60 = 3/2 = 150% Thus B is the correct answer. #### B QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:An article is bought for Rs.600 and sold for Rs.900, find the gain percent? options: A)50% B)63 1/3% C)33 1/3% D)93 1/3% E)33 1/3% SOLUTION:Explanation: 600 ---- 300 100 ---- ? => 50% Answer:A #### A QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 3016=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 12 * 5 = 30 m2 Answer: B #### B QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width? options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3 SOLUTION:2x+2y=50 x+y=25 x+4x=25 5x=25 x=5 Answer C #### C QUESTION:The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is: options: A)587 x 10^13 miles B)999× 1238 miles C)346 × 1012 miles D)247 × 1012 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in one years is: 5,870,000,000,000 = 587 * 10 ^10 The distance of the light travels in 1000 years is: = 587 * 10^10 x 10 ^3 = 587 x 10^13 miles Answer :A #### A QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 * 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:Louie takes out a three-month loan of $2000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month? options: A)A)333 B)B)383 C)C)402 D)D)433 E)E)804 SOLUTION:Here's the calculation for that case, assume monthly payment is X. After 1st month: (2000)(1.1)-X = 2200-X After 2nd month: (2200-X)(1.1)-X = 2420-2.21X After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X Now, the amount after the last payment in 3rd month must bring the total to 0. Hence: 2662-3.31X = 0 X = 2662/3.31 = 804 Answer E #### E QUESTION:Two dice are thrown together.What is the probability that the sum of the number on the two faces divided by 4? options: A)3/9 B)4/9 C)1/9 D)2/9 E)5/9 SOLUTION:n(s)=66=36 Let e be the event that the sum of the numbers on the two faces is divisible by 4 E={(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2)} n(e)=8 p(e)=n(e)/n(s) =8/36 =2/9 Answer is option D #### D QUESTION:A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-39 E)36-37 SOLUTION:10%(32.5) = 3.25 15%(32.5) =4.875 total amount could have been 32.5+3.25 and 32.5+4.875 => could have been between 35.75 and 37.375 => approximately between 36 and 37 Answer is E. #### E QUESTION:Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16 options: A)5 B)7. C)2. D)3 E)9 SOLUTION:A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16. Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it. 58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445 The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16. 5445/16 gives remainder 5. Answer (A) #### A QUESTION:Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank? options: A)IX B)XXIII C)XV D)XI E)None SOLUTION:Explanation: This is a simple addition series; each number is 3 more than the previous number. Answer: D #### D QUESTION:If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)A)60% B)B)85.7% C)C)65% D)D)75% E)of these SOLUTION:A's marks = 70 ; B's marks = 60. Let x% of A = B => x/100 70 = 60 => x = (60 * 100)/80 = 85.7 B's marks is 85.7% of A's marks. ANSWER:B #### B QUESTION:A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:4 E)1:2 SOLUTION:He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33) Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters) Hence the water added would be .1 liter. Therefore the ratio of water to milk is .1/1 = 1/10 ANSWER:B #### B QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race? options: A)450 m B)680 m C)700 m D)900 m E)1000 m SOLUTION:Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race ANSWER C #### C QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are: options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186 SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62. The numbers are 62, 124, 186. ANSWER:A #### A QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 * 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (12523+16225)/125+162 = 24 years Answer is D #### D QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)(25/100)x = 18; => x=480; Ans is (C). #### C QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold? options: A)2 B)5 C)9 D)12 E)15 SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b) => 3(10 + r) + 5(10 + b) = 120 => 30 + 3r + 50 + 5b = 120 => 3r + 5b = 120 - 30 - 50 = 40 => 5b = 40 - 3r => b = 8 - (3/5)r To minimize b, we need to maximize r and it will be a multiple of 5. r = 5, b = 8 - (3/5)5 = 5 r = 10, b = 8 - (3/5)10 = 2 Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets. Answer: D #### D QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 273=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer? options: A)2388 B)2799 C)2877 D)4266 E)2881 SOLUTION:CI = 14800{ [ 1 + 13.5/100]2 - 1 } = 14800 { [1 + 27/200]2 - 1 = 14800 { 2 + 27/200}{27/200} = (74)[2 + 27/200](27) = 1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266.Answer:D #### D QUESTION:The forth proportional to 6,8,15 is? options: A)15 B)12 C)18 D)20 E)24 SOLUTION:Let the fourth proportional to 6,8,15 be x then 6:8::15:x 6x = 815 x = 20 Answer is D #### D QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)124km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5.2 or, x/40 + (250 - x)/60 = 5.2 or, (3x + 500 - 2x)//120 = 5.2 or 500 + x = 624 x=124 ANSWER:D #### D QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)767 m B)240 m C)187 m D)176 m E)186 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m. Answer:B #### B QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball? options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these SOLUTION:similar triangle properties.. 2/r+6 = 6/r-6 giving r = 12. Answer: A #### A QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack? options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13 SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits. Probability of getting spade or a jack: = (13 + 3)/52 = 16/52 = 4/13 Therefore, the probability of getting neither a spade nor a jack: = 1 − 4/13 = 9/13 ANSWER:A #### A QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph SOLUTION:US = 20 DS = 35 M = (35 - 20)/2 = 7.5 Answer:B #### B QUESTION:If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar? options: A)45 B)67 C)75 D)83 E)150 SOLUTION:We are told that 15 percent discount from the original price is more than $10: 0.15{price} > 10; {price} > 1,000/15; {price} > 66 2/3. Answer: B. #### B QUESTION:The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is: options: A)1439 B)1440 C)1459 D)1449 E)1549 SOLUTION:LCM = 1440 1440 - 1 = 1439 ANSWER:A #### A QUESTION:The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 25%? options: A)37.5% B)37.6% C)38.5% D)17.1% E)37.2% SOLUTION:Let marked price = Rs. 100. Then, C.P. = RS. 64, S.P. = Rs. 75 Gain % = 11/64 100 = 17.1%. Answer: D #### D QUESTION:A scuba diver descends at a rate of 30 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 2400feet below the sea level..how long will he take to reach the ship? options: A)70 minutes B)72 minutes C)80 minutes D)76 minutes E)77 minutes SOLUTION:Time taken to reach = 2400/30= 80 minutes ANSWER:C #### C QUESTION:Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ? options: A)24 B)25 C)26 D)27 E)29 SOLUTION:x/2y=3/2 =>x=6y/2=3y =>(7x+8y)/(x-2y)=((7(3y))+8y)/(3y-2y) =>29y/y=29 ANSWER:E #### E QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54 SOLUTION:Let the required means score be x. Then, 20 80 + 25 * 31 + 55 * x = 52 * 100 = 1600 + 775 + 55x = 5200 = 55x = 2825 = x = 565/11 = 51.4. ANSWER:C #### C QUESTION:. A car covers a distance of 390 km in 4 hours. Find its speed? options: A)104 B)55 C)66 D)98 E)100 SOLUTION:390/4 = 98 kmph Answer: D #### D QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)(1/4)S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is: options: A)59 7/12 min. past 3 B)4 p.m. C)58 7/12 min. past 3 D)58 7/11 min. past 4 E)2 3/11 min. past 4 SOLUTION:Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37/4 hrs. 3 min. 5 sec. of this clock = 3 min. of the correct clock. 37/720 hrs of this clock =1/20 hrs of the correct clock. 37/4 hrs of this clock =1/20 x 720/37 x 37/4 hrs of the correct clock. = 9 hrs of the correct clock. The correct time is 9 hrs after 7 a.m. i.e., 4 p.m. Answer: B #### B QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)4% B)4.65% C)6.125% D)7.24% E)7.45% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:As part of a game, two people each must secretly choose an integer between 1 and 2, inclusive. What is the approximate likelihood that all two people will choose different numbers? options: A)9% B)12% C)16% D)20% E)50% SOLUTION:Ans:E 1st person has option no's- (1,2) - there fore probability of getting a no = 2c1/2c1 = 1 2nd person has only one option - there fore probability of getting a no = 1c1/2c1 =1/2 =11/2 =50% #### E QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. If he now has an equal amount of money in each pocket, then how much money did he originally have in his left pocket? options: A)$120 B)$130 C)$140 D)$150 E)$160 SOLUTION:Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120 in his left pocket (and $80 in his right pocket) before moving $20 from his left to his right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120). correct answer E #### E <<<Examples ends QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)240 B)250 C)260 D)230 E)220 SOLUTION:Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 36 => 300+L = 15×36 = 540 => L = 540-300 = 240 meter Answer is A. #### A QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm SOLUTION:r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 ANSWER:C #### C QUESTION:If x and y are different prime numbers, each greater than 10, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer options: A)III only B)I only C)II only D)I,II only E)I,II and III SOLUTION:Given: x and y are different prime numbers, both greater than 10 Statement I: x+y is an even integer Since x and y are prime numbers greater than 10, they will be odd Therefore sum will be even. Correct Statement II: xy is an odd integer Since x and y are prime numbers greater than 10, they will be odd Therefore multiplication will be odd. Correct Statement III: (x/y) is not an integer Since x and y are prime integers, therefore they will not have any common factor apart from 1 Hence (x/y) will not be an integer Correct Hence all three statements I, II and III are correct Answer : E #### E QUESTION:How many even multiples of 55 are there between 549 and 1101? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:550 = 1055 1100 = 2055 The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:If pq = p^3 + q^2 – 2pq, for what value of q is pq equal to p^3 for all values of p? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:C p3 + q2 â€“ 2pq = p3 => q2 - 2pq = 0 => q (q - 2p) = 0 => q = 0 or q = 2p im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI C #### C QUESTION:If 9^y = 3^14, what is y? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:9^y = 3^2y = 3^14 2y=14 y = 7 The answer is E. #### E QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive? options: A)$444 B)$445 C)$446 D)$447 E)$448 SOLUTION:A+B+C = 1200 Given ratio 10:12:13 Let us say the shares of A,B,C deducting 10,20,15 be a,b,c a+b+c = 1200-45= 1155 = 35K c share = (1155X13)/35 = 429 C = chandran share = 429+15 = 444 Option A #### A QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A? options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440 SOLUTION:LCM = 180 Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c = (180/15)/(180/15 +180/20 + 180/45) = (12/25) * 500 = Rs.240 ANSWER:A #### A QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him? options: A)2000 B)3000 C)4000 D)1000 E)5000 SOLUTION:Let the money he took for shopping be m. Money he spent = 30 % of m = 30/100 × m = 3/10 m Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10 But money left with him = $ 2100 Therefore 7m/10 = $ 2100 m = $ 2100× 10/7 m = $ 21000/7 m = $ 3000 Therefore, the money he took for shopping is $ 3000. Answer:B #### B QUESTION:A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform? options: A)277m B)180m C)165m D)278m E)175m SOLUTION:Length of the train be ‘X’ (X + 250)/20 = 15 X = 50m Let the length of the platform be y (y + 50)/15 = (50 + 250)/20 4y + 200 = 900 X = 1750m Answer: E #### E QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 162 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)2287 B)27 C)299 D)287 E)150 SOLUTION:Speed = 60 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer: E #### E QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks? options: A)60 B)80 C)100 D)120 E)140 SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback. If all 160 books were paperbacks, the dealer would earn a profit of $320. Since the actual profit was $400, the dealer must have sold 80 hardbacks. Then the number of paperbacks sold was 160-80 = 80. The answer is B. #### B QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? options: A)3 B)4 C)6 D)9 E)12 SOLUTION:yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as: A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used? So for a job to be done in 2 hours R = 1/2 R_a(Rate of Machine R) = 1/36 R_s(Rate of Machine S) = 1/36 Lets say x machines are used to attain the desired rate, thus x/36+x/36 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours) (x+x)/36 = 1/2 2x/36 = 1/2 x = 9. QA = 9 (ANSWER D) #### D QUESTION:The length of the room is 3m and width is 3m. Find the cost of paving the floor by slabs at the rate of Rs.300 per sq meter? options: A)1800 B)1500 C)1700 D)1600 E)1540 SOLUTION:l=3m w=3m area of the floor = 3 x 3 = 9 sq m cost of paving = 200 x 9 = Rs. 1800 Answer: A #### A QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 3 = Rs.2025 Answer:C #### C QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/1233 = 33 cents. Answer: C. #### C QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7. options: A)150 B)152 C)154 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 7 D = 153 + 7 D = 160 ANSWER E #### E QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number? options: A)74 B)76 C)70 D)68 E)65 SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) Their sum = 8x - 4 = 292 => x = 37 Smallest number is: 2(x - 2) = 70. ANSWER:C #### C QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:If y exceeds x by 25%, then x is less than y by? options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3% SOLUTION:X=100 y=125 125------25 100-------? => 20% Answer:A #### A QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? options: A)1276 B)1200 C)2832 D)1800 E)1236 SOLUTION:Explanation: l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 Answer: Option D #### D QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/7+x/5=1 â‡’5x+7x=35 â‡’12x=35 â‡’x=2.9 km Answer: Option C #### C QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet. The number of revolutions = distance/circumference = 5,280x/t. Answer: A. #### A QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel? options: A)400 B)450 C)500 D)550 E)600 SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour. The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours. The answer is A. #### A QUESTION:1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:1/5 , 1/2 , 1/3 1/52 , 1/22 ,1/32 1/53 , 1/23 ,1/33 1/54 , 1/24 ,1/34 so 1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2 ANSWER:B #### B QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:How many digits are required to number a book containing 260 pages? options: A)784 B)672 C)492 D)372 E)300 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 902=180 digits. 260-(90+9)=161 pages will require 1613=483 digits. The total number of digits is 9+180+483=672. The answer is B. #### B QUESTION:Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate) options: A)7 days B)8 days C)9 days D)10 days E)11 days SOLUTION:Total work is 35 = 15 units. A does 1 day of work every 2 days. B does 2 days of work every 4 days. C does 2 days of work every 5 days. Test the options. In 7 days: A will do 13 + 1 = 4 units (3 complete cycles and 1 day of work). B will do 21+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest). C will do 21 + 2 =4 units (1 complete cycle and 2 days of work). Total = 4 + 4 + 4 = 12 units. In 8 days: A will do 14 = 4 units (4 complete cycles). B will do 22= 4 units (2 complete cycles). C will do 21 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest). Total = 4 + 4 + 4 = 12 units. In 9 days: A will do 14 + 1 = 5 units (4 complete cycles and 1 day of work). B will do 22+ 1 = 4 units (2 complete cycles and 1 day of work). C will do 21 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest). Total = 5 + 5 + 4 = 14 units. In 10 days: A will do 15 = 5 units (5 complete cycles). B will do 22+ 2= 6 units (2 complete cycle and 2 days of work). C will do 22 =4 units (2 complete cycles). Total = 5 + 6 + 4 = 15 units. Therefore, the answer is D. #### D QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)20, 35, 48 E)None of these SOLUTION:Let the present ages are 4x, 7x, 9x. => (4x-8) + (7x-8) + (9x-8) = 56 => 20x = 80 => x = 4 So their present ages are: 16,28,36 ANSWER:B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ? options: A)124 B)144 C)134 D)142 E)143 SOLUTION:The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B #### B QUESTION:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria options: A)10 B)12 C)14 D)16 E)18 SOLUTION:The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50). Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes: 2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times. Since it takes the population 2 minutes to double once it takes 62 minutes = 12 minutes to double nine times. Thus, solution B = 12 is correct. #### B QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468? options: A)1000 B)1100 C)1200 D)1300 E)1600 SOLUTION:Local value of 4 = 4 x 100 = 400 Place value of 4 = 4 There fore = 4 x 400 = 1600 E #### E QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article? options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2 SOLUTION:Explanation: Let C.P. = Rs. 5x and S.P. = Rs. 7x. Then, Gain = Rs. 2x Required ratio = 2x : 5x = 2:5 Answer: Option B #### B QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 532=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing? options: A)50% B)40% C)30% D)20% E)10% SOLUTION:Let x be the percentage of dressing P in the new dressing. 0.3x + 0.1(1-x) = 0.12 0.2x = 0.02 x = 0.1 = 10% The answer is E. #### E QUESTION:Tough and Tricky questions: Work/Rate Problems. If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)8 E)9/7 SOLUTION:80 Workers = 3 hours then, 1 Worker = 380 Hours 30 Workers = (380) /(30) = 8 Answer.D #### D QUESTION:The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3 SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4x. Point (r, r+1) lies on line n means that (r+1)=1/4r --> r=-4/3. Answer: A. #### A QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 12.. so total who won N = 11+12 = 23.. B #### B QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform? options: A)45 B)47 C)49 D)51 E)53 SOLUTION:Let the length of the train be x meters. When a train crosses an electric pole, the distance covered is its own length x. speed = 36 km/h = 36000 m / 3600 s = 10 m/s x = 14 * 10 = 140 m. The time taken to pass the platform = (140 +370)/ 10 = 51 seconds The answer is D. #### D QUESTION:A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago? options: A) 8 B) 10 C) 12 D) 14 E) 7 SOLUTION:Let's say Age of Richard isR Age of David isD Age of Scott isS Now Richard is 6 years older than David, i.e. R = D +6 David is 8 years older than Scott i.e. D = S +8 If in 8 years, Richard will be twice as old as Scott i.e. R+8 = 2x(S+8) i.e. R+8 = 2S + 16 i.e. R = 2S+8 But R = D+6 = (S+8)+6 = S+14 therefore, 2S + 8 = S +14 i.e. S = 6 i.e. R = 20 i.e. D = 14 Now, how old was David 7 years ago? i.e. D-7 = 14-7 = 7 years Answer: Option E #### E QUESTION:In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L? options: A)6 B)-1 C)-2 D)-6 E)-10 SOLUTION:We need to find out the value of p and L to get to the slope. Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving 5 = -p2 +9 p2 = 4 p = + or - 2 simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7. -7 = -t2+9 t = +or - 4 considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1 IMO option B is correct answer. #### B QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)y(y+3) B)y^2(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)y(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit? options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5% SOLUTION:55% is 25%-points above 30% and 5%-points below 60%. So the ratio of Sue's mix to Jane's mix is 1:5. 1/670% = 11.7% The answer is B. #### B QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)100}=4% Answer is A. #### A QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/11/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 4 days ? options: A)X-1/8 B)X-1/16 C)X/8 D)X/16 E)X/32 SOLUTION:LET NO OF LEAVES IX X ..IST DAY X/2 ..2ND DAY X/4 ..3RD DAY X/8 , FOURTH DAY X/16 , 5TH DAY X/32 , 6TH DAY X/64 SO ON SO FOURTH. FINALLY ON LEAVE WILL BE LEFT ..SO ON 3RD DAY LEAVE LOST IS X-1/16 ANSWER B #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:378 = 2 x 3 x 3 x 3 x 7 N must include at least 3, 23, and 33. The answer is C. #### C QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x2+y4=140 heads: x1+y1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true? I. b-a = 2 II. abc is an even integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and II only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, thenb= a + 1, from which it follows that b - a = 1. So, I is false. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: D. #### D QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)145 B)155 C)165 D)175 E)185 SOLUTION:The number of ways to form a group of 3 is 12C3 = 220 The number of groups with no senior partner is 7C3 = 35 The number of groups with at least one senior partner is 220-35 = 185 The answer is E. #### E QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the W odds that x^2+y^2>1? options: A)1. pi/4 B)2. W=pi/16 C)3. W=1-pi/4 D)4. W=1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:John has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:Let there be a pennies , b nickels and c dimes so total amount can be 1+5b+10c cents to 4+5b+10c as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4) So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5. so answer is B #### B QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How many packets of seed are needed for the larger garden? Round each answer to the nearest square foot before continuing. options: A)1 seed packet B)2 seed packets C)3 seed packets D)4 seed packets E)5 seed packets SOLUTION:3.14 x 32 = 28.26 sq. ft. area of small garden 28 sq. ft. rounded 3.14 x 62 = 113.04 sq. ft. area of large garden 113 sq. ft. rounded 113 ÷ 28 = 4.04 or 4 seed packets (rounded) correct answer D #### D QUESTION:Calculate the time it will take for a train that is 240 meter long to pass a bridge of 130 meter length, if the speed of the train is 50 km/hour ? options: A)21.64 seconds B)22.64 seconds C)23.64 seconds D)26.64 seconds E)35.64 seconds SOLUTION:Speed = 35 Km/hr = 50(5/18) m/sec = 13.89 m/sec Total distance = 240+130 = 370 meter Time = Distance/speed = 370 (1/13.89) = 26.64 seconds Answer: D #### D QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The speed at which the train must run to reduce the time of journey to 40min will be. options: A)60kmph B)63kmph C)57kmph D)70kmph E)61kmph SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=ST=485/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph Answer is A. #### A QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of the couple and a child, who was born during the interval, is 22Yrs now. How old is the child now ? options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these SOLUTION:(a+b-6-6)/2=26; a+b=64; a+b+c/3=22; solving both c=2 ANSWER:A #### A QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? options: A)6 B)8 C)3 D)4 E)0 SOLUTION:Explanation: Use formula For a work Members Ã— days = constant 8 Ã— 3 = 4 Ã— a a = 6 so answer is 6 days Answer: A #### A QUESTION:Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is options: A)360 B)240 C)2520 D)480 E)None of these SOLUTION:Solution Order of vowels of fixed âˆ´ required number of ways are 7!/2!. Answer C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000. 36/7 has a remainder of 1. Jan. 8th is: Friday + 1 day = Saturday The answer is D. #### D QUESTION:In how many different number of ways a Committee of 2person of can be selected from 2boys and 2girls such that at least 1 girl is included in the committe options: A)3 B)4 C)2 D)5 E)9 SOLUTION:1G 1B 2G = (2C12C1)+2C2 = (22)+1 = 5 Total 2M 2W 4C2=6 2C2=1 At least one girl = total - with out girl At least one girl = 6-1=5 D) #### D QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pir^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)2121/4 = 346.5 sq m answer :C #### C QUESTION:A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? options: A)1/5 B)2/7 C)2/9 D)3/10 E)4/11 SOLUTION:The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9. The answer is C. #### C QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? options: A)240 B)235 C)245 D)250 E)260 SOLUTION:Speed = 45 5/18 = 25/2 m/sec. Time = 30 sec Let the length of bridge be x meters. Then, (130 + x)/30 = 25/2 x = 245 m. Answer: Option C #### C QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 6 other contributions made before john's, what is the size of his donation? options: A)$225 B)$150 C)$200 D)$250 E)$450 SOLUTION:Cavg = average contribution before John Cavg1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by $25, he must put in $25 for each of the 6 people. so $150. But, he also has to put in the average for himself (the seventh person), so add $75. So $225 is your answer. Answer A #### A QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs.2(1/9) B)Rs.2(2/9) C)Rs.3(1/9) D)Rs.1(1/9) E)Rs.2(2/5) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10100/((100-10 )5) = Rs.2(2/9) B #### B QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ? options: A)d B)3d C)15d D)d + 5 E)d + 15 SOLUTION:If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change. If we increase or decrease each term in a set by the same percent (multiply by a constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5. Answer: D. #### D QUESTION:Find the value of y from (12)^3 x 6^4 ÷ 432 = y? options: A)3452 B)2343 C)2435 D)2578 E)5184 SOLUTION:Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 E #### E QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)76.5 B)36.5 C)46.5 D)16.5 E)26.5 SOLUTION:Explanation: Correct Sum = (36 50 + 48 - 23) = 1825. Correct mean = = 1825/50 = 36.5 Answer: B #### B QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? options: A)90r B)75r C)48r D)24r E)(64π)/3 SOLUTION:Interesting to note that the larger wheel has a diameter of 48 (86) while the smaller one has a diameter of 32 (84)... If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 101.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 6001.5 = 900 revolutions per hour. If r = 10, then the answer choice must be b. A. 90r #### A QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants? options: A)4!5c2 21c2 B)4!5c3 21c2 C)5!5c2 21c2 D)7!5c2 21c5 E)6!5c2 21c2 SOLUTION:combination for 2 vowels out of 5 = 5c2 ways combination for 5 consonants of 21 = 21c5 ways Additionally the arrangement can be = 7! total arrangements =7!5c2 21c5 D #### D QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 71+1 (71+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:Tough and Tricky questions: Combinations. Seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? options: A)6 B)7 C)12 D)16 E)21 SOLUTION:Number of ways First-place medal can be awarded to four contestants = 7 Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3 Therefore number of possibilities = 73 =21 Answer:E #### E QUESTION:How many numbers from 29 to 79 are exactly divisible by 11 options: A)5 B)7 C)8 D)9 E)11 SOLUTION:29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers Option 'A' #### A QUESTION:A worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $100? options: A)30 B)33 C)35 D)38 E)40 SOLUTION:Every two days, the net total is $5. After 32 days, the worker will have $80. On day 33, the worker will receive $20 for a net total of $100. The answer is B. #### B QUESTION:Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd? options: A)15/56 B)3/8 C)15/28 D)5/8 E)3/4 SOLUTION:Total number of combinations=12C3=220................(1) Total number of combinations including 2 and two other numbers=11C2=55......................(2) Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165 So, probability=165/220=3/4 E #### E QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected? options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9) SOLUTION:x red balls y green balls x+4+y+5 is the total =x+y+9 x+5 is the number of red balls so (x + 5)/(x + y + 9) the answer is C #### C QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is? options: A)625 B)298 C)269 D)200 E)267 SOLUTION:Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown? options: A)26 B)19 C)11 D)8 E)6 SOLUTION:No of dogs=45 Long fur=36 Brown=27 Neither long fur nor brown=8 Therefore, either long fur or brown=45-8=37 37=36+27-Both Both=26 Answer A #### A QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 46 x = 12 Answer is B #### B QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x4x=900 x^2= 225 x= 15 Length= 415= 60 difference= 60-15= 45 E is the answer #### E QUESTION:How many words can be formed by using all letters of the word “BIHAR” options: A)452 B)320 C)365 D)456 E)120 SOLUTION:The word BIHAR contains 5 different letters. Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120 Ans: E #### E QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)22 B)287 C)48 D)277 E)21 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: C #### C QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)9 1/2 SOLUTION:Son's 1day work = 1/3 - 1/5 = 2/15 Son alone can do the work in 15/2days = 7 1/2 days Answer is C #### C <<<Examples ends QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528(80/100)(90/100) = 380 Answer: C #### C QUESTION:Calculate the circumference of a circular field whose radius is 6 centimeters. options: A)2 π cm B)1 π cm C)15 π cm D)12 π cm E)19 π cm SOLUTION:Circumference C is given by C = 2πr = 2π6 = 12 π cm Answer: D #### D QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 920+7100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together? options: A)300 B)325 C)350 D)375 E)400 SOLUTION:At 6:45, the first train is 75 km ahead. The second train gains 25 km each hour. The time it takes the second train to catch the first train is 75 / 25 = 3 hours. In this time, the second train travels 3125=375 km. The answer is D. #### D QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20. Answer: C. #### C QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 7 C) 5 D) 9 E) 12 SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:How many words can be formed by using all letters of the word “BIHAR” options: A)452 B)320 C)365 D)456 E)120 SOLUTION:The word BIHAR contains 5 different letters. Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120 Ans: E #### E QUESTION:By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is? options: A)50 B)25 C)400 D)200 E)150 SOLUTION:Marked price = Rs. 300 C.P. = 100/300 * 300 = Rs. 100 Sale price = 90% of Rs. 300 = Rs. 270 Required gain % = 200/100 * 100 = 200%. Answer:D #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years? options: A)14000 B)14400 C)14500 D)15625 E)14700 SOLUTION:Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D #### D QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 3200 = 400 Answer: D #### D QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4. 6000 /4 = 1500 toys correct answer B #### B QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40 SOLUTION:SOL: Lets consider h(100): => 2468.........98100 => (21) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50) => (2^50) * (1234........4950) => h(100) = (2^50) (50!) We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100). But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50; ANSWER:E #### E QUESTION:If Susan can paint a house in 4 hours, and Jeff can paint the same house in 6 hours, how long will it take for both of them to paint the house together? options: A)2.4 hr B)2.6 hr C)3.0 hr D)5.0 hr E)5.2 hr SOLUTION:If Susan can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house. If Jeff can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house. Let x = number of hours it would take them together to paint the house so, 1/4 + 1/6 = 1/x x=12/5 or 2.4 hours Answer: A #### A QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate. options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10 SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity. Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job. Answers E, A and C are illogical, since the individual times must both be greater than 10 days. so we can TEST the values for Answers B and D. Using the values for Answers C and D... Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match Final Answer: C #### C QUESTION:A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? options: A)14 B)45 C)54 D)65 E)81 SOLUTION:Just check the answers and reverse the numbers until you get 63. 81 - 18 = 63 Answer E #### E QUESTION:There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection? options: A) 100 B) 103 C) 106 D) 108 E) 109 SOLUTION:Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x = 3p+1 x can take values 100 , 104 , 109 If the cards are counted 4 at a time , there is 1 left over x= 4q+4 x can take values 100 , 108 Therefore , x = 100 Answer A #### A QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)1.6 B)1 C)0.4 D)0.16 E)0.016 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi1610 = pih100100 (h is distance that the oil level dropped) h = 160/10,000 = 16/1000 = 0.016 ft The answer is E. #### E QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = xx is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of shelves. 11x - 30 = 7(x-1) + 5 4x = 28 x = 7 The answer is C. #### C QUESTION:Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-? options: A)Rs.24600 B)Rs.38169 C)Rs.38989 D)Rs.23200 E)None of these SOLUTION:Explanation: 112% of CP = Rs.42750 :. CP = Rs.42750x100/112 = Rs.38169. Answer: Option B #### B QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? options: A)100 B)72 C)110 D)135 E)145 SOLUTION:Explanation : Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x. .'. 60% of x = 36 +5/6 36 =>60/100 x = 66 =>x = 110 Answer : C #### C QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:Rahul went to a shop and bought things worth Rs. 28, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Rs 15 B)Rs 12.10 C)Rs 22.70 D)Rs 26.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 28 - 5 - 0.30 =22.70 Answer : C #### C QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy? options: A)57 B)60 C)63 D)66 E)69 SOLUTION:M + H = 90 H = 90 - M 4M + 5H = 390 4M + 5(90 - M) = 390 M = 60 The answer is B. #### B QUESTION:A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately). options: A)22.48% B)20.48% C)24.48% D)25.48% E)26.48% SOLUTION:Let the total money=300 A's part=100 B's part=200 After 2 years A's part=73.46 (As it depreciates by 14.29% per annum) After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where P=200,r=0.2,n=1,t=2) So, After 2 years total amount=361.46 Therefore % increase in money=(361.46-300)100/300=20.48% ANSWER:B #### B QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ? options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these SOLUTION:Explanation: Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 785/18 m/s = 65/3 m/s Distance = SpeedTime =>800+x=65/3∗60 =>800+x=20∗65=1300 =>x=1300−800=500 So the length of the tunnel is 500 meters. Option C #### C QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:What is the tens digit of 7^1415? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit ) 0 , 4 , 4 , 0 . 1415= 4353 + 3 The ten's digit will be 4 . Answer E #### E QUESTION:What is the sum of all four digit integers formed using the digits 3 ,4 ,5 and 6 (repetition is allowed) options: A)1279874 B)1279872 C)1279875 D)1279876 E)1279870 SOLUTION:n = 4 * 4 * 4 * 4 = 256 <x> = (6666 + 3333) / 2 = 4999.5 Sum = number of integers x average value n * <x> = 256 * 4999.5 = 1279872 answer = B #### B QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm SOLUTION:Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: Option E #### E QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer: D #### D QUESTION:How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4? options: A)Nil B)1 C)2 D)3 E)More than 3 SOLUTION:6,12,18,24,30 are divisible by 6. 12, 24 are divisible by 4 also. So there are 3 numbers exactly divisible by 6 but not by 4 ANSWER:D #### D QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. options: A)5113 B)5117 C)5120 D)8119 E)10115 SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year. If x = initial number of trees = 5120 Year 1 = 5/4x Year 2 = (5/4)(5/4)x Year 3 = (5/4)(5/4)(5/4)x Year 4 = (5/4)(5/4)(5/4)(5/4)x Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500 Hence, correct answer = C #### C QUESTION:John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? options: A)1/16 B)5/16 C)3/8 D)1/2 E)1/4 SOLUTION:John will run farther if he runs at 5 mph and Amanda runs at 4 mph. P(John runs farther) = 1/4 * 1/4 = 1/16 The answer is A. #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum? options: A)337 B)268 C)198 D)697 E)168 SOLUTION:1200 = P [1 + (126)/100] P = 697' Answer:D #### D QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(Ã¢â‚¬â€œ4) 5 (Ã¢â‚¬â€œ4)1 #### A QUESTION:What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)85 C)93 D)97 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88, 90, 93, 93, 95, 96, 98 The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.) C #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? options: A)15002 B)15001 C)15000 D)15007 E)15009 SOLUTION:Principal = (100 5400) / (12 * 3) = Rs. 15000.Answer:C #### C QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest? options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years SOLUTION:Explanation: Time = (100 x 60)/(400 x 12) years = 1.25 years. Answer: D #### D QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= lw = 1/2 wd (l=1/2 d or d=2l) top face area= wd side face area= wd = 1.5 dl (w=1.5l) Volume = lwd= 192 l1.5l2l= 192 l=4 Side face area= ld= l2l= 424 =32 E is the answer #### E QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 â€“ 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 1.16.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? options: A)15 B)11 C)12 D)13 E)14 SOLUTION:IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A #### A QUESTION:Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:D) 6 #### D QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$788 B)$812 C)$864 D)$878 E)$912 SOLUTION:After one year: 1.2 $500 After two years: (1.2)^2 * $500 After three years: (1.2)^3 * $500 = $864 The answer is C. #### C QUESTION:Find the odd man out 2, 5, 10, 17, 26, 37, 50, 64 options: A)50 B)26 C)64 D)27 E)17 SOLUTION:Difference is series of ODD numbers 2+3 = 5 5+5 =10 10+7=17 17+9=26 26+11=37 37+13=50 50+15=65 ANSWER:C #### C QUESTION:During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year? options: A)$2.5 B)$2.55 C)$1.51 D)$3.25 E)$3.0 SOLUTION:finding the Harmonic mean here. HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1 C #### C QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? options: A)14 B)12 C)10 D)16 E)18 SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000, and it is given that length means no of factors. for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal. hence, lets start with smallest no 2. 2^1 =2 2^2 =4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512 2^10 =1024 (it exceeds 920, so, x can't be 2^10) so, max value that X can take is 2^9 , for which has length of integer is 9. now, since x =512 ,x+3y<920 so, 3y<408 ==> y<136 so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7 for 2^7 has length of integer is 7. SO, combined together : 9+7 = 16. D #### D QUESTION:Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? options: A)22 B)16 C)27 D)28 E)20 SOLUTION:Speed Ratio = 1:4/3 = 3:4 Time Ratio = 4:3 1 -------- 4 4 --------- ? 16 m.Answer:B #### B QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is? options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15 SOLUTION:100(90/100)(90/100)(95/100) = 76.95 100 - 76.95 = 23.05 Answer: A #### A QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible? options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6 SOLUTION:So 4C3 for abcd - 4 choices 3 more for dd(b,c or a) 3 more for bb(a,c or d) 3 more for cc(a,b or d) total 4C3+9 Ans : B #### B QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A #### A QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)1 B)4 C)9 D)11 E)13 SOLUTION:221 + 43 = 264/17 = 9 (Remainder) C #### C QUESTION:If 5^29 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 210^p 5^(29) 2 ^ (30) = 2 * (25)^p 5^(29) 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %? options: A)30% B)40% C)50% D)56% E)78% SOLUTION:Gain=16 apples Total 56 apples CP 56-16=40 (16/40)100 =40% Ans B #### B QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)37.5 B)40 C)50 D)48 E)52 SOLUTION:Dividend on 1 share = $(10/10050) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(1002/255)=40 Thus, cost of 1 share =$40 ANSWER B #### B QUESTION:If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)? options: A)-f(x) B)f(x) C)2f(x) D)1/f(x) E)2/f(x) SOLUTION:If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) answer A #### A QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:Two numbers N and 12 have LCM = 48 and GCF = 8. Find N. options: A)24 B)34 C)44 D)54 E)32 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 12 × N = 48 × 8 N = 48 × 8 / 12 = 32 correct answer E #### E QUESTION:The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ? options: A)13 B)15 C)20 D)38 E)56 SOLUTION:Product of three numbers = 336 336 = 678. So, the three numbers are 6, 7 and 8. And Sum of smallest of these two = 6+7 = 13. ANSWER : OPTION A #### A QUESTION:We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c. options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Solution: Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=>c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a) 16=9a+9−a2−a a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1<0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5. Answer A #### A QUESTION:In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is: options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these SOLUTION:Explanation : When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5. According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time. Thus, Both reach at the same time. Answer : A #### A QUESTION:Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd? options: A)15/56 B)3/8 C)15/28 D)5/8 E)3/4 SOLUTION:Total number of combinations=12C3=220................(1) Total number of combinations including 2 and two other numbers=11C2=55......................(2) Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165 So, probability=165/220=3/4 E #### E QUESTION:Remainder of (6^17+17^6)/7= ? options: A)2 B)1 C)0 D)3 E)4 SOLUTION:6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7 17^6/7 = (27+3)^6/7 = 3^6/7 = 27^2/7 =(47-1)^2/7 =(-1)^2/7 = 1/7 so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0 ANSWER:C #### C QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. options: A)Rs. 1900 B)Rs. 2660 C)Rs. 2800 D)Rs. 2840 E)Rs. 3000 SOLUTION:Explanation: For managing, A received = 5% of Rs. 7400 = Rs. 370. Balance = Rs. (7400 - 370) = Rs. 7030. Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3) = 39000 : 42000 : 30000 = 13 : 14 : 10 B's share = Rs.(7030 X 14/37)=Rs. 2660. ANSWER IS B #### B QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")(Number of ways the vocalist can sing "new songs")= 1510=150 Answer: C #### C QUESTION:For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ? a) 4 b) -3 c) -6 options: A)a only, B)b only, C)c only, D)a and b only E)b and c only SOLUTION:Notice that the question asks which of the following MUST be in the set, not COULD be in the set. Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure. Answer: E. Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set. #### E QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 960/45 = 94/3 = 12 New time in minutes to cross 9 miles stretch = 960/35 = 912/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 12=45,0008 1:1 Madhu's share=1/260,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30 The fraction of work remaining is 1 - 20/30 = 10/30 The number of days required for Z is 10 days. The answer is E. #### E QUESTION:The compound ratio of 5:1, 3:1 and 2:5? options: A)6:1 B)1:3 C)1:5 D)1:1 E)1:6 SOLUTION:5/1 3/1 * 2/5 = 30/5 6:1 Answer: A #### A QUESTION:If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ? options: A)1 B)2 C)3 D)6 E)12 SOLUTION:Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If x is three times as large as n OR simply, If x is three times n.C #### C QUESTION:A shopkeeper sold an article offering a discount of 4% and earned a profit of 26%. What would have been the percentage of profit earned if no discount was offered? options: A)24 B)28 C)31 D)32 E)34 SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 126 Let marked price be Rs. x. Then, 96/100 x = 126 x = 12600/96 = Rs. 131.25 Now, S.P. = Rs. 131.25, C.P. = Rs. 100 Profit % = 31%. ANSWER:C #### C QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 * (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)(5 choose 2) = 410 = 40 Jaune X = (4 choose 2)(5 choose 1) + (4 choose 3) = 65 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank? options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:If e<0, which of the following must be true? options: A)–100 < e < 100 B)e ≤ –1 C)e ≤ 1 D)e^2 ≥ 1/4 E)–100 < e < 0 SOLUTION:e is a negative number. A. –100 < e < 100e can be a negative number less than -100 B. e ≤ –1e can be a fraction, in which case it would be greater than -1 C. e ≤ 1must be true since 1 is positive and e is negative D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5 E. –100 < e < 0e can be a negative number less than -100=C #### C QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:Set Q consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set Q, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:A = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of Q = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B? options: A)7 B)9 C)8 D)11 E)10 SOLUTION:Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 22 ⇒ 5x = 20 ⇒ x = 4. Hence, B's age = 2x = 8 years. Answer: C #### C QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9% B)4% C)6% D)3% E)5% SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4% Answer:B #### B QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 90, what is the value of c âˆ’ a? options: A)25 B)90 C)100 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=180 --2 subtracting 1 from 2 we have c-a=90; ANSWER:B #### B QUESTION:A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree? options: A)16 hours. B)19 hours. C)12 hours. D)18 hours. E)13 hours. SOLUTION:The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet. Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet. In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours. Answer D #### D QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 40007 = 28000. Answer : Option A #### A QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 3 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)3/23 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 3x Hence, a1+a2+..+a20+n = 23x So, the fraction asked = 3x/23x =3/23 Answer E #### E QUESTION:A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg? options: A)Rs.120 B)Rs.125 C)Rs.130 D)Rs.135 E)Rs.140 SOLUTION:Explanation: 2400(40/100) = 960 ---- 8 ? ---- 1 => Rs.120 Answer: A #### A QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test? options: A)768 B)243 C)246 D)280 E)224 SOLUTION:Let the maximum mark in each test be M. The candidate failed by 66 marks in the second test. pass mark in the second test = 249 + 66 = 315 45/100 M = 315 Pass mark in the first test = 40/100 M = 40/45 * 315 = 280. Answer:D #### D QUESTION:Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? options: A)320 B)384 C)400 D)408.3 E)440 SOLUTION:The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed. The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles. Answer B. #### B QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3(20/60) = 7 hr Answer is D #### D QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)66 B)52 C)58 D)55 E)56 SOLUTION:Though 2(8C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches. Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches. This continues like this and the total matches are 14+12+10...+2 14+12+...+2 = 2(7+6+...+1) = 2((78)/2) = 78 =56. ANSWER:E #### E QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)288 B)200 C)279 D)992 E)208 SOLUTION:(80033)/100 = 72 920 + 72 = 992 Answer: D #### D QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(90033)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:If (5^15)(9^8)=3(15^x), what is the value of x? options: A) 7 B) 9 C) 11 D) 13 E) 15 SOLUTION:(5^15)(9^8)=3(15^x) => 5^15 * 3^16 = 3 * 3^x * 5^x => 5^15 * 3^16 = 3^(x+1) * 5^x Value of x = 15 Answer E #### E QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? options: A)240 B)235 C)245 D)250 E)260 SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec. Time = 30 sec Let the length of bridge be x meters. Then, (130 + x)/30 = 25/2 x = 245 m. Answer: Option C #### C QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01$330=$333.30. The answer is D. #### D QUESTION:Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? options: A)65% p.a B)88% p.a C)20% p.a D)66% p.a E)44% p.a SOLUTION:Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year. Rate of interest = (100 * 240) / (100 * 1) = 20% p.a Answer: C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/9 D)5/12 E)5/33 SOLUTION:First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve. We will use the formula: nC2 = n(n-1)/2 which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here 12C2=12(11)/2=611=66 That’s the total number of pairs we could pick from the twelve employees. That’s our denominator. For the numerator, we want every combination of two from the five female employees. That’s 5C2=5(4)/2=52=10 That’s the number of pairs of female employees we could pick from the five. That’s our numerator. probability= 10/66 =5/55 Answer = E #### E QUESTION:At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Sol. Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then, 4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5. ∴ Deepak’s age = 3x =15 years. Answer C #### C QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:If you roll one fair six-sided die, what is the probability that the number is even or less than 4? options: A)1/6 B)1/3 C)2/ 3 D)3/4 E)5/6 SOLUTION:Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5 Total possible outcome= 6 Probability=5/6. Answer: Option E #### E QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) * 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)52% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16 so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52% ANSWER:D #### D QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 * 100 = 33 1/3% Answer: A #### A QUESTION:The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is? options: A)35 B)30 C)31 D)28 E)27 SOLUTION:Age of the 15th girl = 1515 - (1213+314) = 225-198 = 27 years Answer is E #### E QUESTION:Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year? options: A)$2000 B)$6000 C)$4000 D)$1333 E)$3000 SOLUTION:Explanatory Answer Let the profit made during the year be $3x Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 7 : 3. i.e., 70% of 2x would go to Mary and 30% of 2x would go to Mike. Hence, Mary would get (70 - 30)% of 2x more than Mike Or 40% of 2x = $800 i.e.,(40/100)2x = 800 or 2x = 2000. Hence, the profit made by the company during the year $3x = $3000. The correct choice is (E) #### E QUESTION:Kunal electronic services assemble computers. Over a period of time the engineers made the following observation regarding the two vital components - the USB port and CD drive. The probability that USB port is defective is 0.1, that both the USB port and CD drive are defective is 0.02, while the probability that only the CD drive is defective is 0.03 . The probability that the USB port is defective when the CD drive has been found to be defective is? options: A)0.2 B)0.3 C)0.25 D)0.4 E)0.6 SOLUTION:Explanation : USB Defective USB OK Total CD Defective 0.02 0.03 (0.05) CD OK (0.08) (0.87) (0.95) Total 0.1 (0.9) The figures enclosed in brackets follow as conclusions. The probability that USB part is defective, when the CD drive is found to be defective is 0.02/0.02+0.03 = 2/5 = 0.40 Answer : D #### D <<<Examples ends QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k? options: A)3/4 B)1 C)4/3 D)2 E)7/2 SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k. {{k + 4}/4} = k k + 4 = 4k 4 = 3k k = 4/3 Answer = C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112 SOLUTION:Let S be the sample space. Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = \inline {\color{Black}13C_{1}\times 13C_{1} } = 169. P(E) = n(E)/n(S) = 169/1326 = 13/102. Answer: D) 13/102 #### D QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)? options: A) 1 B) 21 C) 26 D) 52 E) 1014 SOLUTION:x = 14 + 16 + ... + 54 = (largest + smallest)/2 (# of terms) = (14 + 54)/221= 3421. GCD of 21 and 3421 is 21 Answer: B. #### B QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 420=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics? options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3 SOLUTION:Lets pick smart numbers. Total number of students: 12 Biology (1/2): 6 Chemistry (1/3): 4 Physics (1/6): 2 After leaving school Biology: 4 Chemistry: 4 Physics: 1 New Total number of students: 9 Biology and Physics: 5 Answer 5/9 or C #### C QUESTION:If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is: options: A)8 B)9 C)12 D)14 E)13 SOLUTION:Let the numbers be x and y Then x2-y2=39 And x-y=3 We get x+y=13 Solving x-y=3, x+y=13 X=8, y=5 Larger number 8 ANSWER A 8 #### A QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 2006 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data? options: A) 6 B) 2.5 C) 9 D) 11 E) 13 SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 45=20 seconds it can upload 5100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds. Answer: B. #### B QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? options: A)39 B)41 C)42 D)43 E)44 SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5) = 4 so for 6 children = 6 x 4 =24 so mother's age is 63 - 24 =39 Answer: Option A #### A QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? options: A)10 B)12 C)15 D)18 E)20 SOLUTION:There are 10 numbers divisible by 2 There are 5 numbers divisible by 4 There are 2 numbers divisible by 8 There is 1 number divisible by 16. Hence the total number of 2’s in 20! are 10+5+2+1=18 ANSWER:D #### D QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5? options: A)1 B)3 C)2 D)4 E)5 SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5. Hence, 143= will give units digit as 2 So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2. Option C #### C QUESTION:Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm. options: A)25 B)45 C)35 D)15 E)40 SOLUTION:Required length = H.C.F. of 495 cm, 900 cm and 1665 cm. 495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37. Therefore, H.C.F. = 32 x 5 = 45. Hence, required length = 45 cm. Answer is B. #### B QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x2+y4=140 heads: x1+y1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides? options: A)3 B)6 C)5 D)9 E)1 SOLUTION:S = (1 + 2 + 7)/2 = 5 Answer:C #### C QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc... The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc... The distances between marks are 3/12, 1/12, and 2/12. The answer is C. #### C QUESTION:A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in. options: A)23 days B)25 days C)21 days D)26 days E)29 days SOLUTION:C 21 days WC = 2:1 2x + x = 1/7 x = 1/21 => 21 days #### C QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!3! = 51840 - 4320 = 47520 ways A #### A QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number? options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63 SOLUTION:Let the numbers be 5x, 6x, 8x. Largest number = 8x. Smallest number = 5x. Third number = 6x. 8x + 5x = 6x + 49 7x = 49 =>x=7 6x=42=> third number is 42. Answer:D #### D QUESTION:In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls? options: A)20 B)22 C)24 D)26 E)29 SOLUTION:Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls) => (4c3) * (4c2) = 24 C #### C QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+10)=4/5 20x=4(3x+10) 8x=40 x=5 Quantity of alcohol = (4 x 5) litres = 20 litres. Answer is D. #### D QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: options: A)21 B)22 C)20 D)45 E)30 SOLUTION:2nd day he earns = 3(2 – 5) 3rd day he earns = 3(3 – 5) On 20th day he earns 3(20 -5) = 45 rupees ANSWER:D #### D QUESTION:The average of 11 numbers is 11. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is options: A)10.4 B)11.5 C)81.5 D)11.5 E)21.5 SOLUTION:Explanation: Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4. Answer: A #### A QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil? options: A)9 B)5 C)7 D)8 E)4 SOLUTION:Let the total length be xm Then black part =x/8cm The remaining part=(x-x/8)cm=7x/8cm White part=(1/2 7x/8)=7x/16 cm Remaining part=(7x/8-7x/16)=7x/16cm 7x/16=7/2 x=8cm Answer is D. #### D QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern? options: A)15 min B)45 min C)25 min D)40 min E)50 min SOLUTION:1/3 of the cistern can fill in 20 min 3/4 of the cistern can fill in = 2033/4 = 45min Answer is B #### B QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:A day-trader plans to invest a total of $23,600 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$4,000 C)$3,500 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,600 So, the HUNDREDS DIGITS of the 15th investment must be 0 Answer: B #### B QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is: A 6, B 12, C 24, D 36, E 48 n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B #### B QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly? options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20 SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/51/4 = 9/10. Answer: D. #### D QUESTION:If n = 20! + 19, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:19 divides 20! so 19 also divides 20! + 19. 15 and 17 divide 20! so they do not divide 20! + 19. The answer is C. #### C QUESTION:The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4? options: A)87 B)16 C)10 D)84 E)17 SOLUTION:Average after 11 innings = 44 Required number of runs = (44* 11) - (40* 10) = 484- 400 = 84. Answer: D #### D QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:Find the ratio between whole surfaces of a sphere and a hemisphere? options: A)4:3 B)3:4 C)3:2 D)5:2 E)4:6 SOLUTION:4 Ï€r2 : 3 Ï€r2 => 4:3 ANSWER A #### A QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail? options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8 SOLUTION:Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {HHH,HTH,THH,HHT} P(E) = n(E)/n(S) =4/8 = 1/2 Answer is D #### D QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=5015/85=8.82 ANSWER:E #### E QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food. options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400 SOLUTION:Part of salary left =1-(2/5+3/10+1/8) =7/40 Let the monthly salary be $x Then (7/40) of x=1400 X=8000 Expenditure on food=$2400 Option D #### D QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 800018 : (80008) + (400010) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres? options: A)120 B)80 C)60 D)40 E)None of these SOLUTION:Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x⁄3 m. Area of hall = 2x⁄3 × x = 2x2⁄3 or, 2x2⁄3 = 2400 or x = 60 m Answer C #### C QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? options: A)4 months B)5 months C)6 months D)7 months E)8 months SOLUTION:Explanation: Assume that C was there in the business for x months A:B:C =40000×12:60000×10:120000 × x =40×12:60×10:120x =40:5×10:10 x =8:10:2x =4:5:x C's share =375000 x/ 9+x=375000 x/9+x ⇒375000 x/9+x=150000 ⇒375x9+x=150 ⇒15x=6(9+x) ⇒5x=18+2x ⇒3x=18 ⇒x=6 It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined. Answer: Option A #### A QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)2200 B)1897 C)8799 D)2000 E)2782 SOLUTION:P(11/10)4 - P(6/5)2 = 482 P = 2000 Answer: D #### D QUESTION:In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack? options: A)10 B)11 C)12 D)15 E)18 SOLUTION:This question can be solved by TESTing THE ANSWERS. Answer C: 12 total cards With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is... (11/12)(10/11) = 110/132 ~= 5/6 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: C #### C QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price? options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050 SOLUTION:C $1000 90% 104% -------- 14% ---- 140 100% ---- ? => $1000 #### C QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:0.90.007= _________ options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63 SOLUTION:97=63 Sum of decimal places= 4 So, 0.90.007= 0.0063 ANSWER:B #### B QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(34)+x/(35)=84/60 x=6 km ANSWER:C #### C QUESTION:A coin is tossed 6 times. What is the probability of getting exactly 5 heads? options: A)3/8 B)3/16 C)5/16 D)3/32 E)7/64 SOLUTION:The number of possible outcomes is 2^6 = 64 There are 6 ways to get exactly 5 heads. P(exactly 5 heads) = 6/64 = 3/32 The answer is D. #### D QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 57400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 65006 : 84005 : 100003 = 656 : 845 : 1003 = 136 : 84 : 203 = 132 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 (14/37) = 19014 = 2660 Answer is C #### C QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number options: A)400 B)256 C)120 D)490 E)None of these SOLUTION:Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 x = 14 * 5040 x = (145040)/144 = 490 Option D #### D QUESTION:How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2. options: A)4:3 B)4:7 C)4:9 D)4:2 E)4:1 SOLUTION:Explanation: No explanation is available for this question! ANSWER: A #### A QUESTION:Given f(x) = 3x – 5, for what value of x does 2[f(x)] – 4 = f(3x – 6) options: A)3 B)4 C)6 D)7 E)13 SOLUTION:Answer = A = 3 f(x) = 3x – 5 2[f(x)] – 4 = f(3x – 6) 2(3x-5) -4 = 3 (3x-6) - 5 6x - 14 = 9x - 23 x = 3 #### A QUESTION:Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 50 people bought tickets to the concert, what was the total revenue from ticket sales? options: A)$600 B)$740 C)$860 D)$980 E)$1,140 SOLUTION:Price of 1 ticket = 20$ Revenue generated from sales of first 10 tickets = 10 (60/100 * 20 ) = 10 * 12 = 120 Revenue generated from sales of next 20 tickets = 20 (85/100 20 ) =2017 = 340 Revenue generated from sales of last 20 tickets = 20 20 = 400 Revenue generated from sales of 50 tickets = 120 + 340 + 400 = 860 $ Answer C #### C QUESTION:If p is a natural number and p! ends with w trailing zeros, then the number of zeros that (5p)! ends with will be options: A)a) (p+w) trailing zeros B)b) (5p+y) trailing zeros C)c) (5p+5y) trailing zeros D)d) (p+5y) trailing zeros E)e) none of them above SOLUTION:Let p = 1. p! = 1! = 1, which means w= 0 (5p)! = 5! = 120, trailing zeros = 1 1 = 1 + 0 = p + w Answer (A). #### A QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 x = 9 6 * 1000 or x = 961000/ 410 = 1350 Answer : B #### B QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? options: A)32 B)55 C)6 D)78 E)81 SOLUTION:S = (100 + 300)/45 = 400/45 18/5 = 32 Answer: A #### A QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer B #### B QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:How many positive factors do 160 and 96 have in common? options: A)6 B)12 C)16 D)18 E)24 SOLUTION:The number of common factors will be same as number of factors of the Highest Common Factor(HCF) HCF of 160 and 96 is 32 Number of factors of 32 = 6 Answer :A #### A QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? options: A)2% B)17% C)25% D)65% E)83% SOLUTION:New Value – Old Value)/Old Value x 100 We are given: February sales this year = 400 million February sales last year = 320 million We need to determine the percent increase between sales from last year to sales this year. Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula. (New Value – Old Value)/Old Value x 100 [(400 – 320)/320] x 100 = 25%. The answer is C. #### C QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 12) X=9/5 = 1.80 Answer: C #### C QUESTION:In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C? options: A)50 B)50/9 C)8500/9 D)500/9 E)None of these SOLUTION:A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m. Answer: D #### D QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 78. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 81 C)(c) 82 D)(d) 65 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (78-6)/6+1=13 such multiples. So, final number of sets is 135=65 Answer: D #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is? options: A)31 B)41 C)51 D)61 E)65 SOLUTION:LCM = 30 => 30 + 1 = 31 ANSWER:A #### A QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference D= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 * 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:Which of these lines in the xy-plane does not contain any point with two negative coordinates? options: A)y = 4x B)y = x + 6 C)y = x^2 - 5 D)y = x^3 + 3x E)y = 2x^4 SOLUTION:2x^4 is 0 when x is 0 and positive for all other values of x. The answer is E. #### E QUESTION:If x=-2, which of the following is(are) true? I. x^2=-\|x\| II \|x\|=-x III x/-3 = -2/3 options: A)II only B)I only C)III only D)I,II only E)II, III only SOLUTION:I. x^2=-\|x\| -2^2 = - \|-2\| Not true II \|x\|=-x \|-2\| =-( -2 ) true III x/-3 = -2/3 Not true Answer : A #### A QUESTION:Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey? options: A)67.0 km /hr B)67.2 km /hr C)69.0 km /hr D)69.2 km /hr E)None SOLUTION:Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B #### B QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:If \|x\| = 4x - 1, then x = ? options: A)3 B)1/2 C)1 and 1/2 D)-1/2 E)-1 SOLUTION:Answer: A Approach: Substituted option A i.e x=1. Inequality satisfied. #### A QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:1397 x 1397 = ? options: A)1951609 B)1951601 C)1951602 D)1951603 E)1951604 SOLUTION:1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer:A #### A QUESTION:The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ? options: A)2 B)3 C)1 D)6 E)5 SOLUTION:I year 2100 II year 2100+147=2247 2100+2247=4347 So 2 Years Answer A #### A QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36. options: A)5 B)4 C)12 D)32 E)35 SOLUTION:First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7. Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc and n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above) Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form n = 5a + 1 and n = 7b + 3 Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10. Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4) Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36 A #### A QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[24+(50-1)2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: options: A)130 B)360 C)500 D)540 E)580 SOLUTION:L = 800 m S = 78kmph = 65/3 mps Time to pass tunnel = 1min = 60 sec t.f (800+X)/(60) = (65/3) =500 ANSWER:C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Option A #### A QUESTION:Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is options: A)Rs. 12500 B)Rs. 1000 C)Rs. 8000 D)Rs. 6000 E)Rs. 15000 SOLUTION:Sol. Saving = [100 - (40 + 20 + 10 + 10]% = 20%. Let the monthly salary be Rs. x. Then, 20% of x = 2500 â‡” 20 / 100x = 2500 â‡” x = 2500 Ã— 5 = 12500. Answer A #### A QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with? options: A)21 B)31 C)41 D)51 E)61 SOLUTION:He start out with 31eggs. In the end, he have 3eggs left. So, 32 +1= 7 72 +1= 15 152 +1= 31 31eggs he had initially. ANSWER:B #### B QUESTION:In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ? options: A)35 B)39 C)48 D)50 E)52 SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 C #### C QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:A train covers a distance of 100km in 1 hour. If its speed is decreased by 25km/hr, the time taken by the car to cover the same distance will be? options: A)1hr B)1hr 20min C)50min D)1hr 30min E)1hr 45min SOLUTION:Speed = 100/1 = 100km/hr New speed = 100-25 = 75 km/hr Time taken = 100/75 = 1hr 20min Answer is B #### B QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : options: A)34 B)43.2 C)40 D)38 E)29 SOLUTION:Solution: Average speed = 2XY / X+Y = 25436 / 54+36 = 43.2 Answer : B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)9 km D)5 km E)1 km SOLUTION:Let the total distance be 3x km. Then, x/3 + x/4 + x/5 = 47/60 47x/60 = 47/60 => x = 1. Total distance = 3 * 1 = 3 km. Answer: B #### B QUESTION:In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State? options: A)7000 B)7200 C)7400 D)7600 E)8000 SOLUTION:State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 E) #### E QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? options: A)13 B)7 C)25 D)20 E)10 SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y be the green marble,z be the blue marble... x+y=15 y+z=13 x+z=12 solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7 ANSWER:B #### B QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x15 x = 9/15=3/5 Answer: D #### D QUESTION:In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.03N + 8,000 SOLUTION:I will go with option E According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option E #### E QUESTION:A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss? options: A)16% loss B)400 C)4000 D)324 E)8% LOSS SOLUTION:(4040)/100 = 16%loss ANSWER:A #### A QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (1213.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:If 5 < x < 11 and y = x + 7, what is the greatest possible integer value of x + y? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:x+y = x+x+7 = 2x+7 We need to maximize this value and it needs to be an integer. 2x is an integer when the decimal of x is .0 or .5 The largest such value is 10.5 Then x+y = 10.5 + 17.5 = 28. The answer is C. #### C QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? options: A)1276 B)1200 C)2832 D)1800 E)1236 SOLUTION:Explanation: l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 Answer: Option D #### D QUESTION:In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? options: A)0.44 B)0.55 C)0.65 D)0.75 E)0.85 SOLUTION:Number of people whose age is less than 20 is given by 160 - 90 = 70 Probability P that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer A #### A QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:The rate of the pump + leak = 5/14 1/2 - leak's rate = 5/14 leak's rate = 1/2 - 5/14 = 1/7 The leak will empty the tank in 7 hours. The answer is D. #### D QUESTION:Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups? options: A)25 B)31 C)15 D)26 E)23 SOLUTION:Answer We need to maximize the median in each group in order to maximize the average of all the medians. The highest possible median is 41 as there should be 4 numbers higher than the median in a group of 9. So, if we have a group that has a, b, c, d, 41, 42, 43, 44, 45, the median will be 41. In this set, it is essential not to expend any more high values on a, b, c, or d as these do not affect the median. The median of a group that comprises 1, 2, 3, 4, 41, 42, 43, 44, 45 will be 41. The next group can be 5, 6, 7, 8, 36, 37, 38, 39, 40. The median will be 36. Extrapolating the findings in the two sets listed above, to maximize medians in all the 5 groups, the medians of the 5 groups will have to be 21, 26, 31, 36 and 41. The average of the highest possible medians will be the average of these 5 numbers = 31. Answer B #### B QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone? options: A)6 days B)8 days C)12 days D)10 days E)5 days SOLUTION:Explanation: A and B 1day's work = 1/6 A alone can do 1day's work = 1/12 what time B will take to do the work alone? B = (A+B) - A = (1/6) - (1/12) = 12 Days Answer: Option C #### C QUESTION:If w,x,y,z are consecutive positive integers ; then which of the following is always odd? [1] wx+(y+2)^2z [2] w^x + z^y [3] 13x^2 options: A)1 B)2 C)3 D)1 and 2 E)2 and 3 SOLUTION:Plug in some numbers w = 1 x = 2 y = 3 z = 4 Check the options - [1] wx+(y+2)^2z = 12 + (3+2)^2 4 => 2 + 254 = 102{ Not an odd Number } [2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number } [3] 13x^2 = 134 =52 even [2] B #### B <<<Examples ends QUESTION:A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years. options: A)Rs. 376000 B)Rs. 204000 C)Rs. 36000 D)Rs. 18000 E)Rs. 260000 SOLUTION:Investments-- A=14000x4+16000x20=376000 B=12000x2+10000x18=204000 C=20000x18=360000 So C's Share = 94000xC/(A+B+C)=36000 ANSWER:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple? options: A)225 B)228 C)230 D)231 E)235 SOLUTION:CP = 1402+1503+1604+1701=1540 SP = 1.51540=2310 Total no.of kgs=2+3+4+1=10 SP per kg=2310/10=231 ANSWER:D #### D QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)8 B)9 C)10 D)20 E)30 SOLUTION:x ------- 6 (x + 10) ---- 3 x * 6 = (x + 10)3 x = 10 ANSWER:C #### C QUESTION:Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20 options: A)15 ÷ 3 x 3 - 5 = 20 B)15 + 3 ÷ 3 + 5 = 20 C)15 x 3 + 3 + 5 = 20 D)15 x 3 ÷ 3 + 6 = 20 E)15 x 3 ÷ 3 + 5 = 20 SOLUTION:Answer : E #### E QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 70 = 210 A + B + C + D = 4 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:Worker A takes 12 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days SOLUTION:A's one hour work = 1/12. B's one hour work = 1/15. (A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20. Both A & B can finish the work in 20/3 days E #### E QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500? options: A)5000 B)5500 C)4991 D)5600 E)5700 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991 C #### C QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ? options: A)12 B)16 C)18 D)9 E)12 SOLUTION:Explanation: Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 27 3x = 27 x = 9. Answer:D #### D QUESTION:A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there? options: A)1260 B)2100 C)3600 D)3200 E)5200 SOLUTION:Let the total number of trucks = 3x total number of sedans = 7x total number of motorcycles = 2x total number of sedans = 11200 => 7x = 11200 => x = 1600 total number of motorcycles =2x = 21600 =3200 Answer D #### D QUESTION:A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not green? options: A)15/28 B)1/4 C)9/16 D)1/32 E)1/16 SOLUTION:The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not green, green; 2) green, Not green; 3) green, green; 4) Not green, not green; The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are green P(4) = 6/85/7=15/28 1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/86/7) + (2/81/7)] = 1 - [26/87] = 1 - [13/28] = 15/28 A #### A QUESTION:A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day at 1 mile faster than 2nd day for same hours. How many miles in total did she walk? options: A)63 B)44 C)58 D)60 E)62 SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day Second day - 4 miles per hour and 5 hours - 20 miles Third day - 5 miles per hour and 5 hours - 25 miles Total 18+20+25 = 63 Answer: option A. #### A QUESTION:A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)4857 B)4184 C)4012 D)4991 E)5291 SOLUTION:Let the sale in the sixth month =x Then (6435+6927+6855+7230+6562+x)/6 =6500 =>6435+6927+6855+7230+6562+x =6×6500 => 34009+x=39000 => x=39000−34009 =4991 ANSWER:D #### D QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged? options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200 SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}. 6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways. Therefore the final answer is 6!2!2!=2,880. Answer: C. #### C QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z? I. 9 II. 10 III. 11 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:Average gives us an idea that 3 nos. are close to 10. so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations. Let us see options. If 9 has to be median W. 1st term has to less than 9 or equal to 9. (also maintain z-x = 3) 9 9 12 --> satisfies all conditions so 9 can be a median value. If 11 has to be a median 3rd term has to be 11 or more than 11. (also maintain z-x = 3) 8 11 11 -->satisfies all conditions so 9 can be a median value. Now for 10 to be median. z+ x = 20 and z-x = 3, we wont have integer values of z. 10 cannot be a median E is the answer. #### E QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)No profit, no loss B)5% C)8% D)10% E)11% SOLUTION:Explanation: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =80/100X100%=5% ANSWER IS B #### B QUESTION:An escalator moves towards the top level at the rate of 7 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length. options: A)5sec B)25sec C)20sec D)15sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (7+2) = 20sec Answer : C #### C QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have? options: A)5 B)10 C)30 D)40 E)50 SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)100% = 60% Now by Alligation Rule: A . ......... B 20% . . . 80% . . 60% . . (80-60) . (60-20) =20 : =40 Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration) So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%) So as per above ration Qty B mixed will be 50 gallons. Qty of water in mixture B = 20% of 50 = 10 gallons. ANSWER:B #### B QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of: options: A)19 B)22 C)25 D)20 E)36 SOLUTION:2nd day he earns = 3(2 – 3) 3rd day he earns = 3(3 – 3) On 15th day he earns 3(15 -3) = 36 rupees ANSWER:E #### E QUESTION:The average of first 11 prime numbers is? options: A)14.55 B)11.11 C)12.11 D)13.11 E)14.11 SOLUTION:Sum of 11 prime no. = 160 Average = 160/11 = 14.55 ANSWER: A #### A QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 320000/5=12000 ANSWER:E #### E QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5 SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) #### B QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:If 7^t is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of t? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:So the question just means that we have to find all the multiples t of 7 between 1 to 100 So there are 14 multiples of 7 ( 7 - 98) But 49 and 98 contain two 7's as factors so we have to add 14 + 2 = 16 E #### E QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ? options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830. Answer: B #### B QUESTION:If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area? options: A)120 B)772 C)288 D)266 E)240 SOLUTION:The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 24 * 20 = 240 cm2 Answer: E #### E QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:You have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs. options: A)163 B)166 C)162 D)164 E)165 SOLUTION:67 + 52 + 47 = 166 Answer: E #### E QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3x ANSWER:D #### D QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph SOLUTION:Length = Speed time Speed = L/T S = 700/20 S = 35 M/Sec Speed= 3518/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 126 Kmph Answer: A #### A QUESTION:A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set? options: A)25 B)30 C)35 D)45 E)46 SOLUTION:for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same.. here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5.. remaining 6= 2011-5=215.. therefore each valueof these 6 int =215/6=35 ans C #### C QUESTION:In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? options: A)3:16. B)2:3. C)4:9 D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C #### C QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent? options: A)70% B)45% C)48% D)30% E)40% SOLUTION:Explanation: 840 ---- 380 100 ---- ? => 45% Answer: B #### B QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 45!. Answer: C. #### C QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 1110^e < 1/10 ? options: A) –4 B) –3 C) –2 D) –1 E) 0 SOLUTION:Just putting values, the LHS becomes e=0 --> 11 e=-1 --> 11/10 e=-2 --> 11/100 e=-3 --> 11/1000 Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3. Answer is B. #### B QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:A car travels uphill at 30 km/hr and downhill at 70 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? options: A)32kmph B)33kmph C)34kmph D)35kmph E)37kmph SOLUTION:avg speed=total distance/total time. total distance traveled=100+50=150km; time taken for uphill journey=100/30=10/3; time taken for down hill journey=50/60=5/7; avg speed=150/(10/3+5/7)=37kmph ANSWER:E #### E QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d? options: A) 16% B) 32% C) 48% D) 84% E) 92% SOLUTION:16% ________________________________________________ a+d 34% ________________________________________________ a 34% ________________________________________________ a-d 16% since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a. thus 16% lie below a-d and 16% lie above a+d now below a+d = 16+34+34 = 84% hence D #### D QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%? options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33% SOLUTION:10 CP = 15 SP 15 --- 5 100 --- ? => 33.33% (Loss) Answer:E #### E QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be? options: A)20 B)40 C)80 D)160 E)180 SOLUTION:3 kg costs $30 1 kg costs $10 8 kg costs $80 The answer is C. #### C QUESTION:16 people can write 52 book in 12 days working 8 hour a day.then in how many day 206 can be written by 64 people? options: A)309/26 B)309/28 C)309/22 D)319/26 E)339/26 SOLUTION:work per day epr hour per person= 52/(12816) // eq-1 people= 64; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 206/(p864) // eq-2 eq-1==eq-2; p= 309/26 ANSWER:A #### A QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){2, 10} B){16, 16} C){10, 18} D){9, 11} E){7, 13} SOLUTION:answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is one unit. therefore accepted answer is D mean is 10 and S.D decreases minimum. D #### D QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks? options: A)60 B)80 C)100 D)120 E)140 SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback. If all 160 books were paperbacks, the dealer would earn a profit of $320. Since the actual profit was $400, the dealer must have sold 80 hardbacks. Then the number of paperbacks sold was 160-80 = 80. The answer is B. #### B QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi12/4 =12- pi3 ANSWER:B #### B QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true? I. c is even II. ab is even III. ab > 0 options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above. II only.letter B #### B QUESTION:Sum of the numbers from 1 to 35 is options: A)630 B)660 C)670 D)450 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 35. So S20=35Ã—36/2=630 Correct Option: A #### A QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 155/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 35 60 = 1750 m Answer is B #### B QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ? options: A)12 B)27 C)26 D)11 E)22 SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11. Answer: D #### D QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years. options: A)10% B)15% C)20% D)12% E)23% SOLUTION:Explanation: principal P = 2400/- Rate of interest R = ? Time T = 5 years Accumulated Amount A = Rs.10400/- A = P + I A = P + PTR/100 A = P(1+ TR/100) 2400[ 1 + (5 x R)/100] = 3600 2[(20 + R)/20] = 3 20 + R = 30 R = 10% Answer: Option A #### A QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) options: A)9/(25xy) B)xy/225 C)225/(xy) D)225xy E)25xy/9 SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 25 / (xy/9) = 225/(xy). The answer is C. #### C QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:How many options are there for a code consisting of 2 even digits followed by 2 odd digits? options: A)4^5 B)5^4 C)5^5 D)4^4 E)10^4 SOLUTION:Even Numbers = 5 digits { 0 , 2 , 4 , 6 , 8 } Odd Numbers = 5 digits { 1 , 3 , 5 , 7 , 9 } EVEN EVEN ODD ODD No of ways is 5555 = 5^4 Hence, correct, answer must be (B) 5^4 #### B QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)\|x - 1\| < 7 B)\|x + 2\| < 6 C)\|x + 3\| < 5 D)\|x - 2\| < 6 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => \|x-2\| < 6. Hence, answer is D #### D QUESTION:If k is an integer and 121 < k^2 < 225, then k can have at most how many values? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:given k is an integer 121 < k^2 < 225 11 < \| k\| < 15 K=-12,-13,-14,12,13,14 ANSWER:D #### D QUESTION:An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)53 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:B #### B QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)(1/4)S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:What is the sum of this series? 1, 3, 5, 7, 9, ...... 45. options: A)600 B)529 C)612 D)512 E)589 SOLUTION:Number of odd numbers between 1 and 45 is (45+1)/2=23 Therefore Sum of odd numbers 2323= 529 ANSWER: B #### B QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Asha=25 Nisha =n Usha =3n Asha=2a Nisha =a Usha =34 The difference of all ages must be same 25-2a=n-a=3n-34 We will get two equation 2n+a=34 n+a=25 From the equation we will get n=9 and a=16 The ages are Asha=2a=32 Nisha =16 and Usha =34 Sum of the ages =100 (32+x)+(16+x)+(34+x)=100 82+3x=100 3x=18 x=6 Age of Usha =34+6=40 ANSWER:D #### D QUESTION:If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b = options: A)−48 B)−2 C)8 D)9 E)48 SOLUTION:i.e. if a = -1 then b = 9 or if a =9 then b = -1 But in each case a+b = -1+9= 8 Answer: option C #### C QUESTION:5+3 options: A)8 B)13 C)28 D)6 E)2 SOLUTION:A #### A QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 9990 E)Rs. 10000 SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:A box contains 7 pairs of shoes (14 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/19 D)1/13 E)1/9 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 14, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/11/13(as after taking one at random there are 13 shoes left and only one is the pair of the first one)=1/13 Answer: D. #### D QUESTION:Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner? options: A)2/7 B)3/7 C)4/7 D)9/14 E)11/14 SOLUTION:Let x be the amount of jam at the beginning. After lunch, the remaining jam was (2/3)x. After dinner, the remaining jam was (6/7)(2/3)x = (4/7)x. The answer is C. #### C QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/32/32/32/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)3:4 B)B)8:9 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 5x and 7x years respectively. Then, 7x - 5x = 4 => x = 2 Required ratio = (6x + 4) : (7x + 4) 16 : 18= 8:9 ANSWER:B #### B QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get? options: A)57% B)57.3% C)65% D)90% E)80% SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates) percentage of the total votes recd by the winning candidate = 10011620/20280 = 57.3% ANSWER:B #### B QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 85. Find the third number? options: A)A)37 B)B)85 C)C)48 D)D)43 E)E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 85 6x = 85 => third number is 85. Answer: Option B #### B QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price options: A)Rs.500/- B)Rs.510/- C)Rs.515/- D)Rs.720/- E)Rs.540/- SOLUTION:Loss = 80010/100 = 80 S.P = C.P - Loss = 800- 80 =Rs.720/- Answer :D #### D QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Solution: 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. Answer C #### C QUESTION:In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was? options: A)1.42liters B)2.5liters C)3liters D)5.6liters E)7liters SOLUTION:Let the original quantity be x liters alcohol solution in x liters = 30/100 x = 3x/10 kg (3x/10)/(x+20) = 20/100 3x = x/5 + 4 14x = 20 x = 1.42liters Answer is A #### A QUESTION:495 x 495 = ? options: A)250000 B)250025 C)5000 D)245025 E)240000 SOLUTION:495 x 495 = (495 )2 = (500 - 5)2 = (500)2 + (5)2 - (2 x 500 x 5) = 250000+ 25 - 5000 = 250025 - 5000 =245025. D) #### D QUESTION:If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number. options: A)5 : 3 B)2 : 5 C)4 : 7 D)5 : 2 E)None of these SOLUTION:Explanation: Let the first number is A and second number is B. As per question (40/100)A = (2/3)B A/B = 2/3 x 100/40 A/B = 5/3 =>A:B = 5:3 Answer: Option A #### A QUESTION:If you throw two dice at a same time. Can you find the probability of getting sum as 10 of the two numbers shown ? options: A)1/16 B)2/14 C)1/12 D)1/19 E)1/17 SOLUTION:C 1/12 All possible cases can be 36 (66) Case we need : [(4,6), (5,5), (6,4)] = 3 probability => 3/36 = 1/12 #### C QUESTION:How many factors of 60 are odd numbers greater than 1? options: A)3 B)4 C)5 D)3 E)7 SOLUTION:prime factors of 60 are 2^2,3^1,5^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,) = (1+1)(1+1)=4 since we need odd divisors other than 1 =>4-1 = 3 odd divisors D is the answer #### D QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x? options: A)4 B)5 C)3 D)9 E)6 SOLUTION:9 x + x = 13 + 27 10 x = 40 => x = 4 Answer:A #### A QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)12 B)3 C)5 D)8 E)10 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER A 12 #### A QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs.7500 B)Rs.7502 C)Rs.7529 D)Rs.7596 E)Rs.7506 SOLUTION:A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs.7500. Answer:A #### A QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? options: A)602 sq.cm B)620 sq.cm C)200 sq.cm D)605 sq.cm E)600 sq.cm SOLUTION:Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225) = √400 = 20, AC = 20 + 20 = 40 cm. Area of a rhombus = 1/2 * d1d2 = 1/2 * 40 * 30 = 600 sq.cm. Answer: E #### E QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B? options: A)75% B)80% C)100% D)120% E)125% SOLUTION:B. For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For B, r=10/pi. Its capacity = (5pi)^2 8 = 200pi P/B = 160pi/200pi = 0.8 #### B QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:The middle number is 40. Let the smallest number be x. Then the largest number is 2x+20. To make x as small as possible, let's make the remaining numbers as large as possible. So the second largest = the largest = 2x+20. The second smallest should be equal to the median. The numbers are x, 40, 40, 2x+20, 2x+20. x + 40 + 40 + 2x + 20 + 2x + 20 = 540 = 200 5x = 80 x = 16 The answer is B. #### B QUESTION:The sale price shirts listed for Rs.1000 after successive discount is 15% and 2% is? options: A)338 B)823 C)833 D)337 E)733 SOLUTION:1000(85/100)(98/100) = 833 Answer: C #### C QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:What are the next two letters in the following series and why? W A T N T L I T F S _ _ Hint : Look into the title of the Riddle options: A)A and W B)A and E C)B and W D)A and C E)S and W SOLUTION:A A and W. The letters are the first letters of the words in the question. Thus, the next two letters are A and W. #### A QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 24)/2 = 288 Answer: D #### D QUESTION:If (x - 1)(x - 2) = x^2 + x, what is a possible value of x? options: A) 1/2 B) 2 C) -1 D) 1 E) -2 SOLUTION:Rearranging the given expression: (x - 1)(x - 2) = x^2 + x i.e. x^2 - 3x + 2 = x^2 + x i.e. -4x = -2 i.e. x = -4/-2 = 2 Answer: Option B Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible #### B QUESTION:The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all? options: A)10 B)19 C)04 D)12 E)07 SOLUTION:Add the numbers of watches. 2 + 1 + 1 =4. Answer is C. #### C QUESTION:How many positive integers will divide evenly into 440? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:520 = 10134 = 8513 = 2^3513 We need to positive integers will divide evenly into 520 or simply the factors of 520 If a number is of the form 2^a3^b5^c, Total factors = (a+1)(b+1)(c+1) Therefore, number of factors of 520 = (3+1)(1+1)(1+1) = 422 = 18 Option D #### D QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)30% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 45 are employed males, hence 19% are employed females. (employed females)/(total employed people)=19/64=30% Answer: C. #### C QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:A man rows his boat 90 km downstream and 70 km upstream, taking 3 hours each time. Find the speed of the stream? options: A)76 kmph B)6 kmph C)3.5 kmph D)4.5 kmph E)4 kmph SOLUTION:Speed downstream = d/t = 90/(3) = 30 kmph Speed upstream = d/t = 70/(3) = 23 kmph The speed of the stream = (30 - 23)/2 = 3.5 kmph Answer:C #### C QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of? options: A)150 B)339 C)342 integers D)359 E)362 SOLUTION:1-digit integers Number of 1-digit integers (1 to 9) = 9 - 1 + 1 = 9 Number of digits used = (9)(1) = 9 2-digit integers Number of 2-digit integers (10 to 99) = 99 - 10 + 1 = 90 Number of digits used = (90)(2) = 180 3-digit integers Number of 3-digit integers (100 to 150) = 150 - 100 + 1 = 51 Number of digits used = (51)(3) = 153 TOTAL # of digits uses = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? options: A)15% B)20% C)25% D)29% E)80% SOLUTION:Listed selling price of chair = 84.95 $ Discounted selling price of chair = 59.95 $ Discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = (25/84.95) * 100% = 29 % approx Answer D #### D QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)5 B)7 C)3 D)1/2 E)4 SOLUTION:Explanation: M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: C #### C QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ? options: A)10 hr B)50 C)20 D)250 E)260 SOLUTION:Explanation: 6C4 * 7C3 = 50 B #### B <<<Examples ends QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2. Answer: C. #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many positive factors do 160 and 96 have in common? options: A)6 B)12 C)16 D)18 E)24 SOLUTION:The number of common factors will be same as number of factors of the Highest Common Factor(HCF) HCF of 160 and 96 is 32 Number of factors of 32 = 6 Answer :A #### A QUESTION:Rice weighing 3power3/4 pounds was divided equally and placed in 4 containers. how many ounces of rice were in each? options: A)15 ounces B)25 ounces C)12 ounces D)22 ounces E)35 ounces SOLUTION:3power3/4 / 4 pounds, = (4x3+3)/4 ponds. = (15/4) /4 ponds. = (15/4) / (1/4) ponds. = 15/16 pounds. 1 pound = 16 ounces. therefore, 15/16 pounds = 15/1616 ounces = 15 ounces. Correct answer : (A) #### A QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)46 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 9) years. (x+9+10)=2(x�10) hence x=39. Present age of B = 39 years Answer: Option C #### C QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? options: A)600 B)320 C)500 D)520 E)720 SOLUTION:Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x. 2x/(x - 160) = 2 + 2(extra) => 2x - 320 = x => x = 320. ANSWER:B #### B QUESTION:Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income? options: A)54.5% B)52.5% C)59.5% D)51.5% E)55.5% SOLUTION:Camilla's income = 100 (assume); Cathy's income = 35 (65 percent less than Camilla's income); Bernice's income = 59.5 (70 percent more than Cathy's income). Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100). Answer: C #### C QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x1/10 + Nx1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:Two dice are thrown together.What is the probability that the sum of the number on the two faces divided by 4? options: A)3/9 B)4/9 C)1/9 D)2/9 E)5/9 SOLUTION:n(s)=66=36 Let e be the event that the sum of the numbers on the two faces is divisible by 4 E={(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2)} n(e)=8 p(e)=n(e)/n(s) =8/36 =2/9 Answer is option D #### D QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 100 = $ 88 after the final reduction of 10% price becomes = 0.9 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 * 5 * 7 * 11 So j= 2, k= 5, l= 7, m= 11 j+ m= 2 + 11 = 13 Answer - B #### B QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 --> In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6. Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8. Answer: B. #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ? options: A)9/10 B)6/10 C)2/10 D)3/10 E)5/10 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20 Let E = event of getting a multiple of 4 or 15 =multiples od 4 are {4, 8, 12, 16, 20} And multiples of 15 means multiples of 3 and 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}. = the common multiple is only (15). => E = n(E)= 6 Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10. Answer is D #### D QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? options: A)600 B)2877 C)208 D)1882 E)191 SOLUTION:Explanation: Cost price = Rs.500 profit = 20% of 500 = Rs.100 Selling price = Cost price + Profit = 500 + 100 = 600 Answer:A #### A QUESTION:A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 2 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? options: A)x/70 B)2x/63 C)3x/70 D)3x/10 E)3x/7 SOLUTION:cost of boat per day = x cost per person =x/7 if three more persons afre there, cost =x/9 difference = x/7-x/9 =2x/63 Ans B #### B QUESTION:Find the distance covered by a man walking for 42 min at a speed of 10km/hr? options: A)7km B)3km C)4km D)5km E)6km SOLUTION:Distance = 1042/60 = 7 km Answer is A #### A QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? options: A)25% B)40% C)50% D)60% E)75% SOLUTION:34% is 9%-points above 25% and 6%-points below 40%. Thus the ratio of mixture Y to mixture X is 2:3. The percent of mixture X is 3/5 = 60%. The answer is D. #### D QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length options: A)20 seconds B)30 seconds C)40 seconds D)50 seconds E)None of these SOLUTION:Explanation: Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 485+140 = 625 meter Time = Distance/speed =625∗2/25=50seconds Option D #### D QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 66 = Rs. 16.50 Answer:D #### D QUESTION:(3 x 10^2) + (2 x 10) + 4 = options: A)302400 B)32400 C)30240 D)3240 E)324 SOLUTION:When you multiply a number by 10 you just add a zero => 3 x 10^2 => add 2 zeros => 3 x 10^2 = 300 =>2 x 10 = 20 => 4 = 4 =>3 x 10^2 + 2 x 10 + 4 = 300 + 20 + 4 = 324 => answer is E ( 324) #### E QUESTION:What positive number, when squared, is equal to the cube of the positive square root of 17? options: A)64 B)32 C)8 D)4 E)2 SOLUTION:Let the positive number be x x^2 = ((17)^(1/2))^3 =>x^2 = 4^3 = 64 => x = 8 Answer C #### C QUESTION:A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? options: A)60 B)90 C)70 D)80 E)40 SOLUTION:Answer is B. Six majors are as follows: a + b + c + d + e + f Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20 4 of the majors have 300 seniors: a + b + c +d = 300 There are a total of 410 seniors. So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90. B #### B QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years? options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150 SOLUTION:P= $2000 R = 20% T = 2 years Machine value before 2 years = P/[(1-R/100)^T] =20005/4 5/4 =$3125 Answer is A #### A QUESTION:The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers. options: A)16,8 B)10,2 C)17,6 D)14,10 E)12,4 SOLUTION:Let numbers be x and y. Equation (i): x - y = 8 Equation (ii): (x + y)/4 = 6 Solve system of equations: x=16, y=8 A is the correct answer. #### A QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value M? options: A)2r B)2s C)r +s D)2r-s E)2s-r SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES. We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value. IF.... R = 8 S = 2 Answer A: 2R = 2(8) = 16 Answer B: 2S = 2(2) = 4 Answer C: R+S = 8+2 = 10 Answer D: 2R-S = 2(8) - 2 = 14 Answer E: 2S-R = 2(2) - 8 = -4 Final Answer: A #### A QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg? options: A)72 B)47 C)40 D)28 E)20 SOLUTION:940(30/100) = 282 ---- 6 ? ---- 1 => Rs.47 Answer:B #### B QUESTION:In a soccer bet,we play 4 teams.first team odd 1.27,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros. how much money we expect to win? options: A)219.5 B)221.26 C)235.01 D)266.74 E)669.0 SOLUTION:in the case we won the bet,we have: 1.27 5.23* 3.25* 2.05.00=219.50 we will win 221.26 so correct answer is B #### B QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/1001000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform? options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m SOLUTION:Speed = 300/24 = 25/2 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 25/2 => x = 187.5 m. Answer:C #### C QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 851 is 0. The answer is A. #### A QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2400? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2400 * 1/3 = 800 Option A #### A QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years? options: A)$125 B)$100 C)$200 D)$215 E)$225 SOLUTION:P= $400 R = 25% T = 2 years Machine value after 2 years = P[(1-R/100)^T] =4003/4 3/4 =$225 approximately Answer is E #### E QUESTION:If w is a positive integer, then 3^w + 3^(w +1) = options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a(a − 1) E)4(3^w) SOLUTION:3^w + 3^(w +1) = 3^w + (3^w 3^1) = 3^w (1 + 3) = 3^w(4) Ans. E) 4(3^w) #### E QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is options: A)10 B)15 C)16 D)13 E)18 SOLUTION:Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D #### D QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench? options: A)700 B)710 C)720 D)800 E)820 SOLUTION:npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) #### C QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? options: A)2400 B)2880 C)2787 D)3087 E)0728 SOLUTION:1200 * 12: x * 9 = 2:3 x = 2400 Answer: A #### A QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:65(90/100)((100-x)/100) = 56.16 x = 4% ANSWER:B #### B QUESTION:A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)3 1/2 sec B)3 5/2 sec C)3 7/2 sec D)8 1/2 sec E)3 1/8 sec SOLUTION:D = 170 S = 72 * 5/18 = 20 mps T = 170/20 = 8 1/2 sec Answer: D #### D QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:The ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages. options: A)20 years. B)30 years. C)40 years. D)50 years. E)60 years. SOLUTION:Sol. Let the age of the younger person be x years. Then, age of the elder perosn = (x + 16) years. ∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10 ⇔ 2x = 28 ⇔ x = 14 Hence, their present ages are 14 years and 30 years. Answer B #### B QUESTION:Ravi and Kavi start a business by investing â‚¹ 4000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year. options: A)2 : 28 B)5 : 28 C)7 : 18 D)1 : 18 E)3 : 18 SOLUTION:Ratio of profit = Ratio of investments = 4000 : 72000 = 1 : 18 Answer : D #### D QUESTION:The sum of two consecutive integers is 15. Find the numbers. options: A)17, 18 B)7, 8 C)5, 6 D)1, 2 E)8, 9 SOLUTION:n + (n + 1) = 15 2n + 1 = 15 2n = 14 n = 7 Answer: B #### B QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml SOLUTION:Explanation: Profit (%) = 9.09 % = \inline \frac{1}{11} Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml] Answer: A) 83.33 ml #### A QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order? options: A)6720 B)5280 C)6240 D)5202 E)4020 SOLUTION:three letters can be arranged in 3! ways. only one combination AEI is required. 8 letters can be arranged in 8! ways. thus 8!/ 3! * 1 = 6720. A #### A QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 16.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)20.4 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 141. Total age of five men added later = 414 - 312 = 202. Hence, the total average of five men = 102/5 = 20.4 ANSWER:D #### D QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 24th September was a Monday. The answer is A. #### A QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:15 men take 20 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? options: A)27.57 B)28.57 C)29.57 D)30.57 E)32 SOLUTION:3W = 2M 15M ------ 20 * 8 hours 21 W ------ x * 6 hours 14 M ------ x * 6 15 * 20 * 8 = 14 * x * 6 x = 28.57 ANSWER:B #### B QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 41(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43 SOLUTION:P(1st ball is even) = 9/18 P(2nd ball is also even) = 8/17 P(both balls are even) = 9/18 * 8/17 = 4/17 The answer is B. #### B QUESTION:Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 16 boys and 44 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic. Table method is shown above; here is how you will use logic: There are 6 happy boys. There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys. We have 6 happy boys and 6 sad boys. Total we have 16 boys. So 16 - 6 - 6 = 4 boys must be neither happy nor sad. Answer (B) #### B QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 1335 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)Rs. 4980 B)Rs. 4991 C)Rs. 4996 D)Rs. 4997 E)Rs. 5000 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991. B) #### B QUESTION:A student is mixing oil and water as part of an experiment. The student's mixture has a 5:3 oil to water ratio. If the student used 12 more units of oil than water, how many units of water were used? options: A)14 B)18 C)19 D)22 E)24 SOLUTION:Let 5u and 3u be the units of oil and water, respectively 5u - 3u = 12 2u = 12 => u = 6 Water => 3u = 18 Answer: B #### B QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6. Answer: B. #### B QUESTION:A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 4016=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:Find the one which does not belong to that group ? options: A)41 B)43 C)53 D)47 E)57 SOLUTION:Explanation: 41, 43, 47 and 53 are prime numbers, but not 57. ANSWER IS E #### E QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:Amal borrowed a sum of money with simple interest as per the following rate structure: (a) 6 p.c. p.a. for the first three years (b) 8 p.c. p.a. for the next five years (c) 12 p.c. p.a. for the next eight years If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow? options: A)8,000 B)10,000 C)12,000 D)6,000 E)None of these SOLUTION:Let x be the amount Amal borrowed. ∴ 18% of x + 40% of x + 48% of x = 5040 or, 106% of x = 5040 ∴ x = 5040⁄106 × 100 = 4754.71 Answer E #### E QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:A large box contains 19 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)475 B)350 C)450 D)550 E)650 SOLUTION:The number of chocolate bars is equal to 19 * 25 = 475 correct answer A #### A QUESTION:Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested? options: A)Rs.20,000 B)Rs.20,028 C)Rs.20,298 D)Rs.20,029 E)Rs.20,291 SOLUTION:Let the second amount be Rs. x. Then, (12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100 120000 + 20x = 16800 + 14x x = 8000 Total investment = 12000 + 8000 =Rs.20,000. Answer:A #### A QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:A square, with perimeter 40, is inscribed in a circle. What is the area of the circle? options: A)50π B)40π C)30π D)25π E)35π SOLUTION:Area of circuscribed circle = pi/2area of square Area of square = (40/4)^2 = 10^2= 100 Area of circle = pi/2100=50pi Answer : A #### A QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 235^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time. options: A)80 B)120 C)140 D)180 E)200 SOLUTION:Upward distance traveled per hour - 15 km, distance traveled after 6 hours = 90 km. He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km (Answer : D) #### D QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)Rs.24028 B)Rs.24000 C)Rs.24003 D)Rs.24029 E)Rs.24029 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs.24000 Answer: B #### B QUESTION:Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set ANSWER:A #### A QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4 SOLUTION:Work done by 20 women in 1 day = 1/15 Work done by 1 woman in 1 day = 1/(15Ã—20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—16) Ratio of the capacity of a man and woman =1/(15Ã—16) : 1/(15Ã—20) = 1/16 : 1/20 = 1/4 :1/5 = 5:4 Answer is E. #### E QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!2=48. Answer: D #### D QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)11 B)25 C)77 D)99 E)21 SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25%.Answer:B #### B QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)25 C)27 D)29 E)31 SOLUTION:Solution: We know that the average value is 24 therefore (a+b+c)/3 = 24 so a+b+c = 72 and b = a + 11 therefore a + (a + 11) + c = 72 The least value of c is when c = b so take c = a + 11 hence, a + (a + 11) + (a + 11) = 72 i.e., a = 50/3 a non integer therefore c is not equal to b so take c = b+1 therefore c = a+12 a + (a + 11) + (a + 12) = 72 i.e., a= 49/3 again a non integer therefore c is not equal to b+1 next take c= b+2 therefore c = a+13 a + (a + 11) + (a + 13) = 72 i.e., a=48/3 = 16 hence, a = 16, b = 27, and c = 29 Answer: D #### D QUESTION:Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is? options: A)100% B)50% C)180% D)200% E)150% SOLUTION:Let the total original sale be $1000 Then original number of visitors = 100 New number of visitors = 1400/5 = 280 Increase % = 180% Answer is C #### C QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)7/30 B)3/14 C)9/38 D)4/21 E)5/26 SOLUTION:P(1st ball is even) = 10/20 P(2nd ball is also even) = 9/19 P(both balls are even) = 10/20 9/19 = 9/38 The answer is C. #### C QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 256/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:3^7+3^7+3^7=? options: A)a) 81^2 B)b) 81^4 C)c) 81^5 D)d) 81^6 E)e) 81^15 SOLUTION:The correct answer is A 81^2 #### A QUESTION:The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is: options: A)28 B)30 C)40 D)50 E)72 SOLUTION:Let the numbers be 1x and 2x. Then, their L.C.M = 2x. So, 2x = 48 or x = 24. The numbers are 24 and 48. Hence, required sum = (24 + 48) = 72. ANSWER:E #### E QUESTION:A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.2 per box per month for the record storage, what is the total amount that the company pays each month for record storage? options: A)a. 150 B)b. 300 C)c. 600 D)d. 120 E)e. 200 SOLUTION:Volume Per Box: 15x12x10 = 1,800 Total Volume: 1,080,000 Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600 Price Per Month: Number of Boxes Price Per Box = 600 * 0.2 = 120 Answer: D #### D QUESTION:here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? options: A)2100 B)1800 C)1245 D)3210 E)4521 SOLUTION:5 subjects can be arranged in 6 periods in 6P5 ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements = 6P5× 5C1 /2!=1800 Ans: B #### B QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)(1+1)=2^3 2^3+2^3=(2^3)(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:If a book is sold at 5% profit instead of 5% loss, it would have brought Rs 13 more. Find out the cost price of the book options: A)75 B)72 C)130 D)70 E)80 SOLUTION:Let C.P. of the book be Rs. ’X’ Given, 1.05 X - 0.95X = 13 => 0.1 X = 13 = 13/0.1 = Rs 130 ANSWER:C #### C QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:One-third of 600 is what percent of 120 ? options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6 SOLUTION:Answer Let one-third of 600 is N% of 120. ∵ 600/3 = (N x 120)/100 ∴ N = (200x 100) / 120 = 166.6 Correct Option: E #### E QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:A certain sum of money at simple interest amounted Rs.780 in 5 years at 4% per annum, find the sum? options: A)337 B)268 C)198 D)650 E)168 SOLUTION:780 = P [1 + (54)/100] P = 650' Answer:D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.870? options: A)Rs.700 B)Rs.780 C)Rs.750 D)Rs.1000 E)None of these SOLUTION:Explanation: 870 = P [1 + (516/5)/100] P= 750 Answer: Option C #### C QUESTION:The area of a triangle is with base 4m and height 6m? options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 4 * 6 = 12 m2 Answer: E #### E QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? (A) The median of S is prime. Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime. (B) The median of T is prime. Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number. (C) The median of S is equal to the median of T. Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true. (D) The sum of the terms in S is prime. Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime. (E) The sum of the terms in T is prime. Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime. D #### D QUESTION:If x > 0 and m is x percent of y, then, in terms of x, y is what percent of m? options: A)a) 100m B)b) 1/100m C)c) 1/m D)d) 10/m E)e) 10,000/x SOLUTION:m= x/100 * y So y= 100/x m So y= (10000/x)/100 m E #### E QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is options: A)4 B)3 C)2 D)1 E)5 SOLUTION:Here we can assume that one subject is of 100 marks so total there are 5 subjects => 1005 = 500. Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total. The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio. Total ratio = 40 For 6 : (300/40)6 = 45 Similarly , we will get for others as 52.5 , 60 , 62.5 , 75. Hence , there are 3 subject where he secured more that 60 %. The answer is 3. B #### B QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour? options: A)30 B)40 C)50 D)55 E)70 SOLUTION:HiBunuel THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55. The question is correct. Here's the explanation: Let distance be D. We can find the total timeequate it, which comes as: 0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D). #### D QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number options: A)400 B)256 C)120 D)490 E)None of these SOLUTION:Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 * x = 14 * 5040 x = (145040)/144 = 490 Option D #### D QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent? options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 24. If he buys 6 a rupee, his CP = 4 He selling at 4 a rupee, his SP = 6 Profit = SP - CP = 6 - 4 = 2 Profit Percent = 2/4 100 = 50 % Answer: C #### C <<<Examples ends QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:990.35=34.65 approx. 35 Answer : B #### B QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x 2/100 * 2/3 = 200 B capital = 150001/6 = 2500.Answer: C #### C QUESTION:The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)65 years B)88 years C)18 years D)55 years E)11 years SOLUTION:9 2 = 18 years Answer: C #### C QUESTION:Which is the middle even number between 6 and 14? options: A)10 B)6 C)8 D)14 E)26 SOLUTION:6+x = 14-x 2 x = 8 X = 4 Now 6+x = 10 ANSWER:A #### A QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 654321 = 720 ANSWER:B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true? I. c - a = 2 II. abc is an odd integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and III only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: C. #### C QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 60 litres of milk = (1⁄4 × 60) litres = 15 litres. Answer C #### C QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to: options: A)0.48 B)5.8 C)0.58 D)0.058 E)0.0058 SOLUTION:= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2/0.09 x 93 x 100 = 489/9 x 93 x 10 = 163/279 x 1/10 = 0.58/10 = 0.058 (or) 0.06. Answer is D. #### D QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up? options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball. Number of arrangements = 9!/(2!)2 3! Answer: E #### E QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36, find P (E\|F) and P(F\|E) options: A)5 B)8 C)2 D)6 E)12 SOLUTION:Here, E and F are events P(E\|F) = P(EnF)/P(F) = 36/36 = 1 P(F\|E) = P(EnF)/P(E) = 36/24 = 2. C) #### C QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3750 C)Rs. 3840 D)Rs. 3900 E)None SOLUTION:EXPLANATION Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5b/2 x 15x + 2y = 4000 15x + 2 x 5/2 x= 4000 20x = 4000 x = 200. So, y = 172 = 500. Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. Answer D #### D QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)197 C)278 D)270 E)279 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x50 = 200040 x=1600 2000 ------- 400 Answer: A #### A QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C43C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A #### A QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? options: A)897 B)164,850 C)164,749 D)149,700 E)156,720 SOLUTION:Explanatory Answer Step 1: Identify the series The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101. The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107. The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998. It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2). So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3. Step 2: Compute the sum Sum of an Arithmetic Progression (AP) = [first term + last term/2]n We know the first term: 101 We know the last term: 998. The only unknown is the number of terms, n. In an A.P., the nth term an = a1 + (n - 1)d In this case, therefore, 998 = 101 + (n - 1) 3 Or 897 = (n - 1) * 3 (n - 1) = 299 or n = 300. Sum of the AP will therefore, be [101+998/2]∗300 = 164,850 Choice B is the correct answer. #### B QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches? options: A) 40 B) 60 C) 80 D) 100 E) 120 SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other. And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E. so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A. Now we are left with is B #### B QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 66 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? options: A)39 B)88 C)3 D)7 E)62 SOLUTION:Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Answer:A #### A QUESTION:Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42? options: A)1/16 B)5/42 C)1/8 D)3/16 E)1/4 SOLUTION:210=2357, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below); 42=237, so out of 16 factors only two are multiples of 42: 42 and 210, itself; So, the probability is 2/16=3/16. Answer: D #### D QUESTION:In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is: options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these SOLUTION:Explanation : When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5. According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time. Thus, Both reach at the same time. Answer : A #### A QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)\|x - 1\| < 7 B)\|x + 2\| < 6 C)\|x + 3\| < 5 D)\|x - 2\| < 6 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => \|x-2\| < 6. Hence, answer is D #### D QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)11 days B)16 days C)13 days D)15 days E)19 days SOLUTION:B 16 days P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. #### B QUESTION:The number 0.650 is how much greater than 1/8 ? options: A)½ B)21/40 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .65-1/8=x 65/100-1/8=x x=21/40 ans B #### B QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-2575)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool? options: A)4 2/3 B)9 1/4 C)9 1/3 D)8 3/4 E)10 1/2 SOLUTION:The answer is D 7 pumps take 5 hours. 1 Pump will take 57 hours . Hence 4 pumps will take (57)/4 = 8 75/100 = 8 3/4 hours #### D QUESTION:4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:5\|5, 10, 15, 20 2\|1, 2, 3, 4 \|1, 1, 3, 2 L.C.M of 5, 10, 15, 20 is 60 60 times B #### B QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre. options: A)Rs. 15,000 B)Rs. 15,500 C)Rs. 15,600 D)Rs. 20,625 E)None SOLUTION:Solution Area of the floor = (5.5 x 3.75)m² = 20.635m ² Cost of paying = Rs. (1000 x 20.625) = Rs.20625. Answer D #### D QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24144)= 30. Answer is C. #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train? options: A)200 metres B)180 metres C)324 metres D)228 metres E)150 metres SOLUTION:Speed= 60 x 5/18 m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9 m = 200 m. Option A #### A QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -1 Prob = 1/12 Answer -A #### A QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price? options: A)s:1000 B)s:1067 C)s:1278 D)s:1028 E)s:1400 SOLUTION:90% 104% -------- 14% ---- 196 100% ---- ? => Rs:1400 Answer: E #### E QUESTION:16.02 Ã— 0.1 = ? options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these SOLUTION:16.02 Ã— 0.1 = 1.602 The answer is C. #### C QUESTION:What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300? options: A) 100 B) 150 C) 140 D) 200 E) 250 SOLUTION:{100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200. Answer: D. #### D QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues? One digit is divisible by 1. Two digits are divisible by 2. Three digits are divisible by 3. Four digits are divisible by 4. Five digits are divisible by 5. Six digits are divisible by 6. Seven digits are divisible by 7. Eight digits are divisible by 8. Nine digits are divisible by 9. Ten digits are divisible by 10. options: A)3816547290 B)3816557290 C)3816547280 D)3813547290 E)3816147290 SOLUTION:A 3816547290 #### A QUESTION:Solution for 4.75+.303+.432 options: A)2.91 B)5.911 C)5.485 D)5.986 E)2.999 SOLUTION:4.75+.303+.432=0 0=0-4.75-0.303-0.432 0=-5.485 answer :C #### C QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:{3, 5, 8, y} For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y options: A)16/5, 28/3 B)4, 16/5 C)4, 16/5, 28/3 D)4, 28/3 E)3, 4, 5 SOLUTION:The set can have the following forms: 1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3 2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4 3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4 4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case. Thus the possible values are 4 and 28/3. D is the correct answer. #### D QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is? options: A)6000 B)12000 C)18000 D)24009 E)24002 SOLUTION:Ratio of investments of A and B is (70000 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 13000 Share of B = 6/13 (13000) = Rs. 6000 Answer: A #### A QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? options: A)3.625 B)3 C)4.5 D)4 E)3.5 SOLUTION:Set up two R x T =D cases. 1. 1/12 km/ min x T = 2.75 from which T= 33 mins. We know total journey time now is 51 +33 =84. The rate is the same ie 1/12km/min. set up second R x T =D case. 1/12 km/min x 84 = 7 km Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5 E. #### E QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer? options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1 SOLUTION:9x^2-16y^2=3x+4y (3x+4y)(3x-4y)=3x+4y 3x-4y=(3x+4y)/(3x+4y) 3x-4y=1 Answer is option C #### C QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres? options: A)20 B)200 C)300 D)90 E)140 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 8480 [4L - 40] = 8480 / 26.50 = 320 4L = 360 L = 360/4= 90 meters. Answer: D #### D QUESTION:The value of x + x(xx) when x = 2 is: options: A)36 B)16 C)18 D)64 E)10 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10 #### E QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was: options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years. SOLUTION:Let the son's present age be x years. Then, (48 - x) = x 2x = 48. x = 24 Son's age 4 years back (24- 4) = 20 years. ANSWER :D #### D QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4 a:b:c = 5:9:63/4 =20:36:63. Answer is D. #### D QUESTION:A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles? options: A)1:18. B)1:20. C)1:4. D)1:36. E)1:16. SOLUTION:Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3D(b) = 32R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D. #### D QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5 SOLUTION:Rate(1)=1/5 Rate(2)=1/8 Combined = 13/40 Work done in 2 days=13/20 Work left = 7/20 Rate Time = Work left 1/8 * Time = 7/20 Time=14/5 C #### C QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities? options: A)5:6 B)25:27 C)15:16 D)20:21 E)It cannot be determined from the information given SOLUTION:The ratio cannot be straight way added any quantity... 1:2means 1X:2X... So when you add a quantity, it becomes 1x + 15 : 2x +15.. So value of x is must.. Ans E #### E QUESTION:Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount. options: A)680 B)700 C)720 D)730 E)750 SOLUTION:From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal. As the annual Interest is to be calculated, the time period T =1. Plugging these values in the simple Interest formula, I = P x T x R = 8,000 x 1 x 0.09 = 720.00 Annual Interest to be paid = $720 answer :C #### C QUESTION:Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed? options: A)1050 B)25200 C)32400 D)5800 E)6800 SOLUTION:Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3) = 6C4 * 3C2 = 6C2 * 3C1 = 65 3 21 = 153= 45 Number of groups, each having 4 consonants and 2 vowels= 45. Each group consists of 6 letters. Number of ways of arranging 6 letters among themselves = 6! = (654321)= 720 Therefore, Required number of words= 45720= 32400 ANSWER:C #### C QUESTION:If a number 105 divides into n with no remainder, which of the following must be a factor of n? options: A)2 B)4 C)6 D)7 E)11 SOLUTION:105 / n = k (with k an integer) (7)(5)(3) / n = k n must have a 7 in his prime factorization to divide 105 without remainder. answer D #### D QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum. options: A)500 B)600 C)700 D)800 E)900 SOLUTION:Difference in S.I. = P×T/100(R1−R2) ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2) ⇒ P = 144×100/6×4=600 Answer B #### B QUESTION:A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? options: A)5,040 B)18,720 C)26,208 D)37,440 E)52,000 SOLUTION:4 character password: DLDD First digit can be chosen in 9 ways. The letter can be chosen in 26 ways. Next digit can be chosen in 8 ways. Next digit can be chosen in 7 ways. This gives us 92687ways Now, the letter can also be DDLD so there will be another 92687 ways Total = 926872 = 26,208 ways C #### C QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:The ratio, by weight, of coffee to sugar to water in a pot of coffee is 7:3:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:The new ratio of coffee to sugar is 3.5:3 The new ratio of coffee to water is 14:15. The new ratio of coffee to sugar to water is 14:12:15. If there are 12 grams of sugar, then there are (15/12)12=15 grams of water. The answer is D. #### D QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)123 B)143 C)166 D)190 E)210 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)1 years B)7 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) = 42 years. Required difference = (42 - 36) = 6 years. Answer: C #### C QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.041.046000 = $6489.60 The answer is B. #### B QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches? options: A)25 B)23 C)22 D)15 E)18 SOLUTION:Area of Carol's rectangle = 245 = 120 Let width of Jordan's rectangle= w Since , the areas are equal 8w = 120 =>w = 15 Answer D #### D QUESTION:If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much percent should he reduce the quantity of gasoline that he buys? options: A)6.66% B)8% C)10% D)12% E)12.5% SOLUTION:Let price of original price of gasoline = 10$ and let original consumption of gasoline = 10 Amount spend on gasoline originally = 1010 = 100$ the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline Increased price of gasoline = 12.5$ Now Ron intends to spend on gasoline =1.15100 = 115$ Consumption of gasoline needs to be = 115/12.5 = 1150/125 = 46/5 = 9.2 Reduction in consumption of gasoline = 10-9.2 = .8 % reduction in consumption of gasoline = .8/10 * 100% = 8% Answer B #### B QUESTION:Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)25 C)27 D)29 E)31 SOLUTION:Solution: We know that the average value is 24 therefore (a+b+c)/3 = 24 so a+b+c = 72 and b = a + 11 therefore a + (a + 11) + c = 72 The least value of c is when c = b so take c = a + 11 hence, a + (a + 11) + (a + 11) = 72 i.e., a = 50/3 a non integer therefore c is not equal to b so take c = b+1 therefore c = a+12 a + (a + 11) + (a + 12) = 72 i.e., a= 49/3 again a non integer therefore c is not equal to b+1 next take c= b+2 therefore c = a+13 a + (a + 11) + (a + 13) = 72 i.e., a=48/3 = 16 hence, a = 16, b = 27, and c = 29 Answer: D #### D QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? options: A)2 B)5 C)15 D)20 E)25 SOLUTION:Audery and Ferris collective Work rate: 1/4 + 1/3 = 7/12 Collective work Time = 12/7 = 1.7 Hrs Job Was actually done in = 2 (Includes breaks) Breaks = Actual time taken - Collective work time = 2 - 1.7 = .3 Hrs = 1/2 so ferrais took 6 breaks =.3/6=.06 hrs = 5 m so Answer is B) 10 mins #### B QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 * 100 = 33% Answer:C #### C QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7. options: A)150 B)152 C)154 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 7 D = 153 + 7 D = 160 ANSWER E #### E QUESTION:What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)82 C)92.25 D)98 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88,92, 93, 95, 96, 98 The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.) C #### C QUESTION:A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length? options: A)48.29 B)50 C)26.8 D)45.29 E)30 SOLUTION:Speed = 29 Km/hr = 29(5/18) m/sec = 145/18 m/sec Total distance = 288+101 = 389 meter Time = Distance/speed = 389 (18/145) = 48.29 seconds. Answer: A #### A QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond? options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525 SOLUTION:Solution Let S be the sample space. Then, n(S) = 52C3 = 22100 Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 26 =13C1 * 13C2= 1372 = 936 P(E) = n(E) / n(S) = 936 / 22100 = 234/5525 = 234/5525. Answer D #### D QUESTION:Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business? options: A)6 : 13 : 90 B)5 : 12 : 90 C)5 : 11 : 80 D)6 : 11 : 90 E)12 : 6 : 90 SOLUTION:Ratio of their investments = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90 Answer D #### D QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 Ã— (1/10) = 1/5 Remaining work = 1 â€“ 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes? options: A)1344 B)3360 C)8400 D)5040 E)67200 SOLUTION:8 machines produce 560 in 1 min 8 machines produce 560 6 in 6 min 12 machine produce 5606(12/8) in 6 minutes 560612/8=5040 answer is D. #### D QUESTION:The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class. options: A)A)48.55 B)B)49 C)C)51 D)D)61 E)E)62 SOLUTION:Required average = (50.25 x 16 + 45.15 x 8)/(16 + 8) = (804 + 361.20)/24 = 1165.20/24 = 48.55kg Answer is A #### A QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)58 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec ANSWER:A #### A QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly? options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20 SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/51/4 = 9/10. Answer: D. #### D QUESTION:A student completes a 3 part exam as follows. The student completes sections A in 6 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour? options: A)7:1 B)9:2 C)8:3 D)5:2 E)6:1 SOLUTION:The time spent on section B and section C is 27 minutes each. The ratio of C to A is 27:6 = 9:2 The answer is B. #### B QUESTION:Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? options: A)2:5 B)1:3 C)2:7 D)3:4 E)1:5 SOLUTION:2% is 2%-points below 4% and 11% is 7%-points above 4%. The ratio of A:B should be 2:7. The answer is C. #### C QUESTION:The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110. options: A)100 B)12 C)35 D)466 E)56 SOLUTION:There are 2 approaches in solving this. Methode 1. HCF LCM = The Actual Number. 100* 10= 1000 So the answer which we are looking for has to be a factor of 1000. So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number. answer is A #### A QUESTION:In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack? options: A)10 B)11 C)12 D)15 E)18 SOLUTION:This question can be solved by TESTing THE ANSWERS. Answer C: 12 total cards With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is... (11/12)(10/11) = 110/132 ~= 5/6 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: C #### C QUESTION:he average of 15 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)14 D)19 E)8 SOLUTION:Average of 15 numbers = 0. Sum of 15 numbers (0 x 15) = 0. It is quite possible that 14 of these numbers may be positive and if their sum is a the 15th number is (-a). Answer: Option C #### C QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it? options: A)10 B)15 C)77 D)55 E)21 SOLUTION:1/6 – 1/10 = 1/15 => 15 Answer: B #### B QUESTION:A die is thrown three times. Events X and Y are defined as below: X : 4 on the third throw Y : 6 on the first and 5 on the second throw What is the probability of X given that Y has already occurred. options: A)1/6 B)1/7 C)1/8 D)1/11 E)1/13 SOLUTION:The sample space has 216 outcomes. Now X = (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4) (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4) (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4) Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)} and X n Y = {(6,5,4)}. Now P(Y) = 6/216 and P (X n Y) = 1/216 Then P(X\|Y) = (1/216)/(6/216) = 1/6. A #### A QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket? options: A) $60 B) $80 C) $90 D) $120 E) $180 SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T. We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have: (1/2)T + (1/3)T + (1/10)T + 8 = T To get rid of the fractions we can multiply the entire equation by 30, and we obtain: 15T + 10T + 3T + 240 = 30T 28T + 240 = 30T 240 = 2T T = 120 John spent $90 at the supermarket. Answer: D #### D QUESTION:At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? options: A)384 B)258 C)215 D)120 E)72 SOLUTION:Five times as many females as males --> F = 7M. Three times as many adults as children --> (F + M) = 2C. The number of people at the party = F + M + C = 2C + C = 3C. The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C. Answer: C. #### C QUESTION:After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? options: A)15% B)50% C)35% D)20% E)25% SOLUTION:Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RDS/S = 20% notRDS/DS = 20% => 100% - 20% => RDS/DS = 80% DS/S = (20)/(80)% = 25% Answer: E #### E QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:How many ways can 8 friends be arranged around a circular dinner table? options: A)1280 B)2460 C)5040 D)40320 E)85670 SOLUTION:The number of ways to order 8 people is 8! However, around a circular table, each pattern would be repeated 8 times. So the number of ways to seat 8 friends around a circular table is 7! = 5040 The answer is C. #### C QUESTION:How many pairs (w, w+1) have one or more prime factors common, where w is an integer and 2 ≤ w ≤9 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:w and w+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. Answer: A. #### A QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)25 days B)24 C)22 days D)27 days E)21 days SOLUTION:B 24 days B = 1/8 – 1/2 = 1/24 => 24 days #### B QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of the interest. If she paid Rs. 432 as interest at the end of the period,what was the rate of interest ? options: A)3.6 B)6 C)18 D)Cannot be determined E)None SOLUTION:Solution Let rate = R% and time = R years.Then, (1200xRxR/100)= 432 = 12R2= 432 = R2=36 =R = 6 Answer B #### B QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these SOLUTION:Explanation: We know perimeter of square = 4(side) So Side of first square = 40/4 = 10 cm Side of second square = 32/4 = 8 cm Area of third Square = 1010 - 88 = 36 cm So side of third square = 6 [because area of square = sideside] Perimeter = 4Side = 46 = 24 cm Option B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)18.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 36 Paise is given as tax => Total tax incurred = 36 Paise = Rs.36/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−36/100−x)6/100 = 36/100 ⇒ 6(25 −0.36 −x) = 36 ⇒ (25 − 0.36 − x) = 6 ⇒ x = 25 − 0.36 − 6 = 18.7 B) #### B QUESTION:A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is: options: A)45m B)50m C)54m D)72m E)70m SOLUTION:Explanation: 2 kmph = ( 2 x5/18)m/sec = 5/9m/sec. 4 kmph =(4x5/18)m/sec =10/9m/sec. Let the length of the train be x metres and its speed by y m/sec. Then, (x/y-5/9)=9and(x/y - 10/9)=10. 9y - 5 = x and 10(9y - 10) = 9x => 9y - x = 5 and 90y - 9x = 100. On solving, we get: x = 50. Therefore Length of the train is 50 m. ANSWER IS B #### B QUESTION:What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years? options: A)29893 B)27773 C)29989 D)28800 E)23400 SOLUTION:Simple interest = (18000 2 * 15)/100 = Rs. 5400 Amount = P + I = 18000 + 5400 = Rs. 23400 Answer: E #### E QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C <<<Examples ends QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered: 2 skeins at $2.50 per skein (not discountable) 8 skeins at $8.40 per skein (discountable) 7 skeins at $5.99 per skein (discountable) Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn? options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64 SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.) 7 x $5.99 = $41.93 $67.20 + $41.93 = $109.13 discountable $109.13 x .10 = $10.91 (rounded) $109.13 - $10.91 = $98.22 for discounted yarn 2 x $2.50 = $5.00 for un-discounted $98.22 + $5.00 = $103.22 cost of yarn $103.22 x 1.13 = $116.64 with tax and shipping (5% + 8% = 13%) correct answer A #### A QUESTION:Two numbers are in the ratio 5:8 and thier H.C.F is 4. Find the numbers. options: A)25 and 40 B)20 and 32 C)30 and 48 D)15 and 24 E)16 and 25 SOLUTION:Explanation: Let two numbers 5x, 8x their H.C.F = 4 Therefore H.C.F is 4 i.e, x in this case. Therefore The numbers are 5 x 4 = 20 8 x 4 = 32 Answer: Option B #### B QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/52/52/5 =36/125 A is the answer . #### A QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)11 B)408 C)2881 D)287 E)221 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 13 + 21 = 34 T = 12 D = 34 * 12 = 408 Answer:B #### B QUESTION:At a meeting of 8 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table? options: A)2400 B)2800 C)3200 D)3600 E)4000 SOLUTION:8 people can be arranged around a table in 7! ways. Consider the two chiefs who will not sit together as a single unit. The number of ways to arrange 7 units around a table is 6! We need to multiply this by 2 as the two people can be switched in each arrangement. The total number of ways to arrange the chiefs is 7! - 26! = 56! = 3600 The answer is D. #### D QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 6 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)3/16 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 6 = 6C2 Total possible outcomes - 2^6 (each child can be either a girl or a boy) Probability=2C16C2/2^6= 26/222222=12/64=3/16 Ans=D #### D QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip? options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300 SOLUTION:total distance =100 ;total time = T t1 = x/30 t2 = 100-x /40 T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200 = (10x+3000)/1200 = x+300/120 av speed = 100120/x+300 = 12000/x+300 E #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? options: A)75% B)67% C)29% D)55% E)45% SOLUTION:600 --- 400 100 --- ? => 67% Answer: B #### B QUESTION:In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg? options: A)5/6 B)3/9 C)5/0 D)5/3 E)5/9 SOLUTION:Explanation: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 Answer: Option A #### A QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:A set consists of 12 numbers, all are even or multiple of 5. If 4 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 12 = 4 + 10 - {Both} + 0; {Both}=2(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: C. #### C QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)231 B)150 C)200 D)450 E)451 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 Ans: C #### C QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? options: A)8 B)9 C)9.5 D)10 E)11 SOLUTION:So, she works 30 hours in 3 days So, she works 16 hours in 2 days So in a week she works 46 hours ( 30 + 16 ) and earns $460 So, Hourly wage is 460/46 => 10 Hence answer will be (D) 10 #### D QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/21/21/21/21/21/21/2= 1/128 case 2 .all girls. 1/21/21/21/21/21/21/2=1/128 We will add the cases to get 1/64 #### A QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 14.5 II. 15.3 III. 9.5 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+21.3 = 14.6 2 SD below mean = 12-21.3 = 9.4 14.5 and 9.5 lies in the range of 2SD from mean Answer: Option C #### C QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings? options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16 SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example GB arrangement is possible). Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/21/2 and the probability that all three siblings are seated that way is 1/21/21/2=1/8. Answer: D. #### D QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph SOLUTION:30 --- 3 DS = 10 ? ---- 1 18 ---- 3 US = 6 ? ---- 1 M = ? M = (10 + 6)/2 = 8 ANSWER:B #### B QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends? options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65 SOLUTION:Praveen spent and gave to his two friends a total of 12.25 + 2x= $4.65, x is the amount spent to one friend. Money left 50.50 -2x = $31.85. Then 2x=$18.65. correct answer is B) $ 18.65 #### B QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 812=96 five-minute intervals, thus total of 9630 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=9630 --> x=2430 and 3x=3(2430)=2490. Therefore, the total revenue from ticket sales that day was 24306+249010=$25,920. Answer: B. #### B QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there? options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 35 ⇒ 1.75x = 35 ⇒ x = 20 coin Answer A #### A QUESTION:Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element? options: A)a) L(1 + K / 5) B)b) L (K/100) - 20L C)c) 20L(1+K/100) D)d) 20(1+K/100)-19L E)e) L(K/5)-19 SOLUTION:Let's assume the value of new element to bea. So converting the word problem into equation, (19L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K But according to the answer options, problem writer wanted to conveyk% percent rise in average value. If we consider this case than resulting equation will be, (19L + a) / ( 19+1 ) = L + (K/100)L ==> 19L + a = 20 [ L + KL/100] ==> a= 20L + KL/5 -19L ==> a= L + KL/5 , which is equivalent to option [A] #### A QUESTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? options: A)5 B)T=9 C)T=10 D)T=20 E)30 SOLUTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? 9^10 = (3^2)^10 = 3^20 D. 20 #### D QUESTION:Two coins are tossed, find the probability that two Tails are obtained options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3 SOLUTION:The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(T,T)} P(E) = n(E) / n(S) = 1/4 B #### B QUESTION:The average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:10 * 5 + 36 – 26 = 60/10 = 6 ANSWER:E #### E QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)124km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5.2 or, x/40 + (250 - x)/60 = 5.2 or, (3x + 500 - 2x)//120 = 5.2 or 500 + x = 624 x=124 ANSWER:D #### D QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)30% B)70% C)100% D)250% E)300% SOLUTION:cp = 100 profit = 320 ans SP = 420 new CP = 125% of RS 100 = Rs 125 New SP = 420 profit = (420-125) = 295 req % (295/420100)% = 1475/21% = 70% ANSWER B #### B QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ? options: A)1/26 B)1/20 C)1/25 D)1/29 E)1/23 SOLUTION:Let E1 be the event of drawing a red card. Let E2 be the event of drawing a king . P(E1 ∩ E2) = P(E1) . P(E2) (As E1 and E2 are independent) = 1/2 1/13 = 1/26.Answer: A #### A QUESTION:Find the odd man out 864, 420, 200, 96, 40, 16, 6 options: A)420 B)200 C)96 D)40 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. ANSWER:C #### C QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 3 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)3/23 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20x (x = average) so, n = 3x Hence, a1+a2+..+a20+n = 23x So, the fraction asked = 3x/23x =3/23 Answer E #### E QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) * 100 ) % = 25% ANSWER A #### A QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:If the number 481673 is completely divisible by 9, what is the the smallest whole number in place of ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let x be the smallest whole number in place of * 481x673 is completely divisible by 9 => (4+8+1+x+6+7+3) is divisible by 9 => (29+x) is divisible by 9 x should be the smallest whole number. Hence, (29+x)=36 =>x=36−29=7 Answer is D. #### D QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 â€“ 4xy (x- y)2 = 625 â€“ 576 => (x â€“ y) = 7 ANSWER: A #### A QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 25 = 10. So, we need 10 to be in x! at least in power of 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)388 B)277 C)266 D)280 E)191 SOLUTION:80 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280 Answer: D #### D QUESTION:A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 40 worth of diesel fuel? options: A)20 seconds B)1 minute C)1 minute 20 seconds D)20 minutes E)1 hour 20 minutes SOLUTION:No. of gallons = 40 / 1.25 = 32 for 2 gallons it takes 5 secs for 32 gallons it will take 80 secs = 1 min and 20 secs Answer: C #### C QUESTION:A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in options: A)40 days B)30 days C)60 days D)70 days E)50 days SOLUTION:Explanation: 12 = (15 * x)/(15 + x) 180+12x=15x 3x=180 X=60 Answer: Option C #### C QUESTION:P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days? options: A)12 days B)12.5 days C)13 days D)13.5 days E)15.5 days SOLUTION:Both together worked for 3 days. In 3 days , P can do = 3 x 1 18 = 1 6 th work In 3 days, Q can do = 3 x 1 15 = 1 5 th work In 3 days , work finished = 1 6 + 1 5 = 11 30 Balance work = 19 30 Balance work finished by Q => Time taken by Q to finish the balance work = 19 30 x 15 = 9.5 days The whole work was completed in 9.5 + 3 = 12.5 days B #### B QUESTION:The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of R is? options: A)A)Rs.4078 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.6400 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10100 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv) Subtracting (i) from (iv), we get, P = 6400. P's monthly income = Rs.6400. Answer: E #### E QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x) Solve the equation. 262.85(32)+3,104.35x = 1,399.45(32 + x) 8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x 8,411.2 + 1,704.9x = 44,782.4 1,704.9x = 36,371.2 x ≈ 21.3 Answer is B. #### B QUESTION:A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? options: A)48 Kmph B)50 Kmph C)52 Kmph D)56 Kmph E)60 Kmph SOLUTION:Time = 6 Distence = 504 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 504/9 = 56 Kmph D #### D QUESTION:Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective? options: A)0.6 B)0.06 C)0.006 D)0.0006 E)6.0e-05 SOLUTION:Suppose machine A produce 1000 units total defective = 9 Machine B then produces=1500 units total defective=6 probability=15/2500 =0.006 C . correct #### C QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is options: A)1/2 B)1 C)2 D)4 E)8 SOLUTION:Given: 5/w + 5/x = 5/ywx=y Find: (w+x)/2 = ? 5(1/w + 1/x) = 5(1/y) - divide both sides by 5 (1/w + 1/x) = 1/y (x+w)/wx = 1/wx - sub'd in y=wx x+w - 1 = 0 x+w = 1 Therefore (w+x)/2 = 1/2 Ans: A #### A QUESTION:The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:The total number of ways to choose three runners 6C3 = 20 The number of trios with only males is 3C3 = 1 The number of trios which include at least one woman is 19. The answer is D. #### D QUESTION:What is the difference between the local value of 1 and 2 in the number 2124? options: A)70 B)75 C)20 D)80 E)60 SOLUTION:Explanation: 100 â€“ 20 = 80 Answer: D #### D QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)4! B)8! C)9! D)10! E)12! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)81 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (654x + 6x 95 + 775x) = 260x+570x+385x = 1215x total number of students = 15x average = 1215x/15x = 81 E is the answer #### E QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: A)4! B)5! C)7! D)8! E)9! SOLUTION:There are seven positions to be filled. The first position can be filled using any of the 7 letters contained in PROBLEM. The second position can be filled by the remaining 6 letters as the letters should not repeat. The third position can be filled by the remaining 5 letters only and so on. 758 Therefore, the total number of ways of rearranging the 7 letter word = 7654321 = 7! Ways. C #### C QUESTION:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $280. Find the original price of petrol? options: A)$11 B)$5 C)$45 D)$400 E)$6.2 SOLUTION:Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (4510/9=50 --> increase 5 gallons). Hence original price was 280/45=$6.2 Answer: E. #### E QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)18% B)22% C)12% D)92% E)14% SOLUTION:Original price = 100 CP = 80 S = 80(140/100) = 112 100 - 112 = 12% Answer: C #### C QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in. options: A)40 min B)25 min C)54 min D)65 min E)58 min SOLUTION:Distance = Speed * time 320/3= 20km New Speed = 18 kmph Therefore time = 20/18 = 10/9= 54min Answer : C. #### C QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next? options: A)52 B)56 C)96 D)128 E)None SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8. Answer: Option B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job? options: A)98 days B)21 days C)48 days D)18 days E)19 days SOLUTION:WC = 1:2 2x + x = 1/32 => x = 1/96 2x = 1/96 => 48 days Answer:C #### C QUESTION:Find the area, diameter = 12m. options: A)113.00 square meter B)113.04 square meter C)113.08 square meter D)113.24 square meter E)113.43 square meter SOLUTION:Diameter = 12 meter. Radius = diameter/2. = 12/2. = 6 meter. Area of a circle = πr2. Here, pi (π) = 3.14 meter, radius (r) = 6. Area of a circle = 3.14 × 6 × 6.. = 3.14 × 36. = 113.04 square meter or 113.04 m2. ANSWER : B #### B QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 1300 = 1040 Option D #### D QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour? options: A)A)5 B)B)10 C)C)20 D)D)30 E)E)40 SOLUTION:Explanation: T = 15/45 * 60 = 20 Answer: Option C #### C QUESTION:Which is the middle even number between 6 and 14? options: A)10 B)6 C)8 D)14 E)26 SOLUTION:6+x = 14-x 2 x = 8 X = 4 Now 6+x = 10 ANSWER:A #### A QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:What distance will be covered by a bus moving at 36 kmph in 30 seconds? options: A)287 B)600 C)289 D)300 E)207 SOLUTION:36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D #### D QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 Â· 70 and the sum of his first 5 scores is 5 Â· 75, so he received 5 Â· 75 âˆ’ 4 Â· 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute? options: A)230/(30+10A) B)230/(30+60A) C)230/38A D)220/(30+10A) E)220/40A SOLUTION:Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution. Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes. 230 Kms in 60 minutes ==> 3.8km/hr. Substitute A with 3 in the answer options. Option A #### A QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:Find the number such that when 15 is subtracted from 7 times the number,the result is 10 more than twice the number? options: A)4 B)3 C)5 D)2 E)6 SOLUTION:Let the number be x. 7x-15=2x+10 7x-2x=15+10 5x=25 x=5 answer is option C #### C QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 22 = 4 Share of all women = (104000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:In an examination a pupil's average marks were 63 per paper. If he had obtained 26 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination? options: A)8 B)9 C)10 D)14 E)12 SOLUTION:Let the number of papers be x. Then, 63x + 26 + 2 = 65x = 2x = 28 = x = 14. ANSWER:D #### D QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between Bunuel, can you please explain this one? options: A)0 and 0.5 B)0.5 and 1 C)1 and 1.5 D)1.5 and 2 E)2 and 2.5 SOLUTION:Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase). Try x=1 --> LHS=3^5=813=243 and RHS=4^4=644=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1. Answer: E. #### E QUESTION:Average of first five multiples of 2 is options: A)9 B)6 C)13 D)15 E)16 SOLUTION:Explanation: Average=2(1+2+3+4+5)5=6 Answer: Option B #### B QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers? options: A)10 B)12 C)14 D)15 E)16 SOLUTION:Solution Let the number be x and (28 - x) = Then, x (28 - x) = 192 ‹=›x2 - 28x + 192 = 0. ‹=›(x - 16) (x - 12) = 0 ‹=›x = 16 or x = 12. Answer B #### B QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:If (A+B) = 5, (B+C) = 6 and (C+D) = 3, what is the value of (A+D)? options: A)16. B)8. C)7. D)2. E)-2. SOLUTION:Given A+B = 5 B+C = 6 C+D = 3 (A+B)-(B+C)+(C+D)=(A+D) => 5 - 6+3 = 2. Option D... #### D QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3(20/60) = 7 hr Answer is D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:85% of a number is added to 24, the result is the same number. Find the number? options: A)28 B)288 C)279 D)160 E)232 SOLUTION:(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D #### D QUESTION:At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? options: A)384 B)258 C)215 D)120 E)72 SOLUTION:Five times as many females as males --> F = 7M. Three times as many adults as children --> (F + M) = 2C. The number of people at the party = F + M + C = 2C + C = 3C. The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C. Answer: C. #### C QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:1 weaver can weave 1 mat in 4 days. 10 weavers can weave 10 mats in 4 days. 10 weavers can weave 25 mats in 10 days. The answer is D. #### D QUESTION:If 6 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:2 C)3:4 D)1:2 E)6:1 SOLUTION:B 2:2 6M + 2B = 4(1M + 1B) 6M + 2B = 4M + 4B 2M = 2B The required ratio of work done by a man and a boy = 2:2 #### B QUESTION:From the given equation find the value of x: x² − 3x + 2 options: A)3 B)2 C)5 D)6 E)7 SOLUTION:(x − 1)(x − 2) x = 1 or 2. C #### C QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 25=55 35=57 GCF = 5 P.S you can make squares with side of 5 Answer : A #### A QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area Q of the triangle in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA Q= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? options: A)93% B)97% C)100% D)107% E)99% SOLUTION:Say Arthur's fortune was $100. Then: A = 201.51.1 = 33 B = 201.51.1 = 33 C = 201.50.4 = 12 D = 200.61.75 = 21 E = 0 Total 33 + 33 + 12 + 21 = 99. Answer: E. #### E QUESTION:One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in? options: A)187 min B)177 min C)144 min D)189 min E)166 min SOLUTION:Let the slower pipe alone fill the tank in x min. Then, faster pipe will fill it in x/3 min. 1/x + 3/x = 1/36 4/x = 1/36 => x = 144 min. Answer:C #### C QUESTION:A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent E of the list price is the lowest possible sale price? options: A)20 B)25 C)30 D)40 E)50 SOLUTION:Let the list price be 2x for min sale price, the first discount given should be 50%, 2x becomes x here now, during summer sale additional 20% off is given ie sale price becomes 0.8x it is given lise price is $80 => 2x = 80 => x = 40 and 0.8x = 32 so lowest sale price is 32, which E is 40% of 80 hence, D is the answer #### D QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4100 So, % increase is 21% Answer will be (E) #### E QUESTION:In a sequence, each term is obtained by adding 8 to the preceding one. If the sum of the first 30 terms is equal to 210, what is the result of the addition of the first 50 terms? options: A)8400 B)8575 C)8650 D)8680 E)8700 SOLUTION:a is first term and d = 8 since the preceding number is always greater than the previous one.. Now 30th term is a+29(2). Sum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+58) = 210 ( given sum of 30 terms is 210) => 15(2a+58) = 210 => 2a+58 = 14 => a = -22 Now to get sum of first 50 terms , we need to get 50th term value i.e. -22+49(8) = 370. Sum of first 50 terms = 50/2( -22 + 370) = 8700. Hence option E is correct answer.. #### E QUESTION:By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.500 D)s.450 E)s.420 SOLUTION:SP = 700 Profit = 25% CP = (SP)[100/(100+P)] = 700 * [100/125] = 560 Loss = 25% = 25% of 560 = Rs.140 SP = CP - Loss = 560 - 140 = Rs.420 ANSWER:E #### E QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:A man buys 1kg of sandalwood and 1kg of teakwood. He sells one for 10% profit and other for 10% loss. What is total profit/loss percentage? options: A)1% loss B)2% loss C)3% loss D)4% loss E)5% loss SOLUTION:if x is both the profit and loss % then it must be loss of x^2/100; so 1010/100=1; 1% loss ANSWER:A #### A QUESTION:What is the remainder of Q= 3^19 when divided by 10? options: A)0 B)1 C)5 D)7 E)9 SOLUTION:I looked for patterns: ^2 - units digit 9 ^3 - units digit 7 ^4 - units digit 1 ^5 - units digit 3 hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9 and we can then see: ^16 - units digit 1, or ^18 - units digit 9 and ^19 - units digit 7 therefore, Q=when divided by 10, the remainder must be 7.D #### D QUESTION:Simplfy b - [b -(a+b) - {b - (b - a+b)} + a] options: A)a B)2a C)4a D)0 E)1 SOLUTION:Explanation: b-[b-(a+b)-{b-(b-a+b)}+a] =b-[b-a-b-{b-(2b-a)}+a] =b-[-a-{b-2b+a}+a] =b-[-a-{-b+a}+a] =b-[-a+b-a+a] =b-[-2a+b+a] =b-b+a =a Option A #### A QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)6 m B)9 m C)10 m D)7 m E)11 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)). options: A)1/50 B)3/50 C)4/50 D)6/50 E)9/50 SOLUTION:Answer is A. #### A QUESTION:X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : options: A)34 B)43.2 C)40 D)38 E)29 SOLUTION:Solution: Average speed = 2XY / X+Y = 25436 / 54+36 = 43.2 Answer : B #### B QUESTION:Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3. options: A)27 B)26 C)28 D)25 E)24 SOLUTION:1/2(6+12)3=27 ANSWER:A #### A QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ? options: A)5% B)6% C)7% D)8% E)9% SOLUTION:S.I. = 1680, R = 4% T = 5 years Principal = (100 1680)/ (54) = 8400 So P = 8400 Rate = (100 1680)/ (8400 * 4) = 5% ANSWER:A #### A QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6d B) 7/3d C) 10/3d D) 7/2d E) 9/2d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet? options: A)267 B)2667 C)200 D)269 E)265 SOLUTION:When the second train leaves Mumbai the first train covers 40 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai. Answer:C #### C QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60100)/36) %=285% Answer E #### E <<<Examples ends QUESTION:What is the are of an equilateral triangle of side 4 cm? options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 4, Area of triangle = √3/4 4 * 4 = 4√3 cm2; Answer:D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3). If 3y = –30, then y = options: A) –15 B) –6 C) -3 D) 6 E) 15 SOLUTION:(3+2)(y-3)=-30.. x-3=-6.. x=-3 C #### C QUESTION:Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there? options: A)2 B)4 C)3 D)5 E)6 SOLUTION:x / 9 – y / 6 = 1/9; 2x – 3y + 2 We can compute that x = 4 and y = 2. Thus, Inlet pipe = x = 4. Answer: B #### B QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks? options: A)60 B)80 C)100 D)120 E)140 SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback. If all 160 books were paperbacks, the dealer would earn a profit of $320. Since the actual profit was $400, the dealer must have sold 80 hardbacks. Then the number of paperbacks sold was 160-80 = 80. The answer is B. #### B QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140 SOLUTION:C. 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220/2 = 110 Answer C #### C QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 45!. Answer: C. #### C QUESTION:The difference between the squares of two consecutive odd integers is a square<1000 whose root equals the combined sum of the digits of the two integers. What is the sum of the digits M of the larger integer? options: A)M=2 B)M=5 C)M=8 D)10 E)11 SOLUTION:Really hard. But let's start with few concepts: 1. Square of an odd integer will be odd. 2. Difference of odd and odd will be even. 3. Any odd integer can be expressed as difference of two squares. 4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4. Assume two odd integers to be (2x-1) and (2x+1). Difference of their squares = (2x+1)^2 - (2x-1)^2 = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x) = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x = 8x Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers. 8 = 2^3, so x needs to be such that itcompletesa perfect square. If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits. Let's check the options, starting with c. For sum to be 8, few possibilities are: 17, 35, 53, 71 If we take 17, the pair is 15 and 17, meaning x = 8. 8x = 64 root of 64 = 4 but 4 is not equal to 1+5+1+7. Reject. If we take 35, the pair is 33 and 35, meaning x = 17. 8x = 817 Reject since perfect square is not possible. If we take 53, the pair is 51 and 53, meaning x = 26. 8x = 826 Reject since perfect square is not possible. If we take 71, the pair is 69 and 71, meaning x = 35. 8x = 835 Reject since perfect square is not possible. I tried each option and the possibilities and then got lost. Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits? Starting with option a, only 2-digit odd integer whose sum is 2 is 101. If we take 101, the pair is 99 and 101, meaning x = 50. 8x = 850 = 400 root of 400 = 20 which is indeed equal to 9+9+1+1. Answer (A). #### A QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:A military garrison in a wild frontier has 600 men who have provisions to last 25 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last? options: A)13 1/3 B)12 1/3 C)38 D)36 E)12 3/4 SOLUTION:Total provisions=600257=105000 Provisions used for in 6 weeks=67600=25200 remaining provisions=79800 remaining provisions need to be split between 900(600+300) people. Number of provisions per person= 79800/900 we need to find the answer in terms of weeks=(79800/900)/7=38 Answer:C #### C QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (1804R)/100 R = 5% Answer: A #### A QUESTION:Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)5 B)6 C)9 D)3 E)1 SOLUTION:3750 = D(100/4)2 D = 6 Answer: B #### B QUESTION:By how much is 50% of 250 greater than 25% of 400. options: A)25 B)26 C)29 D)39 E)26 SOLUTION:(50/100) * 250 â€“ (25/100) * 400 125 - 100 = 25 Answer:B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:A walks at 10 kmph and 5 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A? options: A)100km B)150km C)50km D)120km E)200km SOLUTION:Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 5 hours. x/10 - x/20 = 5 x = 100 km Answer is A #### A QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C * (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.25 – 6.25? options: A)1.5 B)0.5 C)6.25 D)0.25 E)6.0 SOLUTION:Since Z is defined as the greatest positive even integer less than or equal to Z, then 6.25* =6 (the greatest positive even integer less than or equal to 6.25 is 6). Hence, 6.25 – 6.25* = 6.25 - 6 = 0.25 Answer: D. #### D QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common? options: A)2 B)1 C)3 D)0 E)12 SOLUTION:D is a set of multiples of 5. 999 is NOT a multiple of 5, hence none of its factors is a multiple of 5. Therefore, those two sets won't have any overlap. Answer: D #### D QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture? options: A)1/2 B)1/3 C)1/4 D)1/6 E)1/5 SOLUTION:Do not need any computation 30%-----------21%---------12% if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times only possibility is 1/6 D #### D QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence. options: A)1/3 B)2/3 C)4/3 D)5/3 E)1/4 SOLUTION:Let the probability of the man get driving licence is x. so, 1/4 * x = 1/6 x = 2/3. ANSWER:B #### B QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)34 D)12 E)13 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die. options: A)1/2 B)1/6 C)0 D)5/6 E)1 SOLUTION:Determine if E and F are independent. P(E\|F) = the probability of event E occurring given that event F has already occurred P(E\|F) ≠ P(E) as P(E) is changed if it is given that F occurs. Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F) We must use the more complex formula for finding the intersection of E and F: P(E∩F) = P(F)P(E\|F) P(F) = the probability of event F occurring The probability of rolling a 1, 2, or 3 is 3/6 = 1/2 P(E\|F) = the probability of event E occurring given that event F has already occurred If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E\|F) = 1/3 P(E∩F) = P(F)P(E\|F) = (1/2) * (1/3) = 1/6 Answer B #### B QUESTION:Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x? options: A)(16/3)x B)(17/14)x C)(13/4)x D)(19/12)x E)(17/4)x SOLUTION:x = Bradley’s total 3x = James’s total (1/4)x = Charles’s total Add each total x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x Answer : E #### E QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? options: A)322 B)342 C)344 D)328 E)320 SOLUTION:Average mark scored by all the three boys = [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3 300+456+276= 344 Answer: C #### C QUESTION:Which of the following has the most number of divisors? options: A)99 B)101 C)176 D)182 E)179 SOLUTION:Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. Answer: C #### C QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2. #### B QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00 SOLUTION:In one hour and thirty minutes the first train travels 105 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm. The answer is C. #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:605:366:753 100: 72: 75 72/247 7410 = 2160 Answer: A #### A QUESTION:Sum of 53 odd numbers is? options: A)2709 B)2809 C)2909 D)3009 E)3109 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 53 odd numbers = 53^2 = 2809 ANSWER:B #### B QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now? options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9 SOLUTION:G is Gunther's current age. Let Mason's current age be M. given M = 2(G-5). four years from now Mason's age will be = 2(G-5) + 10 = 2G four years from now Gunther's age will be = G+10 Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10 Ans : D #### D QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)28% B)25% C)23% D)45% E)15% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer: B #### B QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget? options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430 SOLUTION:Difficulty level: 600 Each month's budget = 12000/12 = 1000 Budget for 4 months = 41000 = 4000 Actual amount spent = 4540 Amount spent over the budget = 4540 - 4000 = 540 Answer (B), Regards, #### B QUESTION:Each term of a certain sequence is 4 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n? options: A)1 B)13 C)15 D)19 E)47 SOLUTION:We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start. What does this imply?If the sum of the first n terms of the sequence is n Since number of terms will definitely be positive, we are looking for a positive sum. 19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on... Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer. Answer (C) #### C QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum. options: A)500 B)600 C)700 D)800 E)900 SOLUTION:Difference in S.I. = P×T/100(R1−R2) ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2) ⇒ P = 144×100/6×4=600 Answer B #### B QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? options: A)20 B)98 C)66 D)54 E)12 SOLUTION:Let C.P. of each article be Re. 1. Then, C.P. of 50 articles = Rs. 50; S.P. of 50 articles = Rs. 40. Loss % = 10/50 100 = 20% Answer: A #### A QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2? options: A)1/4 B)2/4 C)1/2 D)1/3 E)2/3 SOLUTION:Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3 correct answer D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:A rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is : options: A)24 B)28 C)36 D)48 E)None of these SOLUTION:Solution Required perimeter = (AB + BC +CP + PQ + QR + RA) = AB + BC + (CP + QR) + (PQ + RA) = AB + BC + AB + BC = 2(AB + BC) = [2(8 + 4 )] cm = 24 cm. Answer A #### A QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25100)/20=125 ANSWER:D #### D QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs Actual average weight is 1178/20 = 58.9kgs C #### C QUESTION:Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? options: A)$8 B)$14 C)$5 D)$15 E)$0 SOLUTION:1/5 x $60 = $12 for sandwich 1/6 x $60 = $10 for museum 1/2 x $60 = $30 for book $12 + $10 + $30 = $52 spent $60 - $52 = $8 left over correct answer A #### A QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C43C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is? options: A)7 B)7.67 C)8.75 D)8.98 E)8.28 SOLUTION:(4 3.5)/2 = 7 Answer:A #### A QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics? options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3 SOLUTION:Lets pick smart numbers. Total number of students: 12 Biology (1/2): 6 Chemistry (1/3): 4 Physics (1/6): 2 After leaving school Biology: 4 Chemistry: 4 Physics: 1 New Total number of students: 9 Biology and Physics: 5 Answer 5/9 or C #### C QUESTION:The surface of a cube is 24sq cm. Find its volume? options: A)8 B)6 C)4 D)3 E)1 SOLUTION:6a2 = 24 a = 2 => a3 = 8cc Answer: A #### A QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^102^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x107)/(1002)) – ( (x125)/(1002)) = 40 = (7x/20)-(3x/10)=40 x = (40 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:P and Q are the only two applicants qualified for a short-term research project that pays 300 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? options: A)$5 B)$10 C)$15 D)$20 E)$25 SOLUTION:Let Q's hourly wage be x, then P's hourly wage is 1.5x Let T be the number of hours that Q needs, then P needs T-10 hours to do the job. Since they both are paid an equal total amount of $300: xT=1.5x(T-10) T = 30 hours and Q's hourly wage is 300/30 = $10 P's hourly wage is 300/(T-10) = $15 which is $5 per hour more. The answer is A. #### A QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)30% B)70% C)100% D)250% E)300% SOLUTION:cp = 100 profit = 320 ans SP = 420 new CP = 125% of RS 100 = Rs 125 New SP = 420 profit = (420-125) = 295 req % (295/420100)% = 1475/21% = 70% ANSWER B #### B QUESTION:In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : options: A)35 B)38 C)40 D)42 E)44 SOLUTION:Explanation: Let the number of correct answers be X. Number of incorrect answers = (60 – X). 4x – (60 – x) = 140 => 5x = 200 => x = 40 Answer: C #### C QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 85 on the S scale? options: A)39 B)41 C)43 D)45 E)47 SOLUTION:A change of +18 on the R scale is a change of +30 on the S scale. R = (18/30)S + K = 3S/5 + K 6 = 3(30)/5 + K K = -12 R = 3S/5 - 12 R = 3(85)/5 - 12 = 51-12 = 39 The answer is A. #### A QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Sol. By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6. Answer C #### C QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)? options: A)190 B)200 C)210 D)220 E)230 SOLUTION:Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 140 = 25(x / 15) 10x = 2100 x = 210 meters The answer is C. #### C QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them? options: A)21 B)24 C)27 D)33 E)45 SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6 Given, X + X+3 + X+6 = 90 3X = 81 X = 27 The numbers are 27, 30, 33 Therefore the largest number is 33 Answer D. #### D QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)172 SOLUTION:Explanation: Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. Therefore, 160 x 2.40 + x x 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER IS B #### B QUESTION:The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $744, what is the length of the plot in meters? options: A)11 B)13 C)15 D)17 E)19 SOLUTION:perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20 cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 744 62L = 1054 L = 17 meters The answer is D. #### D QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:which of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d? options: A)0<d<1 B)0<d<5 C)0<d<7 D)1<d<5 E)1<d<7 SOLUTION:This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c . Thus, \|a-b\| < c < a+b \|b-c\| < a < b+c \|c-a\| < b < a+c Thus, if the sides of the triangle are 3,4 and d, 4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer. #### E QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)[100/(100+P)] = 600 [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is? options: A)36km/hr B)50km/hr C)48km/hr D)60km/hr E)55km/hr SOLUTION:Total time taken = 100/40 + 100/60 = 25/6 hrs Average speed = 2006/25 = 48km/hr Answer is C #### C QUESTION:Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now? options: A)24 years B)27 years C)28 years D)30 years E)40 years SOLUTION:Explanation : Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years. Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years. Answer : A #### A QUESTION:Find the number which is nearest to 3105 and is exactly divisible by 21 options: A)1208 B)3108 C)241 D)217 E)3147 SOLUTION:On dividing 3105 by 21, we get 18 as remainder. Number to be added to 3105 = (21 - 18) - 3. Hence, required number = 3105 + 3 = 3108. ANSWER B 3108 #### B QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 393 A=3G P=2.5G 3G+2.5G+G= 393 G=393/6.5= 18 A= 63=54 Difference = 36 'D' is the answer #### D QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)Monday SOLUTION:Explanation: Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer: Option C #### C QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers? options: A)10 B)12 C)14 D)15 E)16 SOLUTION:Solution Let the number be x and (28 - x) = Then, x (28 - x) = 192 ‹=›x2 - 28x + 192 = 0. ‹=›(x - 16) (x - 12) = 0 ‹=›x = 16 or x = 12. Answer B #### B QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train? options: A)382 B)782 C)278 D)270 E)220 SOLUTION:Speed = 72 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 300)/26 = 20 x = 220 m. Answer: E #### E QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!2! or 43/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:852.68 âˆ’ 4.0 + 108.98 = ? âˆ’ 2132.54 options: A)6078.58 B)6078.08 C)6258.58 D)6088.58 E)None SOLUTION:Option 'B' #### B QUESTION:Kunal electronic services assemble computers. Over a period of time the engineers made the following observation regarding the two vital components - the USB port and CD drive. The probability that USB port is defective is 0.1, that both the USB port and CD drive are defective is 0.02, while the probability that only the CD drive is defective is 0.03 . The probability that the USB port is defective when the CD drive has been found to be defective is? options: A)0.2 B)0.3 C)0.25 D)0.4 E)0.6 SOLUTION:Explanation : USB Defective USB OK Total CD Defective 0.02 0.03 (0.05) CD OK (0.08) (0.87) (0.95) Total 0.1 (0.9) The figures enclosed in brackets follow as conclusions. The probability that USB part is defective, when the CD drive is found to be defective is 0.02/0.02+0.03 = 2/5 = 0.40 Answer : D #### D QUESTION:The average of first five multiples of 3 is? options: A)2 B)9 C)8 D)6 E)3 SOLUTION:Average = 3(1 + 2 + 3 + 4 + 5)/5 = 45/5 = 9. Answer:B #### B QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 30 brand B widgets, 30 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.02 B)0.095 C)0.03 D)0.0275 E)0.4 SOLUTION:Given probability of defective items in each brand, So, the number of items defective in brand A=x40, in brand B=0.0630 and brand C=0.0830 Total number of widgets=40+30+30=100 the probability that the widget selected is defective is 0.053=(x40+0.0630+0.0830)/100 => 40x+1.8+2.4 =5.3 =>40x=1.1 >x=1.1/40=0.0275 Ans D #### D QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:0.90.007= _________ options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63 SOLUTION:97=63 Sum of decimal places= 4 So, 0.90.007= 0.0063 ANSWER:B #### B QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? options: A)20 coins B)30 coins C)50 coins D)100 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 175 ⇒ 1.75x = 175 ⇒ x = 100 coins Answer D #### D QUESTION:3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days? options: A)18 B)09 C)07 D)19 E)12 SOLUTION:3 M + 10 B ----- 09 days 7 M + 7 B ------- 8 days 9 M + 9 B -------? 21 M + 70 B = 63 M +63 B 7 B= 42 M => 6 M = 1 B =>1 B =6 M 3 M + 60 M = 63 M ---- 9 days 9 M + 54 M = 63 M -----? => 9 days Answer: B #### B QUESTION:There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number? options: A)25 B)66 C)77 D)60 E)44 SOLUTION:Let the two positive numbers be 5x and 8x respectively. 8x - 5x = 36 3x = 36 => x = 12 => Smaller number = 5x = 60. Answer: D #### D QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)877m B)180m C)786m D)165m E)456m SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B #### B QUESTION:One night a certain hotel rented 1/2 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned? options: A)25% B)30% C)35% D)40% E)50% SOLUTION:The rooms which were not rented is 1/2 The AC rooms which were not rented is (1/3)(3/5) = 1/5 The percentage of unrented rooms which were AC rooms is (1/5) / (1/2) = 2/5 = 40% The answer is D. #### D QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:One-third of 600 is what percent of 120 ? options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6 SOLUTION:Answer Let one-third of 600 is N% of 120. ∵ 600/3 = (N x 120)/100 ∴ N = (200x 100) / 120 = 166.6 Correct Option: E #### E QUESTION:If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ? options: A)500 B)1000 C)1500 D)2000 E)3000 SOLUTION:Explanation: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively. Then, 2x + 3y = 3500 ...(i) and 3x + 2y = 4000 .....(ii) solving (i) and (ii) we get x = 1000, y = 500 ANSWER IS B #### B QUESTION:There are 8 stores in town that had a total of 23 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 8 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:8 people visited 2 stores each for 16 visits. To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is 23 - 16 - 3 = 4, which is the maximum that one person could have visited. The answer is C. #### C QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 987 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 98 / 5432 = 3/5 which is not an integer. The answer is D. #### D QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D QUESTION:A car covers a distance of 630 km in 6 ½ hours. Find its speed? options: A)105 kmph B)176 kmph C)298 kmph D)186 kmph E)268 kmph SOLUTION:630/6 = 105 kmph Answer:A #### A QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 302928 = 24360 Answer: E #### E QUESTION:P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days? options: A)12 days B)12.5 days C)13 days D)13.5 days E)15.5 days SOLUTION:Both together worked for 3 days. In 3 days , P can do = 3 x 1 18 = 1 6 th work In 3 days, Q can do = 3 x 1 15 = 1 5 th work In 3 days , work finished = 1 6 + 1 5 = 11 30 Balance work = 19 30 Balance work finished by Q => Time taken by Q to finish the balance work = 19 30 x 15 = 9.5 days The whole work was completed in 9.5 + 3 = 12.5 days B #### B QUESTION:A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) 15 = 9 minutes The answer is D. #### D QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:Find the simple interest on Rs.300 for 9 months at 6 paisa per month? options: A)142 B)152 C)162 D)172 E)182 SOLUTION:I = (30096)/100 = 162 ANSWER:C #### C QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 987656!/2!=5443200. Answer: C. #### C QUESTION:From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected? options: A)1/10 B)4/9 C)1/2 D)9/15 E)2/3 SOLUTION:The total number of ways to choose 2 children from 6 is 6C2 = 15 The number of ways to choose 1 boy and 1 girl is 33 = 9 P(1 boy and 1 girl) = 9/15 The answer is D. #### D QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)277 C)299 D)266 E)29912 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? options: A)2 B)5 C)15 D)20 E)25 SOLUTION:Audery and Ferris collective Work rate: 1/4 + 1/3 = 7/12 Collective work Time = 12/7 = 1.7 Hrs Job Was actually done in = 2 (Includes breaks) Breaks = Actual time taken - Collective work time = 2 - 1.7 = .3 Hrs = 1/2 so ferrais took 6 breaks =.3/6=.06 hrs = 5 m so Answer is B) 10 mins #### B QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)81.9 C)81.2 D)81.3 E)81.1 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is? options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3 SOLUTION:Correct sum = (36 * 50 + 48 - 23) = 1825. Correct mean = 1825/50 = 36.5 Answer:C #### C QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:The perimeter of one face of a cube is 24 cm. Its volume will be: options: A)216cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 24/4 = 6 cm Volume = aaa = 666 = 216 cm cube Option A #### A QUESTION:John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have? options: A)65 B)68 C)70 D)77 E)80 SOLUTION:Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60. Step 2: Then pencil are distributed in ratio among friends, Rakesh = ( 1 / 2 x 60 ) = 30. Rahul = ( 1 / 3 x 60 ) = 20. Ranjan = ( 1 / 4 x 60 ) = 15. Rohit = ( 1 / 5 x 60 ) = 12. Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x. For minimum number of pencils x = 1 . The person should have atleast 77 pencils. D) #### D QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)P +(1/4)Q = (3/8)P+(3/4)Q 2P=4Q P/Q = 2/1 The answer is D. #### D <<<Examples ends QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! 4! B)11C3 6! 3! C)15C4 9! 3! D)15C2 10! 3! E)16C5 10! 4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)37 sec B)89 sec C)36 sec D)87 sec E)45 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 250 + 120 = 370 m. Time taken = 370/10 =37 sec. Answer: A #### A QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.9281.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed? options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph SOLUTION:424/(13/2) = 4242/13 =65.2 kmph ANSWER:C #### C QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even) Least number = 2 A #### A QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. options: A)None B)I only C)II only D)III only E)I and II SOLUTION:given 2x/y is prime and greater than 2. => 2x/y could be any of the following 3,5,7.... => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set) 1. x = y , can't be true if x=y , 2x/y = 2 which is not odd and prime. 2. y=1. can't be true. if y=1,2x/y = 2x = even which is not odd & prime. 3. x and y are prime integers, need not be true. lets say 2x/y = 3 and say y=2 prime =>x = 6/2 = 3 prime satisfies the given condition here. but when 2x/y = 3 and y=5 prime => x = 15/2 not prime My Answer is A #### A QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 66 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)(3/7)(4/6)(3/5) [4!/(2!2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is: options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222 SOLUTION:Explanation: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x \therefore Cultivated land of village = 384000x \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833 Answer: D #### D QUESTION:If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women? options: A)10 days B)11 days C)13 days D)15 days E)24 days SOLUTION:8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =1240= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E #### E QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%? options: A)8 B)3 C)5 D)6 E)None SOLUTION:C.P. of 9 Headphones= Rs100 S.P. of 9 Headphones = 150% of Rs 100 = Rs150 For Rs.150 , Headphones sold = 9. For Rs. 100,Pens sold=(9/150)100=6 Answer: Option D #### D QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 â€¦. (i) A + B = (25 x 2) = 50 â€¦. (ii) B + C = (28 x 2) = 56 â€¦.(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 â€¦. (iv) Subtracting (i) from (iv), we get : B = 16. Bâ€™s weight = 16 kg. Answer E #### E QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability. options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53 SOLUTION:Explanation : There are total 4 letters. The probability that P gets the first position is 1/4. The probability that O is in the second position is 1/3. Likewise, probability for C and Y are 1/2 and 1/1. Hence, the required probability is:- => (1/4) x (1/3) x (1/2) x 1. => 1/24. Answer : C #### C QUESTION:City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? options: A)56.5 B)57.5 C)61 D)61.5 E)62.5 SOLUTION:The total distance is 1×46+3×60=226 And the total time is 4 hours. Hence, Average Speed=(Total Distance/Total Time) =226/4=56.5 A #### A QUESTION:If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is: options: A)53.33 B)54.68 C)55 D)56 E)None of these SOLUTION:Explanation: Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45) = (2750 + 3300 + 2700/160) = 8750/160 = 54.68 Answer: B #### B QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4 SOLUTION:Work done by 20 women in 1 day = 1/15 Work done by 1 woman in 1 day = 1/(15Ã—20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15Ã—16) Ratio of the capacity of a man and woman =1/(15Ã—16) : 1/(15Ã—20) = 1/16 : 1/20 = 1/4 :1/5 = 5:4 Answer is E. #### E QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase? options: A)3 B)4 C)6 D)9 E)10 SOLUTION:We have 5, 10, 10 and 20 to work with From least to greatest, we have... 5 (the least) 10 15 20 25 30 35 40 45 (the greatest) Total options = 9 Final Answer:D #### D QUESTION:The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9000 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8100 × 100/90 × 100/90 = 10000 E) #### E QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is options: A)74 B)78 C)86 D)92 E)106 SOLUTION:Divisor = (6 * 3) + 7 = 25 5 * Quotient = 25 Quotient = 5. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 5) + 6 = 106. E) #### E QUESTION:A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these SOLUTION:Explanation: Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 34 => 300+L = 15×34 = 510 => L = 510-300 = 210 meter Answer: Option C #### C QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent? options: A)70% B)45% C)48% D)30% E)40% SOLUTION:Explanation: 840 ---- 380 100 ---- ? => 45% Answer: B #### B QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)205 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 * 8 * 4) = 160. Therefore, 160 * 2.40 + x * 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER:B #### B QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price? options: A)40% B)8% C)25% D)16.66% E)9% SOLUTION:Original cost before weight adjustment: X Cost after 90% weight adjustment: 9/10 X 20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100 Mark up on original cost of X: (108X/100)/X-1 = 8/100 ANSWER:B #### B QUESTION:If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy? options: A)1 B)4 C)5 D)7 E)8 SOLUTION:unit digit of x=4^a will either be 4 or 6 (4 if a is odd and 6 if a is even) and unit digit of y=9^b will either be 1 or 9 (9 if b is odd and 1 if b is even) now we have total 4 possible combinations 1) a=odd, b=odd unit digit=94=6 2)a=odd, b=even unit digit=41=4 3) a=even,b=odd unit digit=69=4 4)a=even, b=even unit digit=61=6 thus, only two values are possible for the unit digits (4 or 6). out of these values only 4 is mentioned in the given choices. hence answer must be B. #### B QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses? options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4 SOLUTION:The ratio of beige:white:brown = 3:6:2 The answer is C. #### C QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} options: A)20 B)40 C)80 D)140 E)60 SOLUTION:Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60. Answer:E #### E QUESTION:A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is options: A)8.95km/hr B)26.7km/hr C)27.8km/hr D)28.5km/hr E)8.45km/hr SOLUTION:average speed = (25020)/50+20 km/hr =28.5 km/hr Answer (D) #### D QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)80. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (20gray+50other) 90gray+40other Answer:D #### D QUESTION:which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2 options: A)II only B)I only C)III only D)I,II only E)I,III only SOLUTION:10=25 15=35 GCF =5 Answer : B #### B QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose? options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0 SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x' The problem boils down to: Rose to Poppy: s+3=x/6 ------- 1 Daisy to Rose: s=(x+18)/10------ 2 so from 1 we can re write x as x=6s+18 substitute the value of x in 2 gives us s=1.8 m/s D #### D QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:How many numbers from 29 to 79 are exactly divisible by 11? options: A)4 B)6 C)8 D)5 E)7 SOLUTION:Numbers=(79/11)-(29/11) =7-2 =5 numbers Option D is answer #### D QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:The digit in unit's place of the product 81 ×82×.....×89 is options: A)0 B)2 C)6 D)8 E)4 SOLUTION:Solution Required digit = Unit digit =(1×2×3×4×5×6×7×8×9) =0. Answer A #### A QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true? I. ab is even II. ab > 0 III. c is even options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6 lets see III option where C is even as per our assumption C can be even and odd, hence it is out. lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out So options B,C,D,E are gone and ans is A #### A QUESTION:If −y ≥ x, and −x < −4, then which of the following must be true? options: A)y = −4 B)y > −4 C)−y > 4 D)y ≤ −4 E)y ≥ −4 SOLUTION:−y ≥ x, and −x < −4 y <= -x < -4 As '-x' is less than '-4' and Y is less than or equal to '-x' we have y < -4 which is similar to -y > 4. C) -y >4 #### C QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr. What is the speed of the boat? options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph SOLUTION:speed upstream = 10/3 speed of boat down stream = 10/6 speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph ANSWER:A #### A QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ? options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49 SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49 SD: Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7. So, answer will be D. #### D QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:How much is 90% of 40 is greater than 4/5 of 25? options: A)29 B)776 C)66 D)16 E)99 SOLUTION:(90/100) * 40 – (4/5) * 25 36 - 20 = 16 Answer: D #### D QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/43/43/43/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips? options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these SOLUTION:Explanation: Method : 1 If a car covers a certain distance atxkmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph. By using the same formula, we can find out the average speed quickly Speed with which he travels from A to B = x = 40 km/hr Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr average speed = (2×40×60)/(40+60) = 48 km/hr Assume that distance from A to B = x km Speed with which he travels from A to B = x = 40 km/hr Time to travel from A to B = distance/speed = x/40 hr Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr Time to travel from B to A = distance/speed = x/60 Total distance traveled = x+x = 2x Total time taken = x/40 + x/60 Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60) = 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr Answer: Option A #### A QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 8? options: A)2/13 B)3/45 C)5/36 D)6/73 E)4/15 SOLUTION:n(S) = 66 = 36 E = {(2,6),(3,5),(4,4),(5,3),(6,2)} Probability = 5/36 Answer is C #### C QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ? options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these SOLUTION:ExplanaƟon: Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)�(1/2) = 1/12 => B alone can complete the work in 12 hour Answer: B #### B QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 76 = 42 litres of 2% solution and 36 = 18 litres of 12% solution. Answer (E) #### E QUESTION:An airplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/h. The average speed of the plane around the field in km/h is options: A)384 B)400 C)500 D)284 E)None of these SOLUTION:Explanation : Let each side of the square field be x km. So, average speed of the plane = 4x/((x/800)+(x/600)+(x/400)+(x/200)) = (42400)/(3+4+6+12) = 9600/25 = 384 Answer : A #### A QUESTION:If n is a natural number, then(6n^2+6n) is always divisible by? options: A)6 only B)6 and 12 C)12 only D)by 18 only E)None of these SOLUTION:(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Correct Option: B #### B QUESTION:A group of five people are weighed with the results as follows (in pounds): 135, 140, 165, 178, 199. If the weight of the heaviest person is increased by 9 pounds, which of the following statements best describes the change in the mean and the median of the weights? options: A) The mean and the median will remain unchanged. B) The mean will remain unchanged but the median will increase. C) The mean will increase but the median will remain unchanged. D) The mean and the median will increase by the same amount. E) The mean and the median will increase by different amounts. SOLUTION:Old set = {135, 140, 165, 178, 199}. New set = {135, 140, 165, 178, 208} --> the median (middle term) will remain the same and the mean will increase. Answer: C. #### C QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y? options: A)96 B)75 C)50 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 6.12 and remainder is 6 So .12 X y = 6 hence y= 50 Ans C #### C QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology? options: A)30 B)90 C)120 D)168 E)188 SOLUTION:I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168 Using your analysis: We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232 So, in the image we know that the number of students in the zone with the black boundary = 232 Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize) And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w Since the total number of students = 400, we can write: 232 +b+w= 400 Or,b+w= 400 - 232 = 168 That is,b= 168 -w So, the maximum value ofbwill happen forw= 0 This is how we get, the maximum value ofb= 168 D #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years? options: A)14000 B)14400 C)14500 D)15625 E)14700 SOLUTION:Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D #### D QUESTION:Calculate the number of bricks, each measuring 25 cm 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000. options: A)Rs. 2500 B)Rs. 8500 C)Rs. 7200 D)Rs. 8000 E)None of these SOLUTION:Explanation: A = 2B and B = 5C => A : B = 2 :1and B : C = 5 : 1 => A : B : C = 10 : 5 : 1 Ratio of capitals of A, B and C = 10 : 5 : 1 B's share = Rs.[(5/16) × 8000] = Rs. 2500 Answer: Option A #### A QUESTION:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X? options: A)30% B)33 1/3% C)37 1/2% D)40% E)50% SOLUTION:Initial solution => 8 kg (x:w :: 2.4:5.6) After evaporation Initial solution => 6 kg (x:w:: 2.4:3.6) New solution => 2 kg (x:w::0.6:1.4) Mixing (Initial solution + New solution) => 6 kg (2.4:3.6)+ 2 kg (0.6:1.4) = = 8 kg [(2.4+0.6) : (3.6+1.4)] = 8 kg (x : water :: 3kg : 5 kg) Hence % of x = 3/8 = 37.5% ANSWER:C #### C QUESTION:An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)56 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 8P2 = 8!/2! = 56. IMO option C is correct answer.. #### C QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed) options: A)60 B)75 C)65 D)55 E)45 SOLUTION:There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and 4 ways respectively. Required number of numbers =3x5x4=60. Ans: A #### A QUESTION:If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ? options: A) 3 B) 4 C) 5 D) 6 E) 7 SOLUTION:Given that (10a + b) - (10b + a) = 36 --> 9a - 9b =36 --> a - b = 4. Answer: B. #### B QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D QUESTION:If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. The actual distance traveled by him is? options: A)50 B)65 C)70 D)61 E)60 SOLUTION:Let the actual distance traveled be x km. Then, x/12 = (x + 20)/16 x - 60 =>x = 60km. Answer: E #### E QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:John earned 40% more per month than Oscar. If john salary is decreased 10% and Oscar’s salary is increased by 10%, then john would be earning what percent more than Oscar? options: A)10% B)9.09% C)15.54% D)14.54% E)It cannot be determined from the information given. SOLUTION:This Q is all about taking the correct BASE for taking %s.. the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 60 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 140.. 100 increases 10% =110.. 140 decreases 10%=126.. so the increase is 16.. again the BASE is 110, so answer 16/110 * 100= 14.54% C without calculations, answer cannot be equal to or greater than 16, as 16 is on 110.. so D is the only one left #### D QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? options: A)116 B)132 C)148 D)164 E)180 SOLUTION:3/10P are ponies with horseshoes, so P is a multiple of 10. 5/83/10P = 3/16P are Icelandic ponies with horseshoes, so P is a multiple of 16. The minimum value of P is 80. Then H = P+4 = 84. The minimum number of horses and ponies is 164. The answer is D. #### D QUESTION:The area of a triangle is with base 3m and height 4m? options: A)4 m2 B)6 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 3 * 4 = 6 m2 Answer: B #### B QUESTION:If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? options: A)$ 4 B)$ 8 C)$ 12 D)$ 16 E)$ 432 SOLUTION:Solution Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408 Amount (SI) = P+PTR/100 = 5000+(500018/100)=5400 Difference = 5408-5400=8 $ ANSWER:B #### B QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys? options: A)120 B)140 C)185 D)190 E)210 SOLUTION:The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are: (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a '''' (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185 C #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? options: A)13 B)7 C)25 D)20 E)10 SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y be the green marble,z be the blue marble... x+y=15 y+z=13 x+z=12 solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7 ANSWER:B #### B QUESTION:A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is options: A)31 years B)32 years C)33 years D)34 years E)35 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+40. => 2(x+6) = (x+40+6) => 2x+12 = x+46 => x = 34 years Answer: Option D #### D QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers? options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by x = 2y - 4 We use the sum of the two numbers to write a second equation. x + y = 20 Substitute x by 2y - 4 in x + y = 20 to obtain 2y - 4 + y = 20 Solve for y to find y = 8 and x = 2y - 4 = 12 Answer B #### B QUESTION:There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen? options: A)2 B)3 C)14 D)16 E)20 SOLUTION:60% of 30 = 18. So, there are 18 red socks and there are 12 blue socks. Check out this possible cases once we have selected TWO socks: case a: 2 red socks, in which case we have a pair of matching socks. DONE! case b: 2 blue socks, in which case we have a pair of matching socks. DONE! case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet. Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock. If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock. In both cases, we are guaranteed to have a pair of matching socks. So, selecting 3 socks guarantees that we have a pair of matching socks. ANSWER:B #### B QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone? options: A)6 B)12 C)14 D)15 E)17 SOLUTION:Renuâ€™s one dayâ€™s work = 1/6 Sumaâ€™s one dayâ€™s work = 1/3 - 1/6 = 1/6 Suma can do it alone in 6 days. ANSWER:A #### A QUESTION:The difference between the squares of two consecutive odd integers is a square<1000 whose root equals the combined sum of the digits of the two integers. What is the sum of the digits M of the larger integer? options: A)M=2 B)M=5 C)M=8 D)10 E)11 SOLUTION:Really hard. But let's start with few concepts: 1. Square of an odd integer will be odd. 2. Difference of odd and odd will be even. 3. Any odd integer can be expressed as difference of two squares. 4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4. Assume two odd integers to be (2x-1) and (2x+1). Difference of their squares = (2x+1)^2 - (2x-1)^2 = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x) = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x = 8x Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers. 8 = 2^3, so x needs to be such that itcompletesa perfect square. If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits. Let's check the options, starting with c. For sum to be 8, few possibilities are: 17, 35, 53, 71 If we take 17, the pair is 15 and 17, meaning x = 8. 8x = 64 root of 64 = 4 but 4 is not equal to 1+5+1+7. Reject. If we take 35, the pair is 33 and 35, meaning x = 17. 8x = 817 Reject since perfect square is not possible. If we take 53, the pair is 51 and 53, meaning x = 26. 8x = 826 Reject since perfect square is not possible. If we take 71, the pair is 69 and 71, meaning x = 35. 8x = 835 Reject since perfect square is not possible. I tried each option and the possibilities and then got lost. Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits? Starting with option a, only 2-digit odd integer whose sum is 2 is 101. If we take 101, the pair is 99 and 101, meaning x = 50. 8x = 850 = 400 root of 400 = 20 which is indeed equal to 9+9+1+1. Answer (A). #### A QUESTION:On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences? options: A)6 B)7 C)8 D)10 E)12 SOLUTION:If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does: (w + 4) = 4(p - 4) If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded: p + 5 = w - 5 Solving gives p = 10 and w = 20. Answer: D. #### D QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)ab D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 Ã— 15 = 180 m. Then, speed of train = 180â„18 = 10 m/s Now, length of train = 9 Ã— 15 = 135m âˆ´ Required time = 135â„10 = 13.5 sec. Answer E #### E QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:200002+8x=1566510 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009? options: A)80 B)126 C)95 D)100 E)108 SOLUTION:Assume a value at the beginning of 2007. As this is a % question, assume P=100. At the end of 2007 it becmae = 1.2100=120 At the end of 2008 it decreased by 25% = 120.75 = 90 At the end of 2009 it increased by 40% = 901.2 = 126 Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer. #### B QUESTION:For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive? options: A)None B)One C)Two D)Three E)Four SOLUTION:$ is basically a factorial of a number. So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive. From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range. For example: 7!+2=2(34567+1) --> a multiple of 2, thus not a prime; 7!+3=3(24567+1) --> a multiple of 3, thus not a prime; ... 7!+10=10(3467+1) --> a multiple of 10, thus not a prime. Answer: A. #### A QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 5/18 = 40/9 m/s Hence time taken to cover 40 m = 409/40 = 9 seconds. Answer: C #### C QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)270 m B)245 m C)235 m D)220 m E)240 m SOLUTION:Explanation: Assume the length of the bridge = x meter Total distance covered = 135+x meter total time taken = 30s speed = Total distance covered /total time taken = (135+x)/30 m/s => 45 Ã— (10/36) = (135+x)/30 => 45 Ã— 10 Ã— 30 /36 = 135+x => 45 Ã— 10 Ã— 10 / 12 = 135+x => 15 Ã— 10 Ã— 10 / 4 = 135+x => 15 Ã— 25 = 135+x = 375 => x = 375-135 =240 Answer: Option E #### E QUESTION:Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)326 B)372 C)375 D)381 E)312 SOLUTION:A+B+C = 1500 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 1500 => 375 Answer: C #### C QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D QUESTION:Tough and Tricky questions: Mixture Problems. A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture? options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5 SOLUTION:Answer = B) 5:15 ........................ Rum ..................... Coke ................. Total First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2) Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3) Total .................. 10 ............................. 28 .................... 38 Ratio = 10:30 = 5:15 B #### B QUESTION:The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is? options: A)187 B)169 C)152 D)178 E)175 SOLUTION:200(80/100)(95/100) = 152 Answer:C #### C QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire? options: A)116 cm B)144 cm C)168 cm D)173 cm E)189 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(4)^2 * h = (4/3)π (12)^3 => h = 144 cm Answer:B #### B QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9124= 6D28 D2 = 9124/68 = 9 ANSWER:B #### B <<<Examples ends QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 800) / 384 = M M = 1050 Answer:E #### E QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected. What is the probability that a smartphone bundle that will be rejected by quality control? options: A) 0.25 B) .05^10 C) 1-0.94^10 D) 1-0.05^10 E) 0.95^10 SOLUTION:Find the probability of the opposite event and subtract from 1. The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10. P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10. Answer: C. #### C QUESTION:A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display? options: A)15/56 B)3/28 C)1/28 D)1/56 E)3/55 SOLUTION:Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator. Total no of ways we can choose 3 from 11 is 11c3, which is the denominator. So, the probability: 9c1/11c3= 3/28 ans is E. #### E QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 17=7.Also 172 gives 1 Hence unit's digit in the product =71=7. Option A #### A QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:Find the next term in series - 25, 37, 49, 61, ? options: A)71 B)72 C)73 D)74 E)75 SOLUTION:Series is Increased by 12. 25 +12 =37 37 +12 =49 49 +12 =61 61 +12 =73 ANSWER:C #### C QUESTION:30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there? options: A)800 B)1000 C)1200 D)1500 E)1800 SOLUTION:800score Official Solution: People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers. Fishermen = (300 / 30) × 100 pers. = 1000 pers. The correct answer is choice (B). #### B QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/41/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/42/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: C. #### C QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take? options: A)80 B)288 C)4^4 D)576 E)288^2 SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate.. Total five means 3 of one and 2 of other.. 1) choose 3 girls and arrange them... 4C33! = 4!= 24 2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C22!= 12 Total ways = 2412 = 288.. 2) same as above.. 2 girls and 3 boys.. 288 Total 2882=576 ANS:D #### D QUESTION:If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.) options: A)6:22 B)6:24 C)6:27 D)6:36 E)6:32 SOLUTION:6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D. Answer: D. #### D QUESTION:Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. options: A)306.05 B)306.00 C)306.04 D)306.05 E)306.01 SOLUTION:A = 5000(51/50)3 = 5306.04 5000 ----------- 306.04 Answer: A #### A QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ? options: A)1.44 % B)2.02 % C)1.04 % D)2.25 % E)3.40 % SOLUTION:Explanation: SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (15)(15)/100 % = 2.25% ANSWER IS D #### D QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:If the average (arithmetic mean) of a and b is 110, and the average of b and c is 150, what is the value of a − c? options: A)−220 B)−100 C)100 D)−80 E)It cannot be determined from the information given SOLUTION:Question: a - c = ? (a + b)/ 2 =110 ===> a + b = 220 (b + c)/2 = 150 ===> b + c = 300 (a + b) - (b + c) = 220 - 300 ===> a + b - b - c = - 80 ===> a - c = - 80 Answer: D #### D QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? options: A)5520 B)2789 C)5550 D)2889 E)2788 SOLUTION:Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600. Average monthly production of salt for that year = 66600/12 = 5550. Answer: C #### C QUESTION:Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 7 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? options: A)$10,350 B)$10,395 C)$10,593 D)$11,500 E)$12,705 SOLUTION:the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10593. So the answer is (C). #### C QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 60 + 27.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:139 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 93+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean? options: A)a) 43.6 B)b) 60 C)c) 72 D)d) 77.5 E)e) 81 SOLUTION:Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it. Here, we're told two things about a group of numbers: 1) The average of the group is 80 2) The standard deviation of the group is 14 If you go 1 SDupfrom the average, you hit.....80+14 = 94 If you go 1 SDdownfrom the average, you hit.....80-14 = 66 If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108 If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52 Etc. Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean.... 2.60 SDsupwould be.....80 + 2.60(14) = 43.6 A #### A QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet) options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy) SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 6. The price per square yard is 27 / (xy/6) = 162/(xy). The answer is E. #### E QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 * 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement? K9D 2$M JUR ? options: A)Î´KW B)Î´K5 C)Î´56 D)Î´W6 E)None of these SOLUTION:Explanation: K +6 2 +6 J +6 Î´ 9 +6 S +6 U +6 5 D +6 M +6 R +6 W ANSWER IS E #### E QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/510000=2000 Answer is A #### A QUESTION:The perimeter of one face of a cube is 24 cm. Its volume will be: options: A)216cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 24/4 = 6 cm Volume = aaa = 666 = 216 cm cube Option A #### A QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges? options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2 SOLUTION:The cost of one orange=5/12=0.416 The cost of ten oranges= 0.416x10= $ 4.16 Answer: B #### B QUESTION:If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)2 B)3 C)5 D)8 E)9 SOLUTION:Mean = (50 + 72 + 108 + 120 + 205)/5 = 111 Median = 108 Difference = 111-108 = 3 Option B #### B QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field? options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m ANSWER:A #### A QUESTION:Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute? options: A)4:5 B)9:25 C)5:4 D)25:9 E)Cannot be determined from the information provided SOLUTION:Same circumferential rate means that a point on both the gears would take same time to come back to the same position again. Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B Time A = 2pi25/Speed A Time B = 2pi20/Speed B Since the times are same, 50pi/Speed A = 40pi/Speed B SpeedA/Speed B = 50pi/30pi = 5/4 Correct Option: C #### C QUESTION:A mixture contains alcohol and water in the ratio 2:5. If 10liters of water is added to the mixture, the ratio becomes 2:7. Find the quality of alcohol in the given mixture. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let the quantity of alcohol and water be 2x and 5x 2x/(5x+10) = 2/7 20x = 4(3x+5) x=5 Quantity of alcohol = 25 = 10liters. Answer is B #### B QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer? options: A)Rs.12880 B)Rs.12000 C)Both are equally good D)None of the above E)Cannot be determined SOLUTION:Explanation: PW of Rs.12,880 due 8 months hence =Rs.[12880×100/100+(18×812)]=Rs.11500= Clearly 12000 in cash is a better offer. Answer: B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:How many quarters are equal to 7 dollars? options: A)1 B)28 C)12 D)9 E)7 SOLUTION:7 * 4 = 28 quarters Answer : B #### B QUESTION:There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)3/4 E)2/3 SOLUTION:total 8 from take one. 8c1=8 red 6 from one 6c1=6 6/8=3/4 ANSWER:D #### D QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k? options: A)y = -4x + 2m B)y = 1/4x - 8m C)y = 4x + 2m D)y = 1/4x + 2m E)y = -1/4x - 8m SOLUTION:The slope of the line is 2m/8m=1/4. The y-intercept is 2m. the equation of the line is: y = 1/4x +2m The answer is D. #### D QUESTION:In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there? options: A)42 B)66 C)98 D)112 E)154 SOLUTION:Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x Total dogs and bunnies = 16x. And we are given that 16x = 352. Hence x = 22. Dogs = 3x = 322 = 66 (Option B) #### B QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be? options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1 SOLUTION:Quantity of milk in 30 liters if mix = 302/3 =20 liters Quantity of milk in 35 liters of new mix = 20+5 = 25 liters Quantity of water in it = 35-25 = 10 liters Ratio of milk and water in new mix = 25:10 = 5:2 Answer is D #### D QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what is the speed of the car? options: A)30km/h B)40km/h C)50km/h D)60km/h E)80km/h SOLUTION:The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t Car x + 5 (V (km/hr)) 4 t (hr) 4(x +5) S (km) Truck X V (km/hr) 4 t (hr) 4x S (km) 4(x+5)+4x=380 4x+4x=380−20 8x=360 x=3608 x=45 Therefore the truck's speed is 45 km/hr, and the car's speed is 45+5=50 km/hr correct answer is C)50km/hr #### C QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference W= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:117 x 217 + 83 x 83=? options: A)79698 B)20578 C)80698 D)81268 E)None of them SOLUTION:=(117)^2 + (83)^2 =(100+17)^2 + (100-17)^2 =2[(100)^2+(17)^2] =2[10000+289] =2 x 10289 = 20578 Answer is B #### B QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A? options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440 SOLUTION:LCM = 180 Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c = (180/15)/(180/15 +180/20 + 180/45) = (12/25) * 500 = Rs.240 ANSWER:A #### A QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ? options: A)1 B)10 C)30 D)20 E)21 SOLUTION:This is a solution from Beatthegmat: even numbers: (60-2)/2 + 1 = 30 even integers. (60+2)/2 = 31 is the average of the even set. sum = avg(#of elements) = 3130 = 930 = a odd numbers: (59-1)/2 + 1 = 30 odd integers. (59+1)/2 = 30 is the average of the odd set. sum = avg(#of elements) = 3030 = 900 = b a-b = 930 - 900 = 30. Answer : C #### C QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone? options: A)6 B)12 C)14 D)15 E)17 SOLUTION:Renuâ€™s one dayâ€™s work = 1/6 Sumaâ€™s one dayâ€™s work = 1/3 - 1/6 = 1/6 Suma can do it alone in 6 days. ANSWER:A #### A QUESTION:There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class. options: A)43 B)36 C)28 D)45 E)11 SOLUTION:Number of students absent on a particular day = 10 % of 50 i.e., 10/100 × 50 = 5 Therefore, the number of students present = 50 - 5 = 45 students. Answer:D #### D QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number? options: A)4 B)10 C)11 D)12 E)15 SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5 So we have 5,15,25,35,45,55,65,75,85,95 =10 Ans B #### B QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship? options: A)13 B)25 C)17 D)12 E)11 SOLUTION:11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 10 = 40 boxes 11 total cartons and 96 boxes #### E QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? options: A)112 B)77 C)267 D)12 E)99 SOLUTION:Explanation: As the division is by 2, 3, 7 together, the numbers are to be divisible by: 237 = 42 The limits are 100 and 600 The first number divisible is 423 = 126 To find out the last number divisible by 42 within 600: 600/42 = 14.28 Hence, 4214 = 588 is the last number divisible by 42 within 600 Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12 ANSWER: D #### D QUESTION:What number has a 3:4 ratio to the number 400? options: A)130 B)100 C)200 D)300 E)120 SOLUTION:3:4 = x: 200 4x = 3400 x=300 ANSWER:D #### D QUESTION:subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 15 pages. options: A)8 B)10 C)12 D)14 E)6 SOLUTION:subhas 's 1 hr copy page=50/10=5 page (subhas+prakash)'s 1 hr copy page=300/40=7.5 page from above prakash's 1 hr copy page= 2.5 page so time taken in 30 page's copy =(15/2.5)=6 hrs ANSWER:E #### E QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:Find the value of 72515 x 9999 = m? options: A)345434667 B)246465757 C)465767867 D)725077485 E)645354643 SOLUTION:72515 x 9999 = 72515 x (10000 - 1) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 D #### D QUESTION:Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 35%. What fraction of the original paint was replaced? options: A)1/35 B)1/5 C)2/3 D)3/5 E)4/5 SOLUTION:35% is 10%-points above 25% and 15%-points below 50%. Thus the ratio of 25%-solution to 50%-solution is 3:2. 3/5 of the original paint was replaced. The answer is D. #### D QUESTION:A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places. options: A)73.41 B)74.31 C)72.43 D)73.43 E)73.82 SOLUTION:Total marks = 35 x 72 =2520 Corrected total marks = 2520 - 35 + 99 =2584 Correct Average = 2584/35 = 73.82 Answer : E #### E QUESTION:v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z? options: A)30 B)35 C)37 D)38 E)40 SOLUTION:sum=150 mid value = 25 minimize 'z'. So, 25 25 25 37 38 answer: D #### D QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:Tough and Tricky questions: Work/Rate Problems. If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)8 E)9/7 SOLUTION:80 Workers = 3 hours then, 1 Worker = 380 Hours 30 Workers = (380) /(30) = 8 Answer.D #### D QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 7 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 14. D #### D QUESTION:A 160 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train? options: A)48 kmph B)54 kmph C)92 kmph D)86 kmph E)76 kmph SOLUTION:S = 160/12 * 18/5 = 48 kmph ANSWER:A #### A QUESTION:A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads? options: A)400 B)1550 C)1575 D)1600 E)1625 SOLUTION:Area Covered by Road Along the Length = 5200 = 1000 Square Meter Area Covered by Road Along the Width = 5120 = 600 Square Meter Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 55 = 25 Total Area of the Roads T= 1000+600-25 = 1575 Answer: option C #### C QUESTION:The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second? options: A)22 B)77 C)22 D)64 E)28 SOLUTION:r = 3 πr2 = 9 r = 5 πr2 = 25 25 π – 16 π 100 ---- ? => 64%.Answer:D #### D QUESTION:In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French? options: A)9 B)10 C)11 D)12 E)8 SOLUTION:let no.of persons who speeks booth latin and french = x so, no.of persons who speeks only latin = 13-x no.of persons who speeks only french= 15-x no.of persons who speeks dont speek any lag = 6 therefore (13-x)+(15-x)+x+6=25 34-x=25 x=9 ANSWER:A #### A QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? options: A)7 B)14 C)21 D)28 E)35 SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice. With 36 liters of milk, we need a total of 48 liters of juice to make drink B. We need to add 21 liters of juice. The answer is C. #### C QUESTION:In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what q percent of all the people in Smithtown are left-handed women? options: A) 50% B) 40% C) 25% D) 20% E) 10% SOLUTION:looking at the ratio we can take total number of people q=20.. ans 5/20 or 25% C #### C QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:How many digits are required to number a book containing 250 pages? options: A)756 B)642 C)492 D)372 E)250 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 902=180 digits. 250-(90+9)=151 pages will require 1513=453 digits. The total number of digits is 9+180+453=642. The answer is B. #### B QUESTION:a, b, c, and d are positive consecutive even integers and a < b < c < d. If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers? options: A)2 B)4 C)8 D)12 E)20 SOLUTION:We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on. The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will. However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8. The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C). #### C QUESTION:A was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old? options: A)4 yr 10 month B)6 yr 10 month C)7 yr 11 month D)7 yr 10 month E)8 yr 10 month SOLUTION:When C is 4yr 6 month i.e. 54 months old A is 79 month old.. B is 15 month older than A When A is 79 months old then, B is 94 months old i.e. 7yr 10 month ANSWER:D #### D QUESTION:By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)20% B)30% C)40% D)50% E)60% SOLUTION:(SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)100]%=50% ANSWER D #### D QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)21:22 B)7:8 C)2:1 D)21:24 E)14:16 SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). = (120/100) 7x and (110/100) 8x = 42x/5 and 44x/5 Therefore, The required ratio = (42x/5):(44x/5) = 21 : 22. Answer is A. #### A QUESTION:A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it? options: A)110 B)120 C)128 D)143 E)145 SOLUTION:First Purchased = 250 Wes= 128 C #### C QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years? options: A)$125 B)$100 C)$200 D)$215 E)$225 SOLUTION:P= $400 R = 25% T = 2 years Machine value after 2 years = P[(1-R/100)^T] =4003/4 3/4 =$225 approximately Answer is E #### E QUESTION:There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? options: A)8300 B)14500 C)7700 D)13000 E)5900 SOLUTION:Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 #### C QUESTION:A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days? options: A)12 B)15 C)8 D)10 E)11 SOLUTION:(A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12 (1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5 (A+B+C) work in 1 day= 1/10 So,all three together finish work in 10 days Answer D #### D QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between Bunuel, can you please explain this one? options: A)0 and 0.5 B)0.5 and 1 C)1 and 1.5 D)1.5 and 2 E)2 and 2.5 SOLUTION:Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase). Try x=1 --> LHS=3^5=813=243 and RHS=4^4=644=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1. Answer: E. #### E QUESTION:A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day? options: A)68 B)69 C)70 D)67 E)76 SOLUTION:let total no of hrs = x they have done 24+17=41 40% of x is 40/100=2/5 x=41+2x/5 x=68.3 ANSWER:A #### A QUESTION:If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 5 * 7 * 11 So j= 2, k= 5, l= 7, m= 11 j+ m= 2 + 11 = 13 Answer - B #### B QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:Which of the following has the most number of divisors? options: A)99 B)101 C)176 D)182 E)179 SOLUTION:Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. Answer: C #### C QUESTION:Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business? options: A)6 : 13 : 90 B)5 : 12 : 90 C)5 : 11 : 80 D)6 : 11 : 90 E)12 : 6 : 90 SOLUTION:Ratio of their investments = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90 Answer D #### D QUESTION:If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:a=105 = 3* 5 7 a^3 = 21 × 25 × 45 × q => a^3 = (73) x (55) x ( 3^2 5) x q => a^3 = 3^3 * 5^3 * 7 x q =>( 3* 5 7) ^3 = 3^3 5^3 * 7 x q q = 7^2 = 49 Answer D #### D QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:Vijay bought 160 shirts at the rate of Rs. 255 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)Rs. 321 B)Rs. 270 C)Rs. 277.5 D)Rs. 285 E)None of these SOLUTION:Total CP per shirt = 255 + 1400/160 + 1.75 + 320/160 = Rs. 267.5 SP = CP[(100 + profit%)/100] = 267.5 * [(100 + 20)/100] = Rs. 321. ANSWER:A #### A QUESTION:x =1 2 3 y= 4 5 18 then what is the relation between x and y options: A)1X)^1 B)1X)^6 C)1X)^7 D)1X)^4 E)1X)^2 SOLUTION:Y=(1X)^2 4=(12)^2 4=4 ANSWER:E #### E QUESTION:In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class? options: A)10.3 Years B)12.3 Years C)12.6 Years D)13 Years E)15 Years SOLUTION:Total age of 48 students (28X 12+20 X 8) = 496 Average = 496/48 = 10.3 Years A #### A QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000? options: A)81000 B)81027 C)81089 D)81027 E)28939 SOLUTION:64000 9/8 * 9/8 = 81000 Answer: A #### A QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000. 36/7 has a remainder of 1. Jan. 8th is: Friday + 1 day = Saturday The answer is D. #### D QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)18 days B)20 days C)24 days D)30 days E)32 days SOLUTION:2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days ANSWER:C #### C QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people? options: A)9 B)13 C)21 D)24 E)23 SOLUTION:work per day epr hour per person= 55/(12810) // eq-1 people=48; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 198/(p848) // eq-2 eq-1==eq-2; p= 9 ANSWER:A #### A QUESTION:Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next? options: A)4.7 B)4.5 C)6.7 D)8.9 E)9.2 SOLUTION:In this simple addition series, each number increases by 0.8. ANSWER A #### A QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(bx) B)Rs.{(bx)/a} C)Rs.{(ab)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b(x/a) = Rs. {(bx)/a} ANSWER B #### B QUESTION:A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is? options: A)1 kmph B)2 kmph C)6 kmph D)8 kmph E)3 kmph SOLUTION:DS = 25 US = 13 S = ? S = (25 - 13)/2 = 6 kmph Answer:C #### C QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together. options: A)181440 B)191440 C)171440 D)182440 E)185440 SOLUTION:Methods to arrange all the letters leaving A = 87654321/(21)(21)(21)= 5040 Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 98/21 = 36 thus total methods are 504036 = 181440 ANSWER:A #### A QUESTION:Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 10x boxes? options: A)13 minutes B)14 minutes C)15 minutes D)16 minutes E)20 minutes SOLUTION:Rate = Work / Time Given Rate of Machine A = X / 10 min Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min . Rate of Machine B = 4x / 10 we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates let's first find the combined Rate of Machine A and B Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10 Now combine Time = combine work needs to be done / Combine Rate = 10x/5x 10 = 6 Min Ans: E #### E QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be. options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=ST=485/6=40km time=45/60hr=3/4hr New speed = 40* 4/3 kmph= 53kmph Answer : B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)? options: A)72 B)180 C)70 D)90 E)140 SOLUTION:Length of side 1= 9+1=10 Length of side 2= 8+1= 9 Area of rectangle= 109= 90 D is the answer #### D QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform? options: A)45 B)47 C)49 D)51 E)53 SOLUTION:Let the length of the train be x meters. When a train crosses an electric pole, the distance covered is its own length x. speed = 36 km/h = 36000 m / 3600 s = 10 m/s x = 14 10 = 140 m. The time taken to pass the platform = (140 +370)/ 10 = 51 seconds The answer is D. #### D QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2(3)^2 = 1009 = 900 Vehicles inspected within 3 hours = 603/9 = 19 P = 19/900 Ans:D #### D QUESTION:Find the ratio between whole surfaces of a sphere and a hemisphere? options: A)4:3 B)3:4 C)3:2 D)5:2 E)4:6 SOLUTION:4 Ï€r2 : 3 Ï€r2 => 4:3 ANSWER A #### A QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/21/3=x/6 Platinum card unspent limit is= x-1/9x=8/9x So if gold card balance is transferred then the rest unspent will be 8/9x-x/6=13/18x So the ans is D #### D <<<Examples ends QUESTION:Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers? options: A)200 B)150 C)160 D)170 E)180 SOLUTION:L.C.M of two numbers is given by (Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200. ANSWER:A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)(r+4)/(y+r+6) D)(y+3)/(y+r+7)(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z? options: A)21 B)15 C)14 D)10 E)6 SOLUTION:The smallest possible product is 21 which is 37. All other products are too big. The answer is A. #### A QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y? options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5 SOLUTION:Explanation: 30 x = 50 y x: y = 30: 50 = 3 : 5 Answer:B #### B QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:What number is 60 more than two-fourth of itself? options: A)180 B)225 C)288 D)324 E)336 SOLUTION:2/4x+60= x That means 60=2/4x x= 603= 180 A is the answer #### A QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:What least value must be assigned to * so that th number 1975462 is divisible by 9? options: A)2 B)4 C)6 D)1 E)3 SOLUTION:Let the missing digit be x Sum of digits = (1+9+7+x+5+4+6+2)=34+x For 34+x to be divisible by 9 , x must be replaced by 2 The digit in place of x must be 2. ANSWER A 2 #### A QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3 SOLUTION:total 9 from take one. 9c1=9 red 5 from one 5c1=5 5/9 ANSWER:C #### C QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: options: A)21 B)22 C)20 D)45 E)30 SOLUTION:2nd day he earns = 3(2 – 5) 3rd day he earns = 3(3 – 5) On 20th day he earns 3(20 -5) = 45 rupees ANSWER:D #### D QUESTION:The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers? options: A)9x + 8 B)3x + 3 C)5x + 1 D)5x + 4 E)15x + 12 SOLUTION:If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8. Answer is A. #### A QUESTION:R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour? options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m; The rest caught a combined total of n fish. Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2. Answer: D. #### D QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ? options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these SOLUTION:Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 ANSWER:C #### C QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-xy C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)27% B)25% C)21% D)85% E)24% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer:B #### B QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)10years B)12 years C)5 years D)3 years E)24 years SOLUTION:Explanation: 9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 years Answer:D #### D QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2430 votes. How many votes were cast? options: A)7500 B)3388 C)8100 D)2888 E)2661 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2430 100%---------? => 8100 Answer: C #### C QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected? options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14 SOLUTION:1- (4c3/8c3) = 13/14 Answer : C #### C QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper? options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers) If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m. Answer (B). #### B QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)425 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence 3x + 5x = 680 Solve for x 8x = 680 x = 85 Number of boys 3x = 3 × 85 = 255 Number of girls 5x = 5 × 85 = 425 A #### A QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 34t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be: options: A)9% less than N B)11% less than N C)Equal to N D)9% greater than N E)11% greater than N SOLUTION:Correct answer is (A). This year, the price of a building is price1=P/N. If this price increases by 50% it becomes Price2=P/N1.1 Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N1.1) i.e. N/1.1 i.e. 0.91N Which is 9% less than N. #### A QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100 = 4 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 8 : 15 : 20 Answer C #### C QUESTION:If a - b =4 and a2+b2=52 , find the value of ab. options: A)8 B)26 C)18 D)42 E)36 SOLUTION:Explanation: We know 2ab=(a2+b2)âˆ’(aâˆ’b)2 2ab=52âˆ’16=36 =>ab=18 Option C #### C QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length? options: A)48.29 B)50 C)26.8 D)45.29 E)30 SOLUTION:Speed = 29 Km/hr = 29(5/18) m/sec = 145/18 m/sec Total distance = 288+101 = 389 meter Time = Distance/speed = 389 * (18/145) = 48.29 seconds. Answer: A #### A QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:The sum of 55 consecutive integers is 5555. What is the greatest integer in the set? options: A)126 B)128 C)130 D)132 E)134 SOLUTION:Let x be the first integer in the set, then x+54 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+54) = 55x + 5455/2 = 55(x+27) Then x+27=101 x=74 The largest integer in the set is 74+54=128 The answer is B. #### B QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)877m B)180m C)786m D)165m E)456m SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B #### B QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent? options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 24. If he buys 6 a rupee, his CP = 4 He selling at 4 a rupee, his SP = 6 Profit = SP - CP = 6 - 4 = 2 Profit Percent = 2/4 100 = 50 % Answer: C #### C QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier so actual day to return home is Friday. Rohit returned after days so Tuesday. ANSWER:C #### C QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$788 B)$812 C)$864 D)$878 E)$912 SOLUTION:After one year: 1.2 * $500 After two years: (1.2)^2 * $500 After three years: (1.2)^3 * $500 = $864 The answer is C. #### C QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 * 24)/2 = 288 Answer: D #### D QUESTION:Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ? options: A)5 B)10 C)22 D)25 E)30 SOLUTION:Let's TEST Answer C: 22 seashells... With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer. C #### C QUESTION:What approximate value should come in place of the question mark (?) in the following equation? 1.542 × 2408.69 + 5134.632 = ? options: A)4600 B)4800 C)5200 D)6400 E)8800 SOLUTION:Explanation 3700 + 5100 = 8800 Answer E #### E QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person? options: A)18 years B)20 years C)24 years D)32 years E)34 years SOLUTION:Explanation: Let the present age of the person be x years. Then, 3(x + 3) - 3(x - 3) = x 3x + 9 - 3x + 9 = x => x = 18 ANSWER IS A #### A QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ? options: A)5 B)4 C)3 D)2 E)-2 SOLUTION:Since x is an integer, (-12x)^(4x) is always positive. So, 12x^4x = 12x^(15 - x) 4x = 15 - x 5x = 15 x = 3 Answer: C #### C QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 94025/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2pir. The perimeter of a semicircle is 2pir/2 + 2r = pir + 2r The perimeter is pi9 + 29 which is about 46. The answer is D. #### D QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1100 B)1200 C)1349 D)1430 E)1340 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 6 = 18. Hence the number is 1349 C #### C QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? options: A)990 B)495 C)1980 D)none E)Cannot be determined SOLUTION:Explanation : For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals. Answer : B #### B QUESTION:If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ? options: A)141 B)200 C)618 D)391 E)412 SOLUTION:The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work). We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as... A + (A+2) + (A+4) = 3A + 6 We know that 3A + 6 COULD equal one of those five answers; we just have to find it... Could 3A + 6 = 141 3A = 135 A = 45 This is NOT an EVEN INTEGER, so 141 is NOT the answer Could 3A + 6 = 200 3A = 194 A = 64.6666 This is NOT an EVEN INTEGER, so 200 is NOT the answer Could 3A + 6 = 618 3A = 612 A = 204 This IS an EVEN INTEGER! The numbers would be 204, 206 and 208. This IS the answer Final Answer: C #### C QUESTION:How much interest will $8,000 earn in 9 months at an annual rate of 6%? options: A)$250 B)$350 C)$360 D)$550 E)$650 SOLUTION:Soln:- 9 months = 3/4 of year; 6% = 6/100=3/50; $8,000(principal)3/50(interest rate)3/4(time)=$360. ANSWER:C #### C QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 3 5 b Therefore (3 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 b Therefore, b = 3^3 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 57 = 35 Correct answer A. #### A QUESTION:Bob bikes to school every day at a steady rate of e miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(x + y) / t B)2(e + t) / ey C)2eyt / (e + y) D)2(e + y + t) / ey E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for e 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28 SOLUTION:Here capital is not the same. Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =( 200006 + 150006) Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ration = (300004 : 500004) Suresh : Kiran = ( 200006 + 150006) : (300004 : 500004) = (206 + 156) : (304 + 504) = (203 + 153) : (302 : 502) = 105:160 = 21:32 Answer is C #### C QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C24C1+4C14C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:A die is thrown twice and the sum of the numbers appearing is observed to be 6. find the conditional probability that the number 4 has appeared at least once? options: A)2/5 B)3/5 C)3/11 D)3/13 E)3/17 SOLUTION:Let E be the event that ‘number 4 appears at least once’ and F be the event that ‘the sum of the numbers appearing is 6’. Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} and F = {(1,5), (2,4), (3,3), (4,2), (5,1)} We have P(E) = 11/36 and P (F) = 5/36 Also EnF = {(2,4), (4,2)} Therefore P(EnF) = 2/36 the required probability P(E\|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5. A) #### A QUESTION:A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 3 music tunes of the same type (1 in _____ ) ? options: A)3 B)9 C)8 D)4 E)5 SOLUTION:1/2^3=1/8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 21/8= 1/4 so ans is 4 ANSWER:D #### D QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil? options: A)9 B)5 C)7 D)8 E)4 SOLUTION:Let the total length be xm Then black part =x/8cm The remaining part=(x-x/8)cm=7x/8cm White part=(1/2 7x/8)=7x/16 cm Remaining part=(7x/8-7x/16)=7x/16cm 7x/16=7/2 x=8cm Answer is D. #### D QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:200002+8x=1566510 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:100 identical coins each with probability 'pp' showing up heads & tossed. options: A)13/101 B)11/101 C)51/101 D)53/102 E)54/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:If x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y? options: A)4 B)12 C)2 D)7 E)6 SOLUTION:For any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards So answer = 6 = E #### E QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:Two angles of a triangle have ratio 5:3, and the third angle is the difference of the other two. Find the smallest angle of such a triangle in degrees. options: A)16 B)18 C)20 D)24 E)36 SOLUTION:The angles are 5x, 3x, and (5x-3x) = 2x [note that 2x is the smallest angle] the angles of a triangle add up to 180, so 5x+3x+2x=180 10x = 180 x = 18 2x is the smallest angle, so 218 = 36 is the smallest angle E #### E QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2. #### B QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4? options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters SOLUTION:4:1 --- 60 1:4 2:8 --------------- 5 5 ----------- 60 5 ----------- ? => 60 liters ANSWER:A #### A QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? options: A)5/16 B)5/12 C)5/19 D)5/17 E)5/15 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 Answer: B #### B QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:If 2x = 3y = 10, then 9xy = ? options: A) 1,200 B) 200 C) 150 D) 40 E) 20 SOLUTION:2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9510/3=150 Answer: C. #### C QUESTION:N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is options: A)(a) 61250 B)(b) 65525 C)(c) 42455 D)(d) 62525 E)(e) 55425 SOLUTION:The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question. To start, we're given information on the sub-sets of numbers: -The 1st set has 1 number -The 2nd set has 2 numbers -The 3rd set has 3 numbers Etc. So the 50th set will have 50 numbers in it. Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching... The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers Etc. This pattern will continue all the way down to... The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'... So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive... Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)... 25(1226+1275) = 25(2501) = 62525 D #### D QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even) Least number = 2 A #### A QUESTION:What is the remainder when you divide 2^200+2 by 7? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:answer is D. this is very similar to the 32^32^32+2 divided by 7 question. #### D QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5SP = 7CP SP = 1.4CP The profit percent is 40%. The answer is D. #### D QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed? options: A)502 B)512 C)523 D)521 E)500 SOLUTION:Let n be the total number of children. More children, less notebooks(Indirect proportion) If the number children = n, number of books each child will get = n/8 If the number children = n/2, number of books each child will get = 16 Hence we can write as children n:n/2}::16:n/8 ⇒n×n/8=n/2×16 ⇒n8=16/2=8 ⇒n=8×8=64 Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512 Answer is B. #### B QUESTION:Convert the following into a fraction: 0.3% options: A)1/3 B)2/3 C)3/10 D)1/6 E)None of the Above SOLUTION:0.3 =3/10 Answer is C. #### C QUESTION:If x < y < 0, which of the following must be true? options: A)x/y is a negative integer B)xy is a negative integer C)x+y is a negative integer D)x-y is a positive integer E)(-x)+ (-y) is positive integer SOLUTION:Given x, y are less than 0. So both will be negative integers negative + negative = negative negative * negative = positive negative / negative = positive x-y is false since x<y eg. x=-2, y=-1 then -2-(-1)=-1 So, option E is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers) Answer : E #### E QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year. options: A)140 B)141 C)142 D)143 E)146 SOLUTION:next year total population=[150^2+90^2]^.5=174.92=175 man decreased by 5% so total man =150.95=142.5 women will be= 175-142.5=32.5 so population after two years= [135^2+32.5^2]^.5=146.15=146 so population after two year= 146 ANSWER:E #### E QUESTION:A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads? options: A)400 B)1550 C)1575 D)1600 E)1625 SOLUTION:Area Covered by Road Along the Length = 5200 = 1000 Square Meter Area Covered by Road Along the Width = 5120 = 600 Square Meter Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 55 = 25 Total Area of the Roads T= 1000+600-25 = 1575 Answer: option C #### C QUESTION:A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000. options: A)Rs. 2500 B)Rs. 8500 C)Rs. 7200 D)Rs. 8000 E)None of these SOLUTION:Explanation: A = 2B and B = 5C => A : B = 2 :1and B : C = 5 : 1 => A : B : C = 10 : 5 : 1 Ratio of capitals of A, B and C = 10 : 5 : 1 B's share = Rs.[(5/16) × 8000] = Rs. 2500 Answer: Option A #### A QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 57400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 65006 : 84005 : 100003 = 656 : 845 : 1003 = 136 : 84 : 203 = 132 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 19014 = 2660 Answer is C #### C QUESTION:A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is options: A)74 B)M=75 C)M=175 D)M=680 E)690 SOLUTION:I solved this question by plugging in numbers from the answer choices. A.) 74 Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5. B.) 75 I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7. 15-7 = 8 so I know the correct answer isB #### B QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)158 m B)150 m C)110 m D)130 m E)157 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) 100 ) % = 25% ANSWER A #### A QUESTION:Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)s.10 B)s.2 C)s.5 D)s.3 E)s.4 SOLUTION:2500 = D(100/4)2 D = 4 ANSWER:E #### E QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? options: A)7 B)14 C)21 D)28 E)35 SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice. With 36 liters of milk, we need a total of 48 liters of juice to make drink B. We need to add 21 liters of juice. The answer is C. #### C QUESTION:If you have 4 New Year greeting cards and you want to send them to 2 of your friends, in how many ways can this be done? options: A)360 B)12 C)16 D)24 E)None SOLUTION:Solution We have to find number of permutations of 2 objects out of 4 objects. This number is 4P2=4(4-1)=43=12 Answer B #### B QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1â„7 hours B)6 2â„7 hours C)8 2â„7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 Ã— 2 = 16 km Distance covered in next two hours = 10 Ã— 2 = 20 km Distance covered in next two hours = 12 Ã— 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 â€“ 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. âˆ´ Time taken = 4â„12 = 1â„3 hour. Total time= 6 + 1â„3 = 6 1â„3 hour Answer E #### E QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed? options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr SOLUTION:Average speed = (24555)/(45+55) = 49.5km/hr Answer is B #### B QUESTION:What is 35% of 4/13 of 845? options: A)58 B)69 C)80 D)91 E)102 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 845, or 1/9 of 845. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 845 is a bit more than 810, so (1/9)845 will be a bit more than 90. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 91, so this is the answer to choose. The answer is C. #### C QUESTION:A small company reduced its faculty by approximately 15 percent to 195 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)229 E)E)302 SOLUTION:If x is the original number of employees, then after 15% reduction in employees number is .85x but we are given .85x = 195 x = 229 So the original number of employees is 229 Correct Answer - D #### D QUESTION:B and C started a business investing Rs. 72,000 and Rs. 45,000 respectively. In what ratio the profit earned after 7 years be divided between B and C respectively? options: A)7:5 B)5:8 C)5:7 D)8:5 E)None of these SOLUTION:B:C = 72000 : 45000 = 8:5. ANSWER:D #### D QUESTION:When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? options: A)32 B)36 C)40 D)45 E)50 SOLUTION:A = 9k+3 = 5j+4 B = 9m+3 = 5n+4 A-B = 9(k-m) = 5(j-n) Thus A-B is a multiple of 9 and 5, so it is multiple of 45. The answer is D. #### D QUESTION:Find the value of (X) in the given equation ? 35% of 1500 + X = 45% of 4200 – 320 options: A)910 B)980 C)1012 D)1045 E)None of these SOLUTION:Explanation: 35% of 1500 + X = 45% of 4200 – 320 (35/100 1500) + X = (45/100 * 4200) – 320 525 + X = 1890 – 320 X = 1890 – 320 – 525 X = 1890 – 845 X = 1045 ANSWER: D #### D QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:The class borrowed a total of 402 = 80 books. The 27 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 132 = 38. To maximize the number of books borrowed by 1 student, let's assume that 12 students borrowed 3 books and 1 student borrowed the rest. 80 - 38 - 312 = 6 The maximum number of books borrowed by any student is 6. The answer is D. #### D QUESTION:Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made? options: A)500 B)1000 C)1500 D)2000 E)None of these SOLUTION:C.P. for one coconut = 150⁄100 = 3⁄2 S.P. for one coconut = 2 Profit on one coconut = 2 - 3⁄2 = 1⁄2 ∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000 Answer B #### B QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision? options: A)2003 B)2009 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009. Answer: B. #### B QUESTION:By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? options: A)9 B)4 C)8 D)7 E)65 SOLUTION:80% --- 12 120% --- ? 80/120 * 12 = 8 Answer: A #### A QUESTION:A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)14 liters B)76 liters C)10 liters D)11 liters E)12 liters SOLUTION:Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (30 + P) and total volume of mixture is (150 + P). (30 + P) = 25/100 * (150 + P) 120 + 4P = 150 + P => P =10 liters. Answer: C #### C QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)285 m B)240 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x = 285 m. Answer: A #### A QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? options: A)34 days B)40 days C)46 days D)50 days E)None of these SOLUTION:Explanation: Less Cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) [Cows1 50 Bags 50 1]::50:x =>x∗50∗1=50∗1∗50 =>x=50 Option D #### D QUESTION:A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway? options: A)1 min B)2 min C)3 min D)4 min E)5 min SOLUTION:C 3 min d = 24 * 1/4 m + 54 m = 60 m T = 60 meters / 20 meters/min = 3 min #### C QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.50.5x = x/4 y%x = 36 (y/100)x = 36 (x/400)x = 36 x^2 = 36400 x = 120 The answer is E. #### E QUESTION:20, 19, 17, ?, 10, 5 options: A)14 B)15 C)13 D)18 E)17 SOLUTION:A 14 The Pattern is - 1, - 2, -3, ... #### A QUESTION:Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow? options: A)1/2 B)1/5 C)3/4 D)1/3 E)3/5 SOLUTION:This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow. So, possible options for this other ball would be: W, W, B, B (as one yellow is already picked) So the probability for that ball to be yellow too is 2/4=1/2. Option A #### A QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B QUESTION:The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute? options: A)230/(30+10A) B)230/(30+60A) C)230/38A D)220/(30+10A) E)220/40A SOLUTION:Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution. Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes. 230 Kms in 60 minutes ==> 3.8km/hr. Substitute A with 3 in the answer options. Option A #### A QUESTION:The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to: options: A)0.48 B)5.8 C)0.58 D)0.058 E)0.0058 SOLUTION:= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2/0.09 x 93 x 100 = 489/9 x 93 x 10 = 163/279 x 1/10 = 0.58/10 = 0.058 (or) 0.06. Answer is D. #### D QUESTION:Albert borrowed a total of $ 6000 from john and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)571 B)581 C)441 D)445 E)631 SOLUTION:Let x be the amount borrowed form john. So amount borrowed form Charlie = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 37/1002100 = 441. C #### C QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 --> In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6. Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8. Answer: B. #### B QUESTION:3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig. options: A)300 B)350 C)400 D)425 E)275 SOLUTION:Explanation: Average price of a hen = Rs.30 total price of 10 hens = 1030 = Rs.300 But total price of 3 pigs and 10 hens = Rs. 1200 Total price of 3 pigs is = 1200 - 300 = 900 Average price of a pig = 900/3 = Rs. 300 Answer: A #### A QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 242=48 Answer(B) #### B <<<Examples ends QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A,B,C can complete a piece of work in 24,6 and 12 days respectively. Working together, they will complete the same work in how many days? options: A)13/8 B)26/11 C)24/7 D)12/13 E)1/2 SOLUTION:(A+B+C)'s 1day work = (1/24)+(1/6)+(1/12) = 7/24 A,B,C together will complete the work in 24/7 days Answer is C #### C QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/9 D)5/12 E)5/33 SOLUTION:First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve. We will use the formula: nC2 = n(n-1)/2 which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here 12C2=12(11)/2=611=66 That’s the total number of pairs we could pick from the twelve employees. That’s our denominator. For the numerator, we want every combination of two from the five female employees. That’s 5C2=5(4)/2=52=10 That’s the number of pairs of female employees we could pick from the five. That’s our numerator. probability= 10/66 =5/55 Answer = E #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9m = 150 m. ANSWER:D #### D QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 1000(1 + 2/100)^4 = 1000 51/50 * 51/50 * 51/50 * 51/50 = $1082.43 C.I. = 1082.43-1000 = $82.43 Answer is B #### B QUESTION:A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips? options: A)48 km/hr B)56 km/hr C)60 km/hr D)52 km/hr E)None of these SOLUTION:Explanation: Method : 1 If a car covers a certain distance atxkmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph. By using the same formula, we can find out the average speed quickly Speed with which he travels from A to B = x = 40 km/hr Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr average speed = (2×40×60)/(40+60) = 48 km/hr Assume that distance from A to B = x km Speed with which he travels from A to B = x = 40 km/hr Time to travel from A to B = distance/speed = x/40 hr Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr Time to travel from B to A = distance/speed = x/60 Total distance traveled = x+x = 2x Total time taken = x/40 + x/60 Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60) = 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr Answer: Option A #### A QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=u ii. u is not equal to v iii. s > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true. Answer: D. #### D QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number options: A)400 B)256 C)120 D)490 E)None of these SOLUTION:Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 x = 14 * 5040 x = (145040)/144 = 490 Option D #### D QUESTION:Find the one which does not belong to that group ? options: A)237 B)232 C)223 D)426 E)111 SOLUTION:Explanation: 525 => 5 52, 39 => 3 32, 24 => 2 22, 636 => 6 62. The above pattern is not followed in 426. Answer: D #### D QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be? options: A)1 B)2 C)3 D)5 E)7 SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number. If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum. Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3. The correct answer is choice (C). Note:1 is not a prime number. #### C QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? options: A)66 B)70 C)72 D)75 E)78 SOLUTION:Let the distance one way be x Time from home to work = x/60 Time from work to home = x/100 Total time = 2 hrs (x/60) + (x/100)= 2 Solving for x, we get x = 75 Time from home to work in minutes= (75)60/60 = 75 minutes Ans= D #### D QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West options: A)I,II only B)II,III only C)II only D)I and III only E)III only SOLUTION:It's evident if we make a diagram for the Movement of N respect to M. From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range. Thus it can only move north or west or anything in that curve. Answer : D #### D QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2 SOLUTION:Ans: Very interesting question. As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls Probability of choosing any box is 1/ 2. So probability of taking one red ball = 12×(1)+12(3864)≃0.8 Answer:B #### B QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). (140/100 * 5x), (150/100 * 7x) and (175/100* 8x) 7x, 21x/2 and 14x The required ratio = 7x : 21x/2 : 14x 14x : 21x : 28x 2 : 3 : 4 Answer = A #### A QUESTION:Calculate the cost of j bottles of wine given that the cost of k bottles of said wine is c rupees? options: A)Rs.(ck) B)Rs.(jk) C)Rs.(j-k) D)Rs.(c/k) E)Rs.(jc/k) SOLUTION:Cost of k bottles = Rs. c. Cost of 1 bottle = Rs. c/k Cost of j bottles = Rs.(c/k)* j= Rs.(jc/k) Answer is E. #### E QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective? options: A)4% B)5% C)6% D)11% E)16% SOLUTION:1/6 of the switches are defective. The defective switches that are not rejected are 1/51/6 = 1/30 = 4/120 of all switches. The non defective switches that are sold are 5/619/20 = 95/120 of all switches. The percent of switches sold that are defective is 4/99 which is about 4%. The answer is A. #### A QUESTION:A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is: options: A)59 7/12 min. past 3 B)4 p.m. C)58 7/12 min. past 3 D)58 7/11 min. past 4 E)2 3/11 min. past 4 SOLUTION:Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37/4 hrs. 3 min. 5 sec. of this clock = 3 min. of the correct clock. 37/720 hrs of this clock =1/20 hrs of the correct clock. 37/4 hrs of this clock =1/20 x 720/37 x 37/4 hrs of the correct clock. = 9 hrs of the correct clock. The correct time is 9 hrs after 7 a.m. i.e., 4 p.m. Answer: B #### B QUESTION:A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? options: A)120 B)335 C)784 D)217 E)210 SOLUTION:Let x be the number he chose, then 2x138=102 2x=240 x=120 correct answer A #### A QUESTION:A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages options: A)30 B)35 C)37 D)41 E)42 SOLUTION:Explanation: Let A's age 10 years ago = x years. Then, B's age 10 years ago = 2x years. (x + 10) / (2x+ lO) = 3/4 => x = 5. So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years Option B #### B QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres? options: A)20 B)200 C)300 D)400 E)100 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 9540 [4L - 40] = 9540 / 26.50 = 360 4L = 400 L = 400/4= 100 meters. Answer: E #### E QUESTION:In the x-y plane, the area of the region bounded by the graph of \|x+y\| + \|x-y\| = 10 is options: A)8 B)625 C)16 D)20 E)24 SOLUTION:I've never seen such kind of question in GMAT before. OK there can be 4 cases: \|x+y\| + \|x-y\| = 10 A. x+y+x-y = 10 --> x=5 B. x+y-x+y = 10 --> y=5 C. -x-y +x-y= 10 --> y=-5 D. -x-y-x+y=10 --> x=-5 The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be2525=625 Answer: B #### B QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B? options: A)96 B)75 C)48 D)25 E)12 SOLUTION:.24 of B = Remainder .24 of B = 18 B = (18100) / 24 = 75. B #### B QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)23% B)56% C)70% D)35% E)20% SOLUTION:C C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 420 - 125 = Rs. 295 Required percentage = 295/420 * 100 = 1475/21 = 70% #### C QUESTION:3,9,27,81,.... options: A)583 B)604 C)616 D)243 E)636 SOLUTION:13=3 33=9 93=27 273=81 813=243 ANSWER:D #### D QUESTION:Calculate the number of bricks, each measuring 25 cm 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long? options: A)40 B)46 C)88 D)77 E)21 SOLUTION:: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 215 = 575 m Required time = 575 * 2/25 = 46 sec Answer:B #### B QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 45678=6720. ANS:A #### A QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? options: A)12500 B)27767 C)16688 D)26678 E)19987 SOLUTION:Let the CP be Rs. x. Had he offered 25% discount, profit = 8% Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500 => 1.08x = 13500 => x = 12500 \Answer: A #### A QUESTION:A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)70 hours B)30 hours C)35 hours D)50 hours E)40 hours SOLUTION:Efficiency of pipes A,B,C =1:2:4 Therefore, in 10 hours, part of the tank filled by A =17 Therefore, pipe A alone requires 10×7=70 hours to fill the tank. Answer: Option A #### A QUESTION:A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ? options: A)10 B)14 C)16 D)18 E)21 SOLUTION:5C1 * 3C1 -1 = 15-1 = 14 B #### B QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square options: A)337 B)297 C)266 D)116 E)130 SOLUTION:Explanation: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 Required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square. Answer: E #### E QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 600 = 80/100 * 600 = 480 Option A #### A QUESTION:Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is : options: A)20% B)12% C)9.09% D)5% E)None of these SOLUTION:Explanation : Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200. Gain% = 7200-6600/6600100 = 9.09% Answer : C #### C QUESTION:How many of the positive factors of 17 are not factors of 34? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 17 - 1, 17 factors of 34- 1, 2, 17, 34, Comparing both, we have three factors of 17which are not factors of 34- no factors The answer is A #### A QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 1215=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? options: A)22 km B)40 km C)65 km D)18 km E)16 km SOLUTION:Distance = Relative Speed * Time = (7 + 3) * 4 = 40 km [ They are travelling in the opposite direction, relative speed = sum of the speeds]. Answer: B #### B QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 * price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in? options: A)8 min B)7 min C)5 min D)9 min E)4 min SOLUTION:1/10 + 1/15 - 1/x = 1/42 x = 7 Answer: B #### B QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (10080)/(8001) = 10% Answer: E #### E QUESTION:By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.300 D)s.450 E)s.550 SOLUTION:SP = 500 Profit = 25% CP = (SP)[100/(100+P)] = 500 [100/125] = 400 Loss = 25% = 25% of 400 = Rs.100 SP = CP - Loss = 400 - 100 = Rs.300 ANSWER:C #### C QUESTION:What least value must be assigned to * so that th number 1975462 is divisible by 9? options: A)2 B)4 C)6 D)1 E)3 SOLUTION:Let the missing digit be x Sum of digits = (1+9+7+x+5+4+6+2)=34+x For 34+x to be divisible by 9 , x must be replaced by 2 The digit in place of x must be 2. ANSWER A 2 #### A QUESTION:24 machines can do a work in 10days. How many machines are needed to complete the work in 40days? options: A)10 B)6 C)4 D)7 E)5 SOLUTION:Required number of machines = 2410/40 = 6 Answer is B #### B QUESTION:The ratio of the prices of three articles X, Y and Z is 8 : 5 : 3. If the prices of X , Y and Z are increased by 25%, 20% and 33 1/3% respectively, then what would be the ratio of the new prices of X, Y and Z? options: A)5 : 3 : 1 B)5 : 3 : 2 C)10 : 7 : 4 D)10 : 8 : 5 E)None of these SOLUTION:Let the prices of X, Y and Z be 8k, 5k and 3k respectively. After increase Price of X = 8k * 125/100 = 10k Price of Y = 5k * 120/100 = 6k Price of Z = 3k * (133 1/3)/100 = 4k Required ratio = 10k : 6k : 4k = 5 : 3 : 2. ANSWER:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)66 B)52 C)58 D)55 E)56 SOLUTION:Though 2(8C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches. Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches. This continues like this and the total matches are 14+12+10...+2 14+12+...+2 = 2(7+6+...+1) = 2((78)/2) = 78 =56. ANSWER:E #### E QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? options: A)1/5 B)2/7 C)2/9 D)3/10 E)4/11 SOLUTION:The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9. The answer is C. #### C QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 8:2. If 80% of the Toyota bought and 20% of the Honda bought were SUVâ€™s. How many SUVâ€™s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)69% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 80 and Honda 20, so total number of SUV's bought for Toyota and Honda respectively 80* 80/100=64 and 20* 20/100=4 so total 68 SUV's were bought out of 100 Vehicles bought..so required % is 68% ANSWER:C #### C QUESTION:In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate? options: A)358000 B)368000 C)357000 D)358000 E)367000 SOLUTION:Total number of invalid votes = 15 % of 560000 = 15/100 × 560000 = 8400000/100 = 84000 Total number of valid votes 560000 – 84000 = 476000 Percentage of votes polled in favour of candidate A = 75 % Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000 = 75/100 × 476000 = 35700000/100 = 357000 Answer:C #### C QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work? options: A)10 days B)77 days C)66 days D)55 days E)54 days SOLUTION:A can do the work in 30/2 i.e., 15 days. A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10 So A and B together can do the work in 10 days. Answer: A #### A QUESTION:How many integers between 500 and 1000 are there such that their unit digit is even? options: A)250 B)150 C)500 D)100 E)200 SOLUTION:500 numbers between - 500 and 1000 Out of which half would be even, half odd. Number of even unit digit number = 250. correct option is A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)22 B)25 C)66 D)77 E)91 SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence? options: A)22 B)77 C)70 D)68 E)71 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 4 years, their ages will be 44 and 24. Sum of their ages = 44 + 24 = 68. Answer: D #### D QUESTION:Find the odd man out 4, 15, 40, 121, 364, 1093, 3280 options: A)4 B)15 C)121 D)364 E)3280 SOLUTION:13+1 = 4 43+1 = 13 133+1 = 40 403+1 = 121 1213+1 = 364 3643+1 = 1093 10933+1= 3280 ANSWER:B #### B QUESTION:A can work four times as fast as B. Together they can finish a job in 12 days. In how many days can A complete the job alone? options: A)14 B)15 C)16 D)17 E)18 SOLUTION:B's rate is x and A's rate is 4x. x + 4x = 1/12 x = 1/60 A's rate is 4x = 1/15 A can complete the job in 15 days. The answer is B. #### B QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? options: A)8 B)9 C)9.5 D)10 E)11 SOLUTION:So, she works 30 hours in 3 days So, she works 16 hours in 2 days So in a week she works 46 hours ( 30 + 16 ) and earns $460 So, Hourly wage is 460/46 => 10 Hence answer will be (D) 10 #### D QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 23 x = 6 Answer is E #### E QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? options: A)112 B)77 C)267 D)12 E)99 SOLUTION:Explanation: As the division is by 2, 3, 7 together, the numbers are to be divisible by: 237 = 42 The limits are 100 and 600 The first number divisible is 423 = 126 To find out the last number divisible by 42 within 600: 600/42 = 14.28 Hence, 4214 = 588 is the last number divisible by 42 within 600 Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12 ANSWER: D #### D QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is options: A)8/17 B)7/15 C)3/15 D)5/12 E)1/4 SOLUTION:Person ( A ) ( B ) ( A+B ) Time - ( 15 ) ( 20 ) (-) Rate - ( 20 ) ( 15 ) ( 35 ) Work -(300) (300) (300) therefore A+B requires (300/35) days to complete entire work For 1st 5 days they work 35 5 = 175 Remaining work is 300 - 175 = 125 Remaining fraction of work is = 125/300 = 5/12 Answer D #### D QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit? options: A)20000 B)10000 C)25000 D)34000 E)40000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000 E #### E QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N * 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:The average of first 20 natural numbers is? options: A)5.6 B)10.5 C)10.1 D)5.8 E)5.2 SOLUTION:Sum of 20 natural no. = 420/2 = 210 Average = 210/20 = 10.5 Answer:B #### B QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is greater than 3? options: A)2 / 3 B)1 / 2 C)3 / 3 D)4 / 5 E)2 / 4 SOLUTION:Only 4, 5 & 6 so, 3 / 6 = 1/2 correct answer B #### B QUESTION:If 0 < a < b and k = (2a + 8b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 10 D)k > 10 E)k > 11 SOLUTION:Here's another approach: k = (2a + 8b)/b = 2a/b + 8b/b = 2(a/b) + 8 Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2. So, we get k = (some number less than 2) + 8 From here, we can see that k must be less than 10 Answer: C #### C QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)50 SOLUTION:Relative speed of the train=63-3=60kmph=605/18=50/3 m/sec t=5003/50=30sec ANSWER:B #### B QUESTION:A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour. To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/65 =6 Answer (E) #### E QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)22 B)30 C)48 D)99 E)12 SOLUTION:Relative speed = 90 + 30 = 120 km/hr. 120 * 5/18 = 100/3 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 3/100 = 30 sec. Answer: B #### B QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!10! 1211/21 =66 ANSWER:D #### D QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:26=12.Answer is B. #### B QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%? options: A)700 B)882 C)772 D)652 E)271 SOLUTION:Cost price = Rs.500 profit = 40% of 500 = Rs.200 Selling price = Cost price + Profit = 500 + 200 = 700 Answer:A #### A QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:For what value of x, is \|x – 3\| + \|x + 1\| + \|x\| = 8? options: A) 0 B) 3 C) -3 D) 4 E) -2 SOLUTION:For what value of x, is \|x – 3\| + \|x + 1\| + \|x\| = 8? It's easiest just to plug in answer choices: (E): -2 \|x – 3\| + \|x + 1\| + \|x\| = 8? \|-2 - 3\| + \|-2 + 1\| + \|-2\| = 8? \|1\| + \|5\| + \|4\| = 8 (E) #### E QUESTION:During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years? options: A)60 percent decrease B)20 percent decrease C)20 percent increase D)60 percent increase E)140 percent increase SOLUTION:Let the value of the stock in 2000 be 100, then in 2001 its value would be 100(1-80/100)=1000.2=20 and in 2002 its value would be 20(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%. Answer: B. #### B QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7% SOLUTION:Explanation: SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago? options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4 SOLUTION:3x-25/2x-25 = 4/3 Therefore x=-25 Age cannot be negative. Answer: D #### D QUESTION:If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))? options: A)1 B)16 C)81 D)256 E)144 SOLUTION:f(x)=x^2 f(f(x)) = (x^2)^2 =x^4 A. 1 , x=1 B. 16 , x=2 C. 81 , x=3 E. 144 f(x)=12 Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) . D. 256 , x=4 Answer E #### E QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P20R)/100 R = 5% ANSWER:E #### E QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:The equation of line q is y = 4/3x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.510075=0.5125 x => x=60; SO answer is 60=C #### C QUESTION:What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1200 B)1256 C)1349 D)1456 E)1590 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3600 B)3890 C)88798 D)2789 E)3500 SOLUTION:Explanation: Manager's monthly salary Rs. (1500 * 21 - 1400 * 20) = Rs. 3500. Answer: E #### E QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)22 days B)77 days C)24 days D)17 days E)18 days SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days Answer: C #### C QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km options: A)200 Km B)222 Km C)224 Km D)248 Km E)None of these SOLUTION:Explanation: Let time taken to travel the first half = x hr Then time taken to travel the second half = (10 - x) hr Distance covered in the the first half = 21x [because, distance = timespeed] Distance covered in the the second half = 24(10 - x) Distance covered in the the first half = Distance covered in the the second half So, 21x = 24(10 - x) => 45x = 240 => x = 16/3 Total Distance = 221(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way] Option C #### C QUESTION:8 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The number of hours required to complete the work is 8818 = 1152 12 × 12 × (x) = 1152 x = 8 The answer is C. #### C QUESTION:A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? options: A)200 minutes B)240 minutes C)220 minutes D)210 minutes E)77 minutes SOLUTION:Time taken to reach = 6400/32= 200 minutes ANSWER:A #### A QUESTION:In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen? options: A)35. B)45. C)40. D)30. E)25. SOLUTION:Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls. Now here 90% are Boys and 10% are Girls. Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%.. If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it. Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ). IMO option A is correct. #### A QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(1001000)/270-100]+100 = 2600 Answer is B #### B QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? options: A)65 B)66 C)67 D)131 E)130 SOLUTION:The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ... The number of 1 letter words (X) that can be made from 65 letters is 65; The number of 2 letter words (XX) that can be made from 65 letters is 6565, since each X can take 65 values. Total: 65+6565. Similarly: The number of 1 letter words (X) that can be made from 64 letters is 64; The number of 2 letter words (XX) that can be made from 64 letters is 6464, since each X can take 64 values. Total: 64+6464. The difference is (65+6565)-(64+6464)=130. Answer: E. #### E QUESTION:A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? options: A)0.09 B)0.15 C)0.54 D)0.75 E)0.91 SOLUTION:According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 5)/60 = 45/60 = 0.75. Answer: D. #### D QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres? options: A)20 B)200 C)300 D)90 E)140 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 8480 [4L - 40] = 8480 / 26.50 = 320 4L = 360 L = 360/4= 90 meters. Answer: D #### D QUESTION:In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is: options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Solution: Let there were x teams participating in the games, then total number of matches, nC2 = 153. On solving we get, => n =−17 and n =18. It cannot be negative so, n = 18 is the answer. Answer: Option C #### C QUESTION:A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is options: A)4 B)3 C)2 D)1 E)5 SOLUTION:Here we can assume that one subject is of 100 marks so total there are 5 subjects => 1005 = 500. Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total. The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio. Total ratio = 40 For 6 : (300/40)6 = 45 Similarly , we will get for others as 52.5 , 60 , 62.5 , 75. Hence , there are 3 subject where he secured more that 60 %. The answer is 3. B #### B QUESTION:Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd? options: A) 1/2 B) 2/3 C) 3/4 D) 4/7 E) 5/8 SOLUTION:All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even. There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd. Therefore the probability that A + K is odd is 4/7. Answer: D. #### D QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:The product of two numbers a and b equals one-quarter their average. What is a in terms of b? options: A)a= b/(8b-1) B)a= b/(7b-1) C)a= b/(8b) D)a= b/(8b-4) E)a= 2b/(8b-1) SOLUTION:a*b = ( a+b)/8 8ab =a+b a= b/(8b-1) ANSWER:A #### A <<<Examples ends QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction? options: A) 49 B) 9 C) 28 D) 26 E) 21 SOLUTION:x/y = 2/5 -> 1 (x+4)/2y = 1/3 -> 2 Divide 1 by 2 : => 2x/(x+4) = 6/5 => 5x = 3x + 12 => x = 6 => y = 5/2 * 6 = 15 so x - y = 9 The answer is B #### B QUESTION:How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. options: A)17280 B)4320 C)720 D)80 E)None of thsee SOLUTION:Explanation: word SIGNATURE contains total 9 letters. There are four vowels in this word, I, A, U and E Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now So total letter are 6. 6 letters can be arranged in 6! ways = 720 ways Vowels can be arranged in themselves in 4! ways = 24 ways Required number of ways = 72024 = 17280 Option A #### A QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(7206)=4320. Answer is E #### E QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:Find the odd number options: A)21 B)17 C)3 D)14 E)12 SOLUTION:Each of the numbers except 14 is an odd number. The number '14' is the only EVEN number. answer :D #### D QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3(20/60) = 7 hr Answer is D #### D QUESTION:The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $744, what is the length of the plot in meters? options: A)11 B)13 C)15 D)17 E)19 SOLUTION:perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20 cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 744 62L = 1054 L = 17 meters The answer is D. #### D QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon? options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x SOLUTION:Amount of gas you added to your car: 19-x Price per gallon: (19-x)/20 Answer: C #### C QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400? options: A)8100 B)3388 C)7767 D)2009 E)22888 SOLUTION:6400* 9/8 * 9/8 = 8100 Answer: A #### A QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? options: A)600 B)320 C)500 D)520 E)720 SOLUTION:Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x. 2x/(x - 160) = 2 + 2(extra) => 2x - 320 = x => x = 320. ANSWER:B #### B QUESTION:Simplify: 256 x 256 - 144 x 144 options: A)761200 B)44800 C)761800 D)761500 E)None of them SOLUTION:(256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800 Answer is B #### B QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:If 280 people, constituting 5 percent of the population of a town, ride bicycles, and the others do not, then how many people in the town do not ride bicycles? options: A)5930 B)5600 C)5320 D)5110 E)4980 SOLUTION:5 % of X is 280 5/100 * X = 280 X = 280100/5 = 5600 So C. 5320 is the correct Answer No. of people Not Riding Bike = 5600 - 280 = 5320 answer is C #### C QUESTION:Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd? options: A)15/56 B)3/8 C)15/28 D)5/8 E)3/4 SOLUTION:Total number of combinations=12C3=220................(1) Total number of combinations including 2 and two other numbers=11C2=55......................(2) Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165 So, probability=165/220=3/4 E #### E QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)(1/5) So it takes 25 men to complete this job = 25 * (1/25) = 1 Answer: C #### C QUESTION:The difference between a number and its three-fifths is 50.What is the number? options: A)75 B)100 C)125 D)Cannot be determined E)None of these SOLUTION:Suppose the number is N. Then N - 3⁄5N = 50 ⇒ 2N⁄5 = 50 ∴ N=50×52=125 Answer.C #### C QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost? options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80 SOLUTION:3J + 2S = 69 2J + 3S = 81 ---------------- 5J + 5S = 150 ----(divide by 5)---> J + S = 30 3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9 39 + 2S = 69 27 + 2S = 69 2S = 42 S = 21 Answer: D #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers. NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations. The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/5 meter and also 1/8 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 8/40, 16/40, 24/40, 32/40, 40/40, etc... The location of the marks for 1/8 meter would be 5/40, 10/40, 15/40, 20/40, 25/40, 30/40, 35/40, 40/40, etc... The distances between marks are 5/40, 3/40, 2/40, 1/40, and 4/40. The answer is E. #### E QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C? options: A)127 B)150 C)177 D)167 E)122 SOLUTION:A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 590 = Rs.150 Answer:B #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? options: A)525 B)665 C)412 D)235 E)856 SOLUTION:Answer: Option B 8 * 84 = 672 â€“ 7 = 665 #### B QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:212 : 312 : 424 1: 3: 4 1/8 3200 = 400.Answer: D #### D QUESTION:What percent is 400 gm of 1 kg? options: A)25% B)40% C)10% D)8% E)12% SOLUTION:1 kg = 1000 gm 400/1000 Ã— 100 = 40000/1000 =40 % Answer is B #### B QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks? options: A)60 B)80 C)100 D)120 E)140 SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback. If all 160 books were paperbacks, the dealer would earn a profit of $320. Since the actual profit was $400, the dealer must have sold 80 hardbacks. Then the number of paperbacks sold was 160-80 = 80. The answer is B. #### B QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+2050/100 = 60) Family Income is same 50 In June Lee's Income percent is 60100/110 ~ 55 Ans is A #### A QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:If k^2 = h^2, which of the following must be true? options: A)k = m B)\|k\| = \|h\| C)k = \|m\| D)k = -\|m\| E)k = -m SOLUTION:Solution: We are given that k^2 = h^2, and we can start by simplifying the equation by taking the square root of both sides. √k^2 = √h^2 When we take the square root of a variable squared, the result is the absolute value of that variable. Thus: √k^2 = √h^2 is \|k\| = \|h\| Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true. Answer: E #### E QUESTION:In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd? options: A)5/18 B)13/36 C)3/8 D)5/8 E)23/36 SOLUTION:player begins with containing tiles 1 to 10 and have equal probability of selecting means Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there. Next , player draws one title , if number is even player stops or otherwise title is odd without replacement player draws second title. If second title is even , player stops or title is odd without replacement player draws third title. in third title , without replacement of first and second title, player draws and stops it. the sum of tilte probability is odd. here two conditions are possible. 1st condition is 1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/105c1. Here are we are not selecting 1st condition as even stops because sum of tile is odd. Here 5 odd numbers are there we can select 1out of 5 odd numbers. without replacement of fist we select second tilte is even. is 5/105c1/9c1. here we are selecting one number out of remaining 9 numbers. so probability is 5/18. we are selecting 1 even number out of 5. 2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title. Then probability is 5/104/93/8=1/12. Finally sum of probability of two conditions is 5/18+1/12 =5/18. so option A is correct. #### A QUESTION:Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids? options: A)8 B)9 C)3 D)7 E)10 SOLUTION:cost of each apple = 4 dollars Apples that Benny can buy with the amount she has=360/4 = 90. Apples that each kid gets evenly = 90/9 =10 Apples. So the answer is E=10 #### E QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 7? options: A)56 B)112 C)224 D)448 E)425 SOLUTION:Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4) so range is 7n+28-7n = 28 if we put the different values of n we will get different but the range will be multiple of 28 and only 425 is not multiple of 28 Answer : E #### E QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:In how many ways can the letters of the word STATE be arranged? options: A)60 B)1348 C)2520 D)3000 E)3478 SOLUTION:STATE has 5 words, but T is repeated two times. Thus ways = 5! / 2! = 60 ways A #### A QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ? options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8 SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed) let E is the event of getting at least 1 head and 1 tail n(E) = TTH , HTT, THT, HHT, HTH, THH = 6 P(E) = n(E) / n(s) = 6/8 = 3/4 Ans- C #### C QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together? options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21) SOLUTION:A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 1/2 days. The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days. Answer:D #### D QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0-10 inclusive to find one smallest other two should be highest so, lets assume three var are a,b,c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 E #### E QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is? options: A)30 B)45 C)50 D)60 E)75 SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2 1^3+2^3+3^3+-----+5^3 = (56/2)^2 = 225 Required average is = 225/5 = 45 Answer is B #### B QUESTION:How many numbers from 29 to 79 are exactly divisible by 11 options: A)5 B)7 C)8 D)9 E)11 SOLUTION:29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers Option 'A' #### A QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ? options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830. Answer: B #### B QUESTION:What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it? options: A)600 B)602 C)604 D)606 E)608 SOLUTION:The nth term is 2+3(n-1). The 201st term is 2 + 3(200) = 602 The answer is B. #### B QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)100 =66 2/3% Ans C #### C QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision? options: A)2003 B)2009 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009. Answer: B. #### B QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 1.16.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time in minutes that the three pipes together will take to fill the cistern is options: A)5 B)6 C)8 D)3 E)9 SOLUTION:A 5 #### A QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3 SOLUTION:total 10 from take one. 10c1=10 red 6 from one 6c1=6 6/10= 3/5 ANSWER:C #### C QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)227 B)299 C)276 D)600 E)211 SOLUTION:Speed = [72 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600 Answer: D #### D QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(200) / 400 = 25% The answer is B. #### B QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence? options: A)2 B)-2 C)0 D)8 E)9 SOLUTION:Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term. An = 282 + (40 - 1)(-7) An = 282 - 273 = 9 E #### E QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:The second of two numbers is two less than three times the first. Find the numbers if there sum is 74. options: A)7-19 B)8-20 C)10-16 D)15-9 E)19-55 SOLUTION:We are looking for two numbers. #1 - x #2 - 3x â€“ 2 The sum is 74. #1 + #2 = 74 Substituting x + 3x â€“ 2 = 74 4x â€“ 2 =74 4x = 76 x = 19 The first number is 19, the second number is two less than three times 19 or 55. correct answer E #### E QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:Three friends (Caleb, Jerry and Elvis) are employees of a company. Their respective salaries are in the ratio of 3 : 4 : 6. Jerry and Elvis's salaries together is Rs. 10000. By what percent is Elvis's salary than that of Sarah? options: A)500%. B)400%. C)300%. D)200%. E)100%. SOLUTION:Explanation: Let the salaries be 3x, 4x and 6x respectively. Then,4x + 6x = 10000 => x = 1000. Caleb's salary = Rs. 3000, , Jerry's salary = Rs. 4000, and and Elvis's salary Rs. 6000. Excess of Elvis's salary over Caleb's=[ (3000 /3000) x 100] = 100%. Answer: E #### E QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.? options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454 SOLUTION:it is given that last 3 digits are randomly dialed Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability = 1/(10)3 = 1/1000 C #### C QUESTION:Which of the following is closest to (-6/7)^199？ options: A)-1 B)-1/2 C)0 D)1 E)2 SOLUTION:(-6/7)^4 = 1296/2401 which is already close to 1/2. For larger exponents, the expression will get closer and closer to zero. The answer is C. #### C QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code? options: A)22 B)23 C)697 D)66P E)82 SOLUTION:Answer: Option B #### B QUESTION:A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum? options: A)22887 B)2677 C)2987 D)8925 E)17711 SOLUTION:Principal = (100 4016.25) / (9 * 5) = Rs. 8925. Answer:D #### D QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible? options: A)252 B)1,680 C)2,340 D)362,880 E)592,704 SOLUTION:The ways to select three employees out of 9 for first project = 9C3 The ways to select three employees out of Remaining 6 for Second project = 6C3 Third Project already has the group of three to be assigned to it so need to select that So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680 Answer: Option B #### B QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is: options: A)240 B)120 C)280 D)160 E)200 SOLUTION:Let C's share = Rs. x Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6 Therefore, x/6 + x/4 + x = 1360 =17x/12 = 1360 x = 1360 x 12/17= Rs. 960 Hence, B's share = Rs. (960/4)= Rs. 240. Answer is A. #### A QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 10050= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 11557.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday? options: A)X. B)X/2. C)2X/3 D)X/3 E)X/4. SOLUTION:Given the value of stock is X dollars. Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value) Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6 Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value) Ans: A is correct option.. #### A QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:If x + \| x \| = 0, which of the following must be true? options: A)x > 0 B)x≥0 C)x < 0 D)x≤0 E)x = 0 SOLUTION:Manipulate the equations: x + \| x \| = 0 \|x\| = -x -x > 0 OR -x = 0 This means x could be 0 or x is less than 0. D. x≤0 E. x=0 Answer: D #### D QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:2^23^32^23^6 = options: A)3^52^5 B)2^93^4 C)2^43^9 D)5^8 E)6^10 SOLUTION:2^23^32^23^6 = A) 3^52^5 B) 2^93^4 C) 2^43^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^43^9. Hence the answer is C #### C QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55800)/100 =>440 15% of his 440 marks is 440(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed? options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph SOLUTION:424/(13/2) = 4242/13 =65.2 kmph ANSWER:C #### C QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : options: A)8 B)9 C)4 D)18 E)None SOLUTION:Ratio of rates of working of A and B = 2 : 1 So, ratio of times taken = 1 : 2 B's 1 day's work = 1/12 Therefore A's 1 day's work = 1/6 (A + B)'s 1 day's work = (1/6 + 1/12)= 1/4 So, A and B together can finish the work in 4 days. Answer: C #### C QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Minimuum should be 1 Maximum should be 4: 1 out of a or b to make the multiplication negative 3 out of c, d, e or f to make the multiplication negative. Negative+Negative<0 Answer:C maximum will be 5.. you dont require both the multiplicatin to be negative for entire equation to be negative... any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers... actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation.. ans D #### D QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 400 paper clips. How many paper clips are contained in 2 cases? options: A)400bc B)400b/c C)800bc D)800b/c E)800/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 400 clips/box = 800bc paper clips The answer is C. #### C QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x15 x = 9/15=3/5 Answer: D #### D QUESTION:If 13 = 13w/(1-w) ,then (4w)2 = options: A)1/4 B)1/2 C)1 D)2 E)4 SOLUTION:13-13w=13w 26w=13 w=1/2 4w=2 4w2=22=4 ANSWER:E #### E QUESTION:Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have? options: A)5 B)10 C)30 D)40 E)50 SOLUTION:Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)100% = 60% Now by Alligation Rule: A . ......... B 20% . . . 80% . . 60% . . (80-60) . (60-20) =20 : =40 Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration) So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%) So as per above ration Qty B mixed will be 50 gallons. Qty of water in mixture B = 20% of 50 = 10 gallons. ANSWER:B #### B QUESTION:The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is? options: A)6.06% B)6.07% C)6.08% D)6.09% E)6.19% SOLUTION:Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% ANSWER:D #### D QUESTION:Two numbers are less than third number by 35% and 37% respectively. How much percent is the second number less than by the first options: A)8% B)10% C)33% D)41% E)42% SOLUTION:Let the third number is x. then first number = (100-35)% of x = 65% of x =65x/100 Second number is (63x/100) Difference =65x/100 - 63x/100 = x/50 So required percentage is, difference is what percent of first number (x/50 * 100/65x * 100 )% = 33% ANSWER :C #### C QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 â€“ 120 = 213 Answer: A #### A QUESTION:The average of four consecutive odd numbers is 24. Find the largest number. options: A)25 B)27 C)29 D)31 E)32 SOLUTION:Explanation: Let the numbers are x, x+2, x+4, x+6, then =>x+(x+2)+(x+4)+(x+6)4=24 =>4x+12)4=24 =>x+3=24=>x=21 So largest number is 21 + 6 = 27 Answer: Option B #### B QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h The answer is D. #### D QUESTION:When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents? options: A)17 years B)11 years C)6 years D)5 years E)8 years SOLUTION:When age of Son=0 ,Mother=23 After 6 years, Son=6 ,Mother=23+6=29 ,Father=34 So difference between ages of Mother & Father=34-29=5 ANSWER:D #### D QUESTION:The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers? options: A)16 B)18 C)13 D)20 E)22 SOLUTION:We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r. The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s. Since s must be greater than r, r can be 10+3 = 13 and s can be 10+4 = 14. So r is 13. Answer (C) #### C QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%. options: A)13.6% B)28.6% C)35.6% D)42.3% E)none SOLUTION:Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90. âˆ´ Gain % = [20/70 * 100]% = 28.6%. Answer B #### B QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(1001000)/270-100]+100 = 2600 Answer is B #### B QUESTION:If w and t are positive integers, wt + w + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let wt + t + w = x Add 1 on both sides: wt + t + w + 1 = x + 1 t(w + 1) + w + 1 = x + 1 (w + 1)(t + 1) = x + 1 Minimum value of (w + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> wt + t + s cannot be 6 Answer: B #### B QUESTION:The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries? options: A)3 : 3 : 10 B)10 : 11 : 20 C)23 : 33 : 60 D)Cannot be determined E)None of these SOLUTION:Explanation: Let A = 2k, B = 3k and C = 5k. A's new salary = 115/100 of 2k=23k/10 B's new salary =110/100 of 3k =33k/10 C's new salary = 120/100 of 5k =6k =23:33:60 Answer is C #### C QUESTION:An employer has 4 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection? options: A)a) 1,490 B)b) 132 C)c) 120 D)d) 60 E)e) 23 SOLUTION:4C3 * 4C2 = 24. Answer C. #### C QUESTION:For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? options: A)50 B)55 C)48 D)42 E)49 SOLUTION:Mean+5SD=86 Mean+2.5SD=67 By solving above equations we get, SD (absolute value)=7.6 Mean=48 ANS. C #### C QUESTION:A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man’s rate in still water and rate of current? options: A)8.5 B)10.0 C)12.5 D)11.0 E)8.25 SOLUTION:Rate of still water = 1/2 (down stream + upstream) = 1/2 (45 + 23) = 34 Kmph rate of current = 1/2 (down stream - upstream) = 1/2 (45 - 23) = 1/2 (22) = 11 kmph Answer is D. #### D QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (543!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color? options: A)2/5 B)1/15 C)1/9 D)1/10 E)1/25 SOLUTION:Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1 Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color). Thus the total probability = 11/15=1/15. B is the correct answer. #### B QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 21 months? options: A)18:11 B)18:15 C)21:11 D)18:121 E)18:112 SOLUTION:A invests Rs.8000 for 21 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 800021 : (80004) + (400014) 168000 : 88000 A:B = 21:11.Answer:C #### C QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A. options: A)240 B)388 C)288 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 * 756 = 288 Answer: C #### C QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (11) = 2. 2(result) + (22) = 6. 6(result) + (33) = 15. 15(result) + (44) = 31. 31(result) + (5*5) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A <<<Examples ends QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 155/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 35 60 = 1750 m Answer is B #### B QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 100 = 33% Answer:C #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability Q that both will be juniors? options: A)1/10 B)1/5 C)2/9 D)2/5 E)1/2 SOLUTION:I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors. 2 seniors = P(Senior) * P(Senior) = 2/9 1 Senior and 1 Junior = (1/2) (5/9)2 = 5/9 Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability Q that it is two juniors is 1- (7/9) = 2/9.C #### C QUESTION:If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches? options: A)Rs 900 B)Rs 800 C)Rs 1,800 D)Rs 2,800 E)None of these SOLUTION:Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425 Profit = Rs (425 - 200) = Rs 225 Profit of 8 watches = Rs 225 x 8 = Rs 1,800 ANSWER:B #### B QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X? options: A)11 B)15 C)12 D)19 E)20 SOLUTION:D 19 (X + Y) â€“ (Y + Z) = 19 X â€“ Z = 19 #### D QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:What is the sum of all even numbers from 1 to 401? options: A)122821 B)281228 C)281199 D)122850 E)40200 SOLUTION:Explanation: 400/2 = 200 200 * 201 = 40200 Answer: E #### E QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:Which of the following numbers is not prime? options: A)50+70 B)150 -23 C)100+67 D)156-7 E)103+36 SOLUTION:10 can be factored out of both 50 and 70. -->50+70= 10(5+7). The correct answer is A. #### A QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out? options: A)678.6 m3 B)36 m3 C)40 m3 D)44 m3 E)None SOLUTION:Solution Volume = πr2h ‹=› (22 /7 ×3×3×24)m3 ‹=›678.6 m3. Answer A #### A QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)40% D)62% E)80% SOLUTION:We need multipliers. multiplier for a 10% increases = 1 + 0.10 = 1.1 multiplier for a 20% decreases = 1 – 0.20 = 0.8 multiplier for a 50% increases = 1 + 0.50 = 1.5 Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3 (0.8)(1.5) = (0.4)(3) = 1.2 Now, multiply this by 1.1 1.21.1 = 1.32 Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B QUESTION:A person walking at 4 Kmph reaches his office 6 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)4 1/5 Km B)4 1/7 Km C)3 1/5 Km D)3 1/7 Km E)2 4/5 Km SOLUTION:Formula = S1S2/S2-S1 T1+T2/60 = 46/2 14/6 = 24/2 * 14/60 = 7 * 2/5 = 14/5 = 2 4/5 Km E) #### E QUESTION:In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school? options: A)5:2 B)2:3 C)10:3 D)3:7 E)2:5 SOLUTION:10% of B = 1/3 G 10B/100 = G/3 B = 10G/3 B/G = 10/3 B:G = 10:3 Answer is C #### C QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32900+83000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 1060 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:Half of 5 percent written as decimal is options: A)5 B)0.5 C)0.05 D)0.025 E)None of these SOLUTION:Explanation: It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025 Answer: Option D #### D QUESTION:A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? options: A)3.6 sec B)18 sec C)36 sec D)72 sec E)None of these SOLUTION:Speed of train relative to jogger = (45 – 9) km/h = 36 km/h = (36 × 5⁄18) m/sec = 10 m/sec Distance to be covered = (240 + 120) m = 360 m. ∴ Time taken = (360⁄10) sec = 36 sec. Answer C #### C QUESTION:The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy? options: A)8 B)10 C)7 D)6 E)5 SOLUTION:6x + 10x + 8x = 40 x =1.6 6x = 10 Answer:B #### B QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum E of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: E=2550+(10050)=7550.B #### B QUESTION:In a class, the average age of 42 boys is 12 years and the average of 28 girls is 10 years. what is the average age of the whole class? options: A)11.2 Years B)12.6 Years C)13 Years D)13.5 Years E)14 Years SOLUTION:Total age of 70 students (42X 12+28 X 10) = 784 Average = 784/70 = 11.2 Years A) #### A QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr? options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1 SOLUTION:Speed = 54 * 5/18 = 15 m/sec Time taken = 100/15 = 6.67 sec. Answer:C #### C QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 3001 = revenue (eq -1) if he reduced his price by 20% then , 240(customer) = 125/100revenue customer = 1.25300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled? options: A)600 B)700 C)800 D)850 E)None of these SOLUTION:Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 280 (406 = 240) 100% -----> 600 (1006 = 600) Answer: Option A #### A QUESTION:If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M. options: A)2574 B)2500 C)1485 D)1574 E)None of these SOLUTION:Explanation: HCF * LCM = 17820, because we know Product of two numbers = Product of HCF and LCM LCM = 17820/12 = 1485 Option C #### C QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is? options: A)100 B)110 C)160 D)130 E)140 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 8 = 160 m. Answer: Option C #### C QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km SOLUTION:M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer: B #### B QUESTION:Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid? options: A)$1116.3 B)$3583.3 C)$3283.3 D)$3683.3 E)$2683.3 SOLUTION:Explanation: Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3 Answer: Option D #### D QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ? options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these SOLUTION:Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 ANSWER:C #### C QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^aq^b no of factors is given by the formula (a+1) (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pir^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)2121/4 = 346.5 sq m answer :C #### C QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 58820 = 44, 100, which is a square of 210 B #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is options: A)25 years B)30 years C)35 years D)40 years E)None SOLUTION:Sol. Let their ages of x years and (x + 10) years respectively. Then, (x + 10) - 15 = 2(x - 15) ⇔ x - 5 = 2x - 30 ⇔ x = 25. ∴ Present age of the elder person = (x + 10) = 35 years. Answer C #### C QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width? options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3 SOLUTION:2x+2y=50 x+y=25 x+4x=25 5x=25 x=5 Answer C #### C QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 40007 = 28000. Answer : Option A #### A QUESTION:The radius of a semicircular plot is 25. What is the approximate perimeter of the plot? options: A)114 B)150 C)129 D)25 E)57 SOLUTION:perimeter of a circle =2pir perimeter of a semicircle = pir + 2r aprox perimiter = 3.1425 + 225 = 128.50 approximately 129 answer C #### C QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is: options: A)6 hours B)10 hours C)15 hours D)30 hours E)35 hours SOLUTION:suppose first pipe filled the tank in x hour so second in x-5 and third in x-9 1/x+1/(x-5)=1/(x-9) by solving it we get x=15 ANSWER:C #### C QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (38 + 24):(48 + 54) 8:13 8/21 672 = 256 Answer: A #### A QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)15 1/3 days B)13 1/3 days C)19 1/3 days D)11 1/3 days E)12 1/3 days SOLUTION:B 13 1/3 days 5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days #### B QUESTION:The area of a triangle is with base 4m and height 5m? options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2 SOLUTION:1/2 * 4 * 5 = 10 m2 Answer:B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 3016=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets? options: A)1 hour and 20 minutes B)1 hour and 24 minutes C)1 hour and 30 minutes D)1 hour and 36 minutes E)1 hour and 40 minutes SOLUTION:(350+250)t=800 600t=800 t=4/3 t=1 hour and 20 minutes Answer: A #### A QUESTION:The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16? options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Given: x=16k (where k is a positive integer) and √x=√16k >16 --> x=16k>16^2 --> divide by 16. So as x/16=k=integer>16, then x/16 can be 17, 18, ... Answer: E. #### E QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was: options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years. SOLUTION:Let the son's present age be x years. Then, (48 - x) = x 2x = 48. x = 24 Son's age 4 years back (24- 4) = 20 years. ANSWER :D #### D QUESTION:The area of a triangle will be when a = 3m, b = 5m, c = 10m, a, b, c being lengths of respective sides? options: A)3 B)6 C)4 D)9 E)1 SOLUTION:S = (3 + 5 + 10)/2 = 9 Answer:D #### D QUESTION:At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.) options: A)96 B)240 C)E=256 D)E=384 E)E=480 SOLUTION:Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers.... We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E #### E QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees. options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3 SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7 Answer is A #### A QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 5/6 = 5 #### C QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __? options: A)276 B)277 C)278 D)279 E)None of these SOLUTION:Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B #### B QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ? options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Expanding we have 6x^2 - 3x + 4x -2 6x^2 + x - 2 Taking coefficients, a = 6, k= 1, n = -2 Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9 The answer is C. #### C QUESTION:Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? options: A)670 B)710 C)750 D)790 E)830 SOLUTION:total pay = 40$12.50 + $0.16x = 620 x = 120 / 0.16 = 750 The answer is C. #### C QUESTION:A company recently conducted a survey and found that 40,000 of its customers live in rural areas. If the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas, how many customers live in urban areas? options: A)90,000 B)91,200 C)92,400 D)93,600 E)94,800 SOLUTION:The number of customers in urban areas is 40,000+1.3740,000=94,800. The answer is E. #### E QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 1045 900 = 2045 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. options: A)1628.4 B)1534 C)1492 D)240 E)None of these SOLUTION:Solution: Let average expenditure of 10 people be x. then, 10x = 205+5(x+4); Or, 10x = 205+5x+20; Or, x = 24; So, total money spent = 2410 = Rs. 240. Answer: Option D #### D QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate. options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10 SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity. Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job. Answers E, A and C are illogical, since the individual times must both be greater than 10 days. so we can TEST the values for Answers B and D. Using the values for Answers C and D... Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match Final Answer: C #### C QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. O=12.56 = 75=E #### E QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 69 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let number of mangoes be x, number of oranges be 12-x 0.80x +(20-x)0.60/20 = 0.69 solving for x, we get x = 9 --> Mangoes 9, Oranges 11 Now, number of oranges to be returned be y 0.809 + (11-y)0.60/20-y = 0.72 solving for y, y = 5 Ans: B #### B QUESTION:How many different positive integers are factors of 196 ? options: A) 1 B) 2 C) 3 D) 49 E) 36 SOLUTION:15, 14×15, 14=7^2 × 2^2 So total factors = (6+1)(6+1) = 49 Answer: D #### D QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390(85/100)(75/100) = 248 Answer: C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross-section is 344 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)40 E)71 SOLUTION:1/2 d (12 + 5) = 344 d = 40 Answer: D #### D QUESTION:The side of a square is increased by 25% then how much % does its area increases? options: A)56.75 % B)56.25 % C)53.85 % D)57.25 % E)56.21 % SOLUTION:a = 100 a2 = 10000 a = 125 a2 = 15625 ---------------- 10000 --------- 5625 100 -------? => 56.25 % Answer:B #### B QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[24+(50-1)2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 35 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)45 E)01 SOLUTION:Explanation: As there is meal for 70 adults and 35 have their meal, the meal left can be catered to 35 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 35 adults = 45 children Hence, the meal can be catered to 45 children. ANSWER: D #### D QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C? options: A)127 B)150 C)177 D)167 E)122 SOLUTION:A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer:B #### B QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface. options: A)142 m sqaure B)122 m sqaure C)135 m sqaure D)188 m sqaure E)None of these SOLUTION:Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(62.25+92.25)]+96 = 122 m square Option B #### B QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed? options: A)502 B)512 C)523 D)521 E)500 SOLUTION:Let n be the total number of children. More children, less notebooks(Indirect proportion) If the number children = n, number of books each child will get = n/8 If the number children = n/2, number of books each child will get = 16 Hence we can write as children n:n/2}::16:n/8 ⇒n×n/8=n/2×16 ⇒n8=16/2=8 ⇒n=8×8=64 Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512 Answer is B. #### B QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number. options: A)42 B)48 C)72 D)67 E)54 SOLUTION:Sol: Let the third number be x. Then second number = 3x. First number=3x/2. Therefore x+3x+(3x/2)=(443) or x=24 So largest number= 2nd number=3x=72 ANSWER :C #### C QUESTION:Find the area of a cuboid of length 10cm , breadth 8 cm . and height 6cm. options: A)400 cm cube B)410 cm cube C)420 cm cube D)430 cm cube E)480 cm cube SOLUTION:Area of a cuboid = lxbxh =10cm x 8cm x 6cm = 480 cm cube answer :E #### E QUESTION:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 1000, what is the least possible value of n? options: A)12 B)11 C)14 D)13 E)15 SOLUTION:1000 = 222555, so we need 3 factors of 2 and 3 factors of 5. Therefore, the smallest value of n is 15, so the answer is E. #### E QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Important point to notice- 2.5% decrease from the original price 2.5% of 22,000= 550 Total reduction in 6 years= 5506= 3300 Final price= 22,000 +1500 - 3300= 20,200 C is the answer #### C QUESTION:Tough and Tricky questions: Combinations. Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? options: A)2 B)4 C)72 D)240 E)720 SOLUTION:2!1!2 = 212 = 4 ways. Ans. B) 4 #### B QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following? options: A)1 B)10 C)10^2 D)10^3 E)10^4 SOLUTION:Because the question asks for what value isclosestthe question invites approximation. Let's look at the numerator: 10^9 - 10^2 10^9 is HUGE compared to 10^2. So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself). Likewise, 10^7 is HUGE compared to 10^3. So 10^7 - 10^3 is very close to 10^7. So we have: 10^9/10^7 or 10^(9-7) = 10^2. Choose C. #### C QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%? options: A)600 B)887 C)256 D)654 E)675 SOLUTION:Cost price = Rs.500 profit = 35% of 500 = Rs.175 Selling price = Cost price + Profit = 500 + 175 = 675 Answer: E #### E QUESTION:Find the odd man out 864, 420, 200, 93, 40, 16, 6 options: A)420 B)200 C)16 D)93 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. 93 ANSWER:D #### D QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 Ã· 16) Ã— 100 #### B QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6 SOLUTION:Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1. ANSWER IS A #### A QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group? options: A)s. 25.6 B)s. 25 C)s. 16.6 D)s. 26 E)s. 25.6 SOLUTION:Total members in the group = 7 Average amount = Rs. 30 Total amount with them = 7 * 30 = Rs. 210 One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150 The average amount with them = 150/6 = Rs. 25 ANSWER:B #### B QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840.At what rate of interest the same amount of interest can be received on the same sum after 5 years ? options: A)6% B)8% C)9% D)10% E)None SOLUTION:Solution S.I. = Rs. 840,R =5%,T= 8 Years. Principal = Rs.(800x840/5x8)= Rs. 2100. Now,P = Rs. 2100,S.I. = Rs. 840, T = 5 years. ∴ Rate =(100x840/2100x5) = 8%. Answer B #### B QUESTION:Which of the below fractions has the highest value? options: A)A)23/77 B)B)23/78 C)C)23/84 D)D)23/87 E)E)23/40 SOLUTION:23/40. Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator. Answer (E). #### E QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there? options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 35 ⇒ 1.75x = 35 ⇒ x = 20 coin Answer A #### A QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5 SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x). Now the sum of greatest three would be 7+8+9=24 so the answer has to be 8x....that is option A #### A QUESTION:How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol? options: A) 7/2 B) 5 C) 20/3 D) 8 E) 300/17 SOLUTION:20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents. If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters. According to the statement; 20+x = 32% of (100+x) OR 20+x=(100+x)8/25 500+25x=800+8x 17x=300 x=300/17 Ans:E #### E QUESTION:A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man’s rate in still water and rate of current? options: A)8.5 B)10.0 C)12.5 D)11.0 E)8.25 SOLUTION:Rate of still water = 1/2 (down stream + upstream) = 1/2 (45 + 23) = 34 Kmph rate of current = 1/2 (down stream - upstream) = 1/2 (45 - 23) = 1/2 (22) = 11 kmph Answer is D. #### D QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:Which of the following is not a prime number ? options: A)502 B)503 C)509 D)521 E)523 SOLUTION:Clearly, 502 is not a prime number. Answer : A #### A QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16 SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800 The number of females older than 70 years old is 0.6850 = 510 The number of people who are either female or younger than 70 is 1800+510 = 2310. P(a person is younger than 70 or male) = 2310/2600 = 231/260 The answer is A. #### A QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 79 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:What least number must be added to 1056, so that the sum is completely divisible by 23 ? options: A)2 B)3 C)16 D)18 E)23 SOLUTION:23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2. Answer: Option A #### A QUESTION:What is the rate percent when the simple interest on Rs.1600 amount to Rs.200 in 4 Years? options: A)4% B)3.125% C)5% D)6% E)7% SOLUTION:Interest for 1 year = 200/4 = 50 Interest on Rs 1600 p/a = 50 interest rate = 50/1600100 = 3.125% Answer : B #### B QUESTION:6 people meet for a business dinner. Each person shakes hands once with each other person present. How many handshakes take place? options: A)30 B)21 C)18 D)15 E)10 SOLUTION:Let's look at the logic. Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people But in this 30 we have counted two times the total handshakes (x shakes hand with y and y shakes hand with x) So just divide 30/2= 15 total handshakes Answer is D #### D QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg? options: A)Rs.120 B)Rs.125 C)Rs.130 D)Rs.135 E)Rs.140 SOLUTION:Explanation: 2400(40/100) = 960 ---- 8 ? ---- 1 => Rs.120 Answer: A #### A QUESTION:A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000/- Rate = (100 * 3000) / (12500 * 4) = 6% ANSWER:C #### C QUESTION:A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? options: A)2 months B)6 months C)7 months D)8 months E)None of these SOLUTION:Explanation : Let B joins for x months. Then A:B = 900012 : x 18000 = 3 : 1 => 912 : 18x= 3 : 1 => 912/ 18x = 3/1 = 3 => 94 /18x = 1 => 2/x = 1 => x = 2. Answer : Option A #### A QUESTION:The average of the marks of 30 students in a class is 45. If the marks of each student are doubled, find the new average? options: A)85 B)77 C)33 D)90 E)75 SOLUTION:Sum of the marks for the 30 students = 30 45 = 1350. The marks of each student are doubled, the sum also will be doubled. The new sum = 1350 * 2 = 2700. So, the new average = 2700/30 = 90. Answer:D #### D <<<Examples ends QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? options: A)7 B)7.5 C)8 D)8.5 E)9 SOLUTION:The sum of the numbers is 6*9 = 54 K+M = 54 - 13 - 8 - 8 - 7 = 18 Since K ≠ M, K and M do not equal 9. Thus one of the two numbers is 8 or less and one is 10 or more. Then middle two numbers in the set are 8 and 8. The median is 8. The answer is C. #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School? options: A)63 B)69 C)74 D)82 E)86 SOLUTION:the total number of students at Parcy School The answer is 86 or any multiple of 43.E #### E QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: options: A)48759 B)51236 C)47619 D)6974 E)1235 SOLUTION:Explanation: By hit and trial, we find that 47619 x 7 = 333333. ANSWER:C #### C QUESTION:If \|z\|/w = 5,which of the following must be true? options: A)z = -5w B)z = 5w C)z^2 = 25w^2 D)z^2 = 25w^3 E)z^3 = 125w^3 SOLUTION:\|z\|/w = 5. \|z\| = 5w. Then z = 5w or -5w and so z^2 = 25w^2. The answer is C. #### C QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2SDtomean + 2SD, thus from 50-250.5=51 to 50+250.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King. Who am I? options: A)Johny B)Jacky C)Ricky D)David E)Alex SOLUTION:D I am DAVID. At the core I have 5 If we talk in roman numeric system, 5 = V Similarly, 500 stands in the beginning and end 500 = D I also include the first letter i.e. A and the first number i.e. I (in roman numeric system) All of them combine to form DAVID. #### D QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n? I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true. Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 1.16.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is: options: A)30 B)27 C)35 D)33 E)37 SOLUTION:Explanation : Let Pencils = 14x, Pens = 4x & Exercise books = 3x. Now, 14x = 140 hence x = 10 Number of exercise books = 3x = 30 Answer : A #### A QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:If each side is 120 feet..then total perimeter is 1504=600 poles every 20 feet hence no of poles= 600/20=30 ANSWER:B #### B QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.) options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08{weight of grapes}=0.8{weight of raisins} --> 0.08x = 0.815 --> x = 150. Answer: C. #### C QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? options: A)356 B)250 C)127 D)279 E)150 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 15 = 250 m Answer: B #### B QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible? options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6 SOLUTION:So 4C3 for abcd - 4 choices 3 more for dd(b,c or a) 3 more for bb(a,c or d) 3 more for cc(a,b or d) total 4C3+9 Ans : B #### B QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer? options: A)2 B)4 C)8 D)10 E)7 SOLUTION:Given 108x is a perfect cube so we will take 216 = 666 108x = 216 x = 216/108 = 2 correct option is A #### A QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:In how many ways can five boys and three girls sit in a row such that all boys sit together? options: A)A)2888 B)B)2885 C)C)2880 D)D)2876 E)E)2224 SOLUTION:Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways. Required number of arrangements = 4! * 5! = 24 * 120 = 2880. Answer:C #### C QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43 SOLUTION:P(1st ball is even) = 9/18 P(2nd ball is also even) = 8/17 P(both balls are even) = 9/18 * 8/17 = 4/17 The answer is B. #### B QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent? options: A)16% B)17% C)18% D)58% E)23% SOLUTION:Total CP = Rs. 36000 + Rs. 15000 = Rs. 51000 and SP = Rs. 62900 Profit(%) = (62900 - 51000)/51000 * 100 = 23% Answer: E #### E QUESTION:If -1 < x < 0, which of the following must be true? I. x^8 < x^3 II. x^4 < 1 – x III. x^3 < x^2 options: A)III only B)II only C)I only D)I,II,III only E)II,III only SOLUTION:Answer : D #### D QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:55 + 40 + 20 = 115 This number includes some people counted twice and some people counted three times. 115 - 88 = 27, and this number represents people counted twice or three times. 7% of the people are counted two extra times. The percentage of people counted one extra time is 27 - 7(2) = 13. The percentage of people who liked more than one product is 7% + 13% = 20%. The answer is B. #### B QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)277 B)277 C)120 D)882 E)272 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:Which of the following inequalities is equivalent to 11 - 11x > 133? options: A) x > -2 B) x > -1 C) x > -3 D) x > -11 E) x > -5 SOLUTION:You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc. The only important thing to note is the following: When you multiply/divide by a negative number, the sign of the inequality flips. To illustrate, 11 - 11x > 133 11x > -122 (Correct) x > -11 (Correct) the correct option is D #### D QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min SOLUTION:1/20 + 1/40 - 1/80 = 5/80 80/5 = 16 ANSWER:E #### E QUESTION:8^100 is divisible by 17. Find the remainder? options: A)10 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:Evaluate 35 / .07 options: A)400 B)500 C)505 D)None of these E)506 SOLUTION:Explanation: 35/.07 = 3500/7 = 500 Option B #### B QUESTION:How many 4 letter words can we make from the letters in an alphabet? options: A)358800 B)358802 C)358801 D)358809 E)358810 SOLUTION:There are 26 letters in an alphabet to choose 4 from these 26 would mean 26P4 = 26!/(26-4)! We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words. Therefore the answer is 26!/ 22! = 26252423 = 358800 Answer:A #### A QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ? options: A)5 B)4 C)3 D)2 E)-2 SOLUTION:Since x is an integer, (-12x)^(4x) is always positive. So, 12x^4x = 12x^(15 - x) 4x = 15 - x 5x = 15 x = 3 Answer: C #### C QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 6 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15 So, T=15-5 = 10.C #### C QUESTION:In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls? options: A)20 B)22 C)24 D)26 E)29 SOLUTION:Solution: Total number of ways = (select 3 boys from group of 4 boys) (2 girls from group of 4 girls) => (4c3) * (4c2) = 24 C #### C QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)4 Km C)4 1/5 Km D)3 2/5 Km E)3 3/5 Km SOLUTION:Formula = S1S2/S2-S1 T1+T2/60 = 46/2 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:Scott's average (arithmetic mean) golf score on his first four rounds was 58.What score does he need on his fifth round to drop his average score by 2 points? options: A)48 B)72 C)78 D)88 E)312 SOLUTION:Average score for first 4 rounds = 58 Average score after 5 rounds = 56 Score Scott needs on his 5th round to drop average score by 2 points = 58 - (25) = 48 Answer A #### A QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is? options: A)11 B)72 C)36 D)99 E)27 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240)/12 => x = 20 Speed of each train = 20 m/sec. = 20 18/5 =72 km/hr. Answer: B #### B QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B QUESTION:A committee of 6 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)360/14 E)3/14 SOLUTION:3/84/71/66! = 3/14. We are multiplying by 6! because we can choose secretary,economist, and accountant is several way: Answer: D. #### D QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 100 = 33 1/3% Answer: A #### A QUESTION:In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly? options: A)1/4 B)1/2 C)3/5 D)9/10 E)16/20 SOLUTION:P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/51/4 = 9/10. Answer: D. #### D QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!2!)= 15 ways 4815=720 ANSWER:E #### E QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3 SOLUTION:total 9 from take one. 9c1=9 red 5 from one 5c1=5 5/9 ANSWER:C #### C QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together? options: A)120 B)200 C)240 D)260 E)270 SOLUTION:The word ‘BULLAT’ contains 6 letters of which 1 letter occurs twice = 6! / 2! = 360 No. of permutations possible with vowels always together = 5! * 2! / 2! = 120 No. of permutations possible with vowels never together = 360-120 = 240. C #### C QUESTION:The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again? options: A)16:00. B)18:00. C)20:00. D)22:00. E)24:00. SOLUTION:Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10 If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours Answer A #### A QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)% SOLUTION:100 – 12 = 88 88------12 100------? => 11 3/22% ANSWER:A #### A QUESTION:1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams options: A)48 paise B)77 paise C)96 paise D)66 paise E)55 paise SOLUTION:Explanation: Let 200 gm potato cost X paise According to question, Cost of 1/4 Kg potato = 60 Paise => Cost of 250 gm potato = 60 Paise => 1 Kg = 1000 gm => 1/4 Kg = 1000/4 gm = 250 gm By direct proportion, more quantity, more cost 200 grams : 250 grams = X : 60 => 20060 = 250 X => 12000 = 250 X => X = 48 => Thus, the cost of 200 grams is 48 paise. ANSWER: A #### A QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 2018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 231 is 6. The answer is C. #### C QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All two 2. One symmetry and other two non 4. All the two letters can be arranged in 2 ways ( 11c2+ 11c1 15c2) 2 ( 1110/ 2 + 11 * 15 * 14 / 2 ) * 2 2420 IMO option D is the correct answer.. OA please...will correct if I missed anything..D #### D QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)8939 B)8383 C)8389 D)4530 E)9392 SOLUTION:Explanation: Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer: Option D #### D QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 237-1. ANSWER:E #### E QUESTION:If Jane takes 12 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/12 B)12x/(60y) C)60xy/12 D)xy/720 E)720x/y SOLUTION:The answer is B. She runs x yards in 12x/y seconds =12x/60y minutes. #### B QUESTION:12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) options: A)6 B)8 C)10 D)20 E)40 SOLUTION:we have 1 litre = 1000cm³ (thanks Bunuel) =>12 litres = 121000 = 12000cm³ Let call the height of the water is x the breadth and length of the water will equal the aquarium The volume of the water: 50 * 30 * x = 12000cm³ => x = 12000/(5030) = 8 cm Answer is B #### B QUESTION:The side of a square is increased by 25% then how much % does its area increases? options: A)56.75 % B)56.25 % C)53.85 % D)57.25 % E)56.21 % SOLUTION:a = 100 a2 = 10000 a = 125 a2 = 15625 ---------------- 10000 --------- 5625 100 -------? => 56.25 % Answer:B #### B QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers? options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by x = 2y - 4 We use the sum of the two numbers to write a second equation. x + y = 20 Substitute x by 2y - 4 in x + y = 20 to obtain 2y - 4 + y = 20 Solve for y to find y = 8 and x = 2y - 4 = 12 Answer B #### B QUESTION:An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)53 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:B #### B QUESTION:There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices. options: A)120 B)116 C)140 D)20 E)10 SOLUTION:Solution: The number of triangle can be formed by 10 points = 10C3. Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3. In the question, given 4 points are collinear, Thus, required number of triangle can be formed, = 10C3-4C3 = 120-4 = 116. Answer B #### B QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg? options: A)72 B)47 C)40 D)28 E)20 SOLUTION:940(30/100) = 282 ---- 6 ? ---- 1 => Rs.47 Answer:B #### B QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)326,040 D)12,870 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All four 2. One symmetry and other three non 3. Two symmetry and other two non 4. Three symmetry and one non 4. All the three letters can be arranged in 24 ways ( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 15c1 ) 6 (330 +5005 + 5775+2475 ) * 24 326,040 IMO option C is the correct answer.. OA please...will correct if I missed anything.. C #### C QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 kmph B)108 kmph C)54 kmph D)71 kmph E)88 kmph SOLUTION:S = 480/16 * 18/5 = 108 kmph Answer:B #### B QUESTION:There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have? options: A)7/17 B)5/12 C)4/11 D)3/10 E)2/9 SOLUTION:P(first stamp is different) = 5/10 P(second stamp is different) = 4/9 P(both stamps are different) = 5/104/9 = 2/9 The answer is E. #### E QUESTION:The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12.5N E)20 SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 + 1.5x$500 = $500 + $750 =$1250 This is 12.5 times the 1992 number, so the correct answer is 12.5N. D #### D QUESTION:A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg? options: A)Rs.120 B)Rs.125 C)Rs.130 D)Rs.135 E)Rs.140 SOLUTION:Explanation: 2400(40/100) = 960 ---- 8 ? ---- 1 => Rs.120 Answer: A #### A QUESTION:A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business? options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500 SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. 15000 x 3/10 = Rs. 4,500. B #### B QUESTION:Which of the following best approximates the percent by which the distance from A to C along a diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD? options: A)30% B)43% C)45% D)50% E)70% SOLUTION:let the sides be 2 units. original distance=2+2=4 units changed distance=2sq.root2 %change=change dist.-original dist./original dist. =(2sq.root 2-4)/4==-.2955 reduced by ~30% Ans A #### A QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 12=45,0008 1:1 Madhu's share=1/260,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:7+2+2^2+2^3+2^4+2^5=？ options: A)(2^3-1)(2^3+1) B)2^6+5 C)2^5-1 D)2^5+1 E)2^5-2 SOLUTION:From 7+2+2^2+2^3+2^4+2^5=69, 2^6+5=69 the correct answer is B. #### B QUESTION:In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds. Estimate the size of the population net increase that occurs in one day. options: A)32,300 B)172,800 C)468,830 D)338,200 E)259,200 SOLUTION:Every 2 seconds, 6 persons are added (7-1). Every second 3 persons are added. In a day 24hrs = 24 60 Minutes = 24 * 60 * 60 = 86400 seconds. 86400 * 3 = 259200 Option E #### E QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 50 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:Annie earned 40x + 10(2x) = 60x Let H be the number of hours that Harry worked. Harry earned 30x + 1.5x(H-30) = 60x (1.5x)(H) = 75x H = 50 hours The answer is C. #### C QUESTION:The first republic day of the India was celebrated on 26th January,1950. It was options: A)221 B)28 C)276 D)20 E)22 SOLUTION:1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995. Number of odd days till 1600 years = 0 1601 to 1700 = 5 1701 to 1800 = 5 1801 to 1900 = 5 49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days 25th January 1950 = 25/7 = 4 odd days Total odd days =15 + 5 + 4 = 24/7 = 3 odd days So 26th January,1950 is Thursday Answer:B #### B QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)6 B)7 C)8 D)4 E)2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1 When B starts: No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1 Solving the above two equations for xy x = 1/8 y = 1/8 → Total work done by AB in a day = 1/8 + 1/8 = 1/4 → No. of days to complete the work when both work together = 4 Answer: D #### D QUESTION:Set S is the prime integers between 0 and 40. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd? options: A)15/56 B)3/8 C)15/28 D)5/8 E)3/4 SOLUTION:Total number of combinations=12C3=220................(1) Total number of combinations including 2 and two other numbers=11C2=55......................(2) Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(220-55)=165 So, probability=165/220=3/4 E #### E QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:How many numbers between 11 and 90 are divisible by 7 ? options: A)23 B)11 C)22 D)32 E)15 SOLUTION:The required numbers are 14, 21, 28, 35, .... 77, 84. This is an A.P. with a = 14 and d = (21 - 14) = 7. Let it contain n terms. Then, Tn = 84 => a + (n - 1) d = 84 => 14 + (n - 1) x 7 = 84 or n = 11. Required number of terms = 11 ANSWER B 11 #### B QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:If xy not equal 0 and x^2y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is: options: A)10/21 B)20/22 C)32/45 D)13/98 E)43/21 SOLUTION:Number of ways of choosing 4 persons out of 9 =9c4 =126 No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2) =60 P(E)=60/126 =10/21 ANSWER A #### A QUESTION:Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?. options: A)Rs. 10000 B)Rs. 20000 C)Rs. 30000 D)Rs. 40000 E)Rs. 50000 SOLUTION:Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev’s share = Rs.(150000×2/6) = Rs. 50000 Answer E #### E QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 6000, brokerage being 1/4%, is: options: A)83.08 B)114 C)114.75 D)124 E)124.75 SOLUTION:Face Value = Rs. 6000. Dividend = 10.5%. Annual Income = Rs. 756. Brokerage per Rs. 100 = Rs. 0.25. Dividend is always paid on the face value of a share. Face Value Dividend / (Market Value + Brokerage per Rs. 100) = Annual income. = 6000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100. = Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 83.33. = Market Value of Rs. 100 stock = Rs. 83.33 - Re. 0.25. = Market Value of Rs. 100 stock = Rs. 83.08 answer : A #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)238 B)288 C)237 D)400 E)281 SOLUTION:Explanation: 212 : 312 : 424 1: 3: 4 1/8 3200 = 400 Answer: D #### D QUESTION:Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick? options: A)5, 12, and 8 kg B)6, 12, and 8 kg C)7, 12, and 8 kg D)8, 12, and 8 kg E)None SOLUTION:Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x+2, respectively. So x+2x+x+2=26 4x=24 x=6 Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively. Answer B #### B QUESTION:If n is an integer, which of the following must be an even integer? options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10 SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 ) A: n^2-n-1 = -1 { If n = 1 } B: n^2-4n+6 = 3 { If n = 1 } C: n^2-5n+5 = 1 { If n = 1 } D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 } E: n^2+2n+10 = 13 { If n = 1 } Thus the only possible answer is (D) #### D QUESTION:Which is the following is divisible by 11 options: A)A)4305 B)B)4825 C)C)1635 D)D)4805 E)E)4906 SOLUTION:Explanation: Sum of first 'n' natural numbers = n(n + 1)/2 Sum of first 9 natural numbers = 5(5 + 1)//2 = 5 x 3 = 15 Sum of first 99 natural numbers = 55(55 + 1)//2 = 55 x 30 = 1650 1650 - 15 = 1635 Answer: Option C #### C QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32900+83000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x? options: A)0 B)1 C)2 D)3 E)It cannot be determined from the information given SOLUTION:d is prime greater than 2 thus d is odd 3d is odd Thus no even factors Ans:A #### A QUESTION:If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? options: A)$28000 B)$15000 C)$12000 D)$10000 E)$9000 SOLUTION:Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,0002)2=$28,000 (after 9 years investment will become $7,0002=$14,000 and in another 9 years it'll become $14,0002=$28,000). Answer: A. #### A QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =441=16/9==> Remainder=7 Answer: E #### E QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? options: A)129 B)128 C)189 D)187 E)112 SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135 SP = CP[(100 + profit%)/100] = 135 * [(100 + 40)/100] = Rs. 189. Answer: C #### C QUESTION:By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: options: A)Rs. 2,600 B)Rs. 2,700 C)Rs. 2,800 D)Rs. 3000 E)NOne SOLUTION:Solution: Let Cost Price was X. X + 14% of X = 2850 X + 14X/100 = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = 100/1142850 = Rs. 2500; SP for a profit of 8% = 108/1002500 = Rs. 2700. Answer: Option B #### B QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)0 SOLUTION:K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^24^25^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . E #### E QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 * 100 = 33% Answer:C #### C QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n(n+1)/2 with n being 23, so equal to 23 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water? options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11 SOLUTION:First mixture: milk and water in the ratio of 3x:4x. Second mixture: milk and water in the ratio 5y:2y. We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3. Answer: A. #### A QUESTION:If n=34p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n? options: A)Six B)Seven C)Eight D)Nine E)Ten SOLUTION:n=3∗2^2∗p Number of divisors = 2 * 3 * 2 = 12 The 12 divisors includes 1, n, 3, 2 and p Number of different non prime divisors excluding 1 and n = 12 - 5 = 7 Answer: B #### B QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)12 B)15 C)16 D)18 E)19 SOLUTION:one day work done by A=1/20 work done by A in 2 days=1/10 work done by A,B,C on 3rd day=1/10+1/10=1/5 1/5th of the work will be completed at the end of 3 days the remaining work =1-1/5=4/5 1/5 of work is completed in 3 days total work wiil be done in 35=15 days ANSWER:B #### B QUESTION:For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning? options: A)01 B)025 C)115 D)125 E)5 SOLUTION:(1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38)) ((1/8)−(9/78))((1/8)−(9/78)) (0.125−approx.0.1111)(0.125−approx.0.1111) Approximately 0.010.01 ANSWER :A #### A QUESTION:Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is: options: A)18 B)19 C)20 D)21 E)22 SOLUTION:Explanation: Let first number be x. So,2nd no. = 4x & 3rd no.=8x. So,x+4x+8x=78 × 3 = 234. 13x = 234 x = 234/13 Hence,smallest Number x=18. Answer: A #### A QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform? options: A)150 B)145 C)165 D)162 E)152 SOLUTION:D = 130 + x T = 20 S = 130+x/15 18/5 = 70 kmph. => (130+x) * 18 = 5250 => 130 + x = 292 => x= 162 m Answer: D #### D QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 1304=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:Positive Integer A gives the remainder of 9 when divided by another positive Integer B. If A/B = 47.45, what is the value of B? options: A)96 B)75 C)48 D)20 E)12 SOLUTION:I think the answer should be 25. This is how i solved. .45 of B = Remainder .45 of B = 9 B = (9 100) / 45 = 20. D #### D QUESTION:A train crosses a platform of 150 m in 10 sec, same train crosses another platform of length 250 m in 15 sec. then find the length of the train? options: A)150m B)180m C)159m D)250m E)50 m SOLUTION:Length of the train be ‘X’ X + 150/10= X + 250/15 3X + 450 = 2X + 500 X = 50m Answer:E #### E QUESTION:The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs. 3. The ratio of the two selling prices is? options: A)52:56 B)52:53 C)52:50 D)54:53 E)52:51 SOLUTION:Let C.P. of the article be Rs. x. Then, required ratio = 108% of x / 106% of x = 108/106 = 54/53 = 54:53 Answer: D #### D QUESTION:During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years? options: A)60 percent decrease B)20 percent decrease C)20 percent increase D)60 percent increase E)140 percent increase SOLUTION:Let the value of the stock in 2000 be 100, then in 2001 its value would be 100(1-80/100)=1000.2=20 and in 2002 its value would be 20*(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%. Answer: B. #### B <<<Examples ends QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)14 B)144 C)777 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways. Hence the total ways are 24 * 6 = 144. Answer:B #### B QUESTION:A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is? options: A)10 B)20 C)50 D)30 E)40 SOLUTION:Man's speed with the current = 15 km/hr => speed of the man + speed of the current = 15 km/hr speed of the current is 2.5 km/hr Hence, speed of the man = 15 - 2.5 = 12.5 km/hr man's speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km/hr Answer is A. #### A QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph SOLUTION:Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 C #### C QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 B)67 C)108 D)26 E)27 SOLUTION:Length = Speed * time Speed = L/T S = 600/20 S = 30 M/Sec Speed= 3018/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C #### C QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y? options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6 SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2. and hence answer B #### B QUESTION:Complete the series: 16, 06 , 68 , 88 , ? , 98 options: A)L8 B)B6 C)S5 D)E8 E)M5 SOLUTION:A L8 To know why, just read the number series upside down and you will find that the numbers are 91, 90, 89, 88, __, 86 So L8 when read upside down reads as 87. #### A QUESTION:A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)9 km D)5 km E)1 km SOLUTION:Let the total distance be 3x km. Then, x/3 + x/4 + x/5 = 47/60 47x/60 = 47/60 => x = 1. Total distance = 3 1 = 3 km. Answer: B #### B QUESTION:A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that \|Y\|<3? options: A)1/7 B)3/7 C)2/5 D)3/11 E)4/7 SOLUTION:\|X\|\|X\| can take 7 values. To get \|X\|<2\|X\|<2 ( i.e., −2<x<+2−2<x ⇒ P(\|X\|<2)= Favourable CasesTotal CasesP(\|X\|<2)= Favourable CasesTotal Cases = 3/7 B #### B QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm. options: A)227 B)299 C)300 D)161 E)212 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (22 + 18) * (15) = 300 cm2 Answer: C #### C QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.915 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.920 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5100 = 107% of 7.5. Answer: B. #### B QUESTION:Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)A)Rs.7000 B)B)Rs.8000 C)C)Rs.8571 D)D)Rs.8600 E)E)Rs.8700 SOLUTION:The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571. C) #### C QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is options: A)100 B)250 C)260 D)416 E)None of these SOLUTION:Explanation: Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 × 32 = 416. Answer: D #### D QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 10050= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 11557.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:What percent of 200 is 55? options: A)0.25% B)4% C)25% D)27.5% E)250% SOLUTION:200x /100 = 55 x = 27.5 Ans: D #### D QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed? options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr SOLUTION:Average speed = (24555)/(45+55) = 49.5km/hr Answer is B #### B QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 1335 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 6 = 6. Answer:C #### C QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did? options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds. SOLUTION:Tom is running alone for 20 seconds. So he will cover a distance of 202.5 = 50 m in 20 seconds=W Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side D is the answer #### D QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:(178% of 1265) ÷ 5.96 = ? options: A)125 B)175 C)225 D)375 E)524 SOLUTION:Explanation : ? = (178 x 1265/100) ÷ 6 = 2250/600 = 375 Answer : Option D #### D QUESTION:A certain office supply store stocks 2 sizes of self-stick notepads, each in 8 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)6 B)8 C)16 D)124 E)128 SOLUTION:Notepads of the same color = 8 (we have 8 colors). As we have two sizes then total for the same color=82=16 Notepads of the different colors = 8C3=56 (we should choose 3 different colors out of 8). As we have two sizes then total for the different color=562=112 Total=112+16=128 Answer: E. #### E QUESTION:An article is bought for Rs.600 and sold for Rs.900, find the gain percent? options: A)50% B)63 1/3% C)33 1/3% D)93 1/3% E)33 1/3% SOLUTION:Explanation: 600 ---- 300 100 ---- ? => 50% Answer:A #### A QUESTION:In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ? options: A)35 B)39 C)48 D)50 E)52 SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 C #### C QUESTION:Find the odd man out 4, 16, 25, 36, 42, 64 options: A)36 B)25 C)42 D)95 E)4 SOLUTION:2^2 = 4 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 ANSWER:C #### C QUESTION:If log1087.5 = 5.9421, then the number of digits in (875)10 is? options: A)30 B)70 C)27 D)26 E)25 SOLUTION:X = (875)10 = (87.5 x 10)10 Therefore, log10X = 10(log1087.5 + 1) = 10(5.9421 + 1) = 10(6.9421) = 69.421 X = antilog(69.421) Therefore, number of digits in X = 70. ANSWER:B #### B QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop. The cost of the bomber is quite interesting. The Cost of 1st bomber is: 2 The Cost of 2nd bomber is: 4 The Cost of 3rd bomber is: 6 The Cost of 4th bomber is: 8 The Cost of 5th bomber is: 10 i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins. How many bombers can you buy using 1000 coins ? ? options: A)61 B)62 C)63 D)64 E)65 SOLUTION:Solution 62 The Cost of 1st bomber is: 2 i.e Total coins spend: 2 The Cost of 2nd bomber is: 4 i.e Total coins spend: 6 The Cost of 3rd bomber is: 6 i.e Total coins spend: 12 The Cost of 4th bomber is: 8 i.e Total coins spend: 20 The Cost of 5th bomber is: 10 i.e Total coins spend: 30 The Cost of 6th bomber is: 12 i.e Total coins spend: 42 The Cost of 7th bomber is: 14 i.e Total coins spend: 56 The Cost of 8th bomber is: 16 i.e Total coins spend: 72 The Cost of 9th bomber is: 18 i.e Total coins spend: 90 The Cost of 10th bomber is: 20 i.e Total coins spend: 110 The Cost of 11th bomber is: 22 i.e Total coins spend: 132 The Cost of 12th bomber is: 24 i.e Total coins spend: 156 The Cost of 13th bomber is: 26 i.e Total coins spend: 182 The Cost of 14th bomber is: 28 i.e Total coins spend: 210 The Cost of 15th bomber is: 30 i.e Total coins spend: 240 The Cost of 16th bomber is: 32 i.e Total coins spend: 272 The Cost of 17th bomber is: 34 i.e Total coins spend: 306 The Cost of 18th bomber is: 36 i.e Total coins spend: 342 The Cost of 19th bomber is: 38 i.e Total coins spend: 380 The Cost of 20th bomber is: 40 i.e Total coins spend: 420 The Cost of 21st bomber is: 42 i.e Total coins spend: 462 The Cost of 22nd bomber is: 44 i.e Total coins spend: 506 The Cost of 23rd bomber is: 46 i.e Total coins spend: 552 The Cost of 24th bomber is: 48 i.e Total coins spend: 600 The Cost of 25th bomber is: 50 i.e Total coins spend: 650 The Cost of 26th bomber is: 52 i.e Total coins spend: 702 The Cost of 27th bomber is: 54 i.e Total coins spend: 756 The Cost of 28th bomber is: 56 i.e Total coins spend: 812 The Cost of 29th bomber is: 58 i.e Total coins spend: 870 The Cost of 30th bomber is: 60 i.e Total coins spend: 930 The Cost of 31st bomber is: 62 i.e Total coins spend: 992 Answer B #### B QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)\|x - 1\| < 7 B)\|x + 2\| < 6 C)\|x + 3\| < 5 D)\|x - 2\| < 6 E)None of the above SOLUTION:We know that \|x\| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => \|x-2\| < 6. Hence, answer is D #### D QUESTION:When 4 dice are thrown, what is the probability that the same number appears on each of them? options: A)1/36 B)1/18 C)1/216 D)1/5 E)1/4 SOLUTION:Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296. Event (Numerator): The chances that all the dice show same number (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6. Probability = Event/ Sample space = 6/64 = 1/63 = 1/216. ANSWER:C #### C QUESTION:Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together? options: A)81 B)81.5 C)82 D)84.5 E)None of these SOLUTION:Explanation : Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a Total of Y = 76b Total of Z = 85c And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b. Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b. Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a. Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c). => 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a . => 978/12 => 81.5 Answer : B #### B QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: Q=2550+(10050)=7550.B #### B QUESTION:Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:Two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have ALL even (being multiple of 8) Probability of number selected being odd = Total Odd Numbers / Total available numbers Probability = 100/500 = 0.2 = 20% Answer: Option A #### A QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (310^-3)^5 = 24310^-15 = 0.24310^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ? options: A)30 B)45 C)42 D)72 E)75 SOLUTION:Let the number of benches in the class be x. Then, 6(x + 1) = 7x - 5 x = 11. Hence, number of students in the class = 6 ( x + 1) = 6 x 12 = 72. ANSWER:D #### D QUESTION:Find the value of a from (15)^2 x 8^3 Ã· 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 Ã· 256 = a = 225 x 512 Ã· 256 = 450 E #### E QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? options: A)897 B)164,850 C)164,749 D)149,700 E)156,720 SOLUTION:Explanatory Answer Step 1: Identify the series The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101. The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107. The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998. It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2). So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3. Step 2: Compute the sum Sum of an Arithmetic Progression (AP) = [first term + last term/2]n We know the first term: 101 We know the last term: 998. The only unknown is the number of terms, n. In an A.P., the nth term an = a1 + (n - 1)d In this case, therefore, 998 = 101 + (n - 1)* 3 Or 897 = (n - 1) * 3 (n - 1) = 299 or n = 300. Sum of the AP will therefore, be [101+998/2]∗300 = 164,850 Choice B is the correct answer. #### B QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11 SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways. The required probability = (9 * 4) = 36/78 = 6/13 Answer: B #### B QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is? options: A)180 B)882 C)277 D)261 E)281 SOLUTION:5x + 12x + 13x = 360 => x = 12 a = 60, b = 144, c = 156 S = (60 + 144 + 156)/2 = 180 Answer: A #### A QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head?? options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these SOLUTION:1Rs coin head=1/2 2Rs coin Tail=1/2 5Rs coin head=1/2 =(1/2)(1/2)(1/2) =1/8 ANSWER:B #### B QUESTION:P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P? options: A)80 B)70 C)85 D)90 E)95 SOLUTION:The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3. Since, they work together, the share of P = 6/13 * 195 = Rs.90 Answer: D #### D QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100100=10,000. Now, the area obtained with wrong measurements would be 11695=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 119 = 99 Answer B #### B QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them? options: A)21 B)24 C)27 D)33 E)45 SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6 Given, X + X+3 + X+6 = 90 3X = 81 X = 27 The numbers are 27, 30, 33 Therefore the largest number is 33 Answer D. #### D QUESTION:A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour. To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/65 =6 Answer (E) #### E QUESTION:What is the prime factors’ number of 36? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:prime factors’ number, as I assume, for a number X=a^nb^mc^od^p... is = n+m+o+p... So, 24 = 2^23^2 prime factors’ number will be 2+2 = 4. Hence, answer is C. #### C QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)8% B)7% C)10% D)12% E)4% SOLUTION:Option E Explanation: 65(90/100)((100-x)/100) = 56.16 x = 4% #### E QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 * 100 = 700 #### C QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)56 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 8P2 = 8!/2! = 56. IMO option C is correct answer.. #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is options: A)9 years B)11 years C)17 years D)21 years E)25 years SOLUTION:Solution Age of the 15th student =[15x15-(14x8+16x6)] = (225 - 208) = 17 years. Answer C #### C QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)50 m B)60 m C)65 m D)75 m E)80 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 22.5 => 675 675 2 = Rs.1350 Answer:A #### A QUESTION:John throws a coin until a series of four consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fifth throw? options: A)1/16 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T ----> P = (1/2)^5 = 1/32 T-H-H-H-H ----> P = (1/2)^5 = 1/32 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/32 + 1/32 = 2/32 = 1/16 Answer(A). #### A QUESTION:A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even? options: A)1/3 B)2/3 C)5/9 D)6/11 E)5/11 SOLUTION:Probability of getting an even number = 2/3 Probability of getting an odd number = 1/3 since the dice is biased. The sum is even if (even,even) or (odd,odd) [P(even).P(even)] + [P(odd).P(odd)] 2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9 ANSWER:C #### C QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 750 = 80/100 * 750 = 600 Option C #### C QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25Ã—26/2=325 Correct Option: B #### B QUESTION:The surface of a cube is 24sq cm. Find its volume? options: A)8 B)6 C)4 D)3 E)1 SOLUTION:6a2 = 24 a = 2 => a3 = 8cc Answer: A #### A QUESTION:The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output? options: A)20% B)27% C)30% D)32% E)79% SOLUTION:The original output increases by 15% and then 20%. Total % change = a + b + ab/100 Total % change = 15 + 20 + 1520/100 = 38% Now, you want to change it to 0, so, 0 = 38 + x + 38x/100 x = -38(100)/138 = 27% approximately Answer is B #### B QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:What percent of a day is 15 hours? options: A)37Ã—1/2% B)16Ã—1/2% C)18Ã—2/3% D)22Ã—1/2% E)None SOLUTION:Solution Required percentage = (15/24Ã—100)% = (75 / 2)%. = 37Ã—1/2%. Answer A #### A QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last? options: A)8 B)10 C)12 D)18 E)20 SOLUTION:Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 . for-^—=18 days. D #### D QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches? options: A)25 B)27 C)30 D)35 E)36 SOLUTION:Average in 5 matches = (230 + 340)/2+3 = 60+120 / 5 = 180/5 = 36 Answer is E #### E QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2. #### B QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)None of these SOLUTION:Solution Average = (76+65+82+67+85 / 5) =(375 / 5) = 75. Answer D #### D QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)100 = (0.9)100 = 90%. A #### A QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip? options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300 SOLUTION:total distance =100 ;total time = T t1 = x/30 t2 = 100-x /40 T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200 = (10x+3000)/1200 = x+300/120 av speed = 100120/x+300 = 12000/x+300 E #### E QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:If s and t are positive integers such that s/t = 84.15, which of the following could be the remainder when s is divided by t ? options: A)2 B)4 C)8 D)20 E)9 SOLUTION:s/t= 84.15 s = 84.15t s = (84 + 0.15)t s = 84t + (15/100)t s = 84t + (3/20)t So remainder will be multiple of 3. The only multiple of 3 is 9. Ans. E #### E QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^41+13^1., 4^13=4^26+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ? options: A)2 B)3 C)1 D)6 E)5 SOLUTION:I year 2100 II year 2100+147=2247 2100+2247=4347 So 2 Years Answer A #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? options: A)20 m B)70 m C)50 m D)Cannot be determined E)None of these SOLUTION:Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 6 = 50 m ANSWER:C #### C QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:Mary and John can do a piece of work in 24 day; John and Vino in 30 days;Vino and Mary in 40 days. If Mary, John and Vino work together they will complete work in ? options: A)77 B)20 C)27 D)19 E)17 SOLUTION:Explanation: Given that Mary and John take 24 days; i.e., (Mary + John)'s 1 day's work = 124124 John and Vino take 30 days; i.e., (John + Vino)'s 1 day's work = 130130 Vino and Mary take 40 days; i.e., (Vino + Mary)'s 1 day's work = 140140 Adding above 3 equations, we get, [(Mary + John) + (John + Vino) + (John + Vino)]'s 1 day's work = 124+130+140124+130+140 2((Mary + John + Vino)'s 1 days work = 124+130+140124+130+140 2(Mary + John + Vino)'s 1 days work = 5+4+31205+4+3120 = 110110 Therefore, (Mary + John + Vino)'s 1 days work = 120120 i.e., Mary, John and Vino together can complete the work in 20 days. Answer: B #### B QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We start by factoring 18. 18 = 29 = 63 = 233. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C. #### C QUESTION:Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? options: A)7.16 B)7.59 C)7.12 D)7.15 E)7.11 SOLUTION:T = (141 + 165)/ (80 + 65) * 18/5 T = 7.59 Answer: B #### B QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants? options: A)4!5c2 21c2 B)4!5c3 21c2 C)5!5c2 21c2 D)7!5c2 21c5 E)6!5c2 21c2 SOLUTION:combination for 2 vowels out of 5 = 5c2 ways combination for 5 consonants of 21 = 21c5 ways Additionally the arrangement can be = 7! total arrangements =7!5c2 21c5 D #### D QUESTION:In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? options: A)3:16. B)2:3. C)4:9 D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C #### C QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:y w v t r p n Next letter in the series options: A)L B)M C)N D)O E)P SOLUTION:y--w(y-2) v--t(v-2) r--p(r-2) n--l(n-2) so ans is l ANSWER:A #### A QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 220500 + 18000 = 59000 Answer: D #### D QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest? options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33% SOLUTION:T = 30 years P= principle amount = x A = total amount = 2x SI = simple interest = A-P = 2x-x = x R = 100SI/PT = 100x/30x =3.33% Answer is B #### B QUESTION:The residents of the town A participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town A, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)- 30 B)- 20 C)- 6 D)- 12 E)- 16 SOLUTION:(21-62)<number of hours that Pat watched television last week <(21-61) =9<W<15 12=C. #### C QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)1/2 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 4 = 4C2 Total possible outcomes - 2^4 (each child can be either a girl or a boy) Probability=2C14C2/2^4= 24/2222=8/16=1/2 Ans=D #### D QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20. options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280 SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83. A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392; C's share = $ (1162 x (20/83))= $ 280. Option C #### C QUESTION:How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal? options: A)201 B)159 C)179 D)189 E)209 SOLUTION:If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals n= 23-1 then 22(22-3)/2 = 209 Correct Option:E #### E QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ? options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these SOLUTION:Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 ANSWER:C #### C QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.61.2^3 = 1.0368 The answer is E. #### E QUESTION:The area of a circle is increased by 800%. By what percent has the diameter of the circle increased? options: A)100% B)200% C)300% D)600% E)800% SOLUTION:A diameter of 2 it's radius = 1 it's area = (1^2)pi = 1pi Answer A: If we increase that diameter 100%, we have.... A diameter of 4 it's radius = 2 it's area = (2^2)pi = 4pi This area has increased (4 pi - 1pi)/1pi = 3pi/1pi = 3 = 300% Answer B: If we increase the diameter 200%, we have... A diameter of 6 it's area = 3 it's area = (3^2)pi = 9pi This area has increased (9pi - 1pi)/1pi = 8 pi/1pi = 8 = 800% ANSWER:E #### E QUESTION:A fruit seller had some apples. He sells 35% and still has 6500 apples. Originally, he had ? options: A)650apples B)600 apples C)772 apples D)700 apples E)None SOLUTION:Answer âˆµ 65% of N = 800 âˆ´ N = (650 x 100)/65 = 1000 Correct Option: E #### E QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)8939 B)8383 C)8389 D)4530 E)9392 SOLUTION:Explanation: Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer: Option D #### D QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.22 B) 0.44 C) 0.55 D) 22 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/1233 = 22 cents. Answer: D. #### D QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ? options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550 SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040 Which is 100 - 20 = 80% of his monthly salary ∴ His salary = 10040x100/80 = 12550 Answer : E #### E QUESTION:6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is options: A)Rs. 150 B)Rs. 170 C)Rs. 180 D)Rs. 190 E)None of these SOLUTION:Explanation: Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2 = 24 : 24 : 12 = 2 : 2 : 1 Money earned by children = 950 x (1/5) = Rs. 190 Answer: Option D #### D QUESTION:A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally? options: A)10 men B)30 men C)40 men D)20 men E)none of these SOLUTION:Let x be the number of men originally Thus, 10x=(10+10)(x-10) 10x=20(x-10) x=2(x-10) x = 20 ANSWER:D #### D QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)288 B)165 C)881 D)1277 E)121 SOLUTION:Speed = 54 5/18 = 15 m/sec. Length of the train = 15 * 25 = 375 m. Let the length of the platform be x m . Then, (x + 375)/36 = 15 => x = 165 m. Answer: B #### B QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+2050/100 = 60) Family Income is same 50 In June Lee's Income percent is 60100/110 ~ 55 Ans is A #### A QUESTION:When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item? options: A)$1,600 B)$1,850 C)$2,250 D)$2,400 E)$2,750 SOLUTION:Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250. Answer: C. #### C QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E <<<Examples ends QUESTION:By how much is 50% of 250 greater than 25% of 400. options: A)25 B)26 C)29 D)39 E)26 SOLUTION:(50/100) * 250 â€“ (25/100) * 400 125 - 100 = 25 Answer:B #### B
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)3000 - (1/10)%3000 = 300 - (1/1000)3000 = 300 - 3 = 297 The answer is B. #### B QUESTION:In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? options: A)25 B)30 C)45 D)20 E)50 SOLUTION:6p2 = 6 x 5 = 30 B) #### B QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is: options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr. SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr. Then, 8x = (440/5) = 88 x = (88/8) = 11 Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr. B #### B QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:A- B = 120 Miles B - C = 60 Miles Avg Speed = 45 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 45 = 180/4t t = 60 B-C = 60 mph Answer E #### E QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00 SOLUTION:In one hour and thirty minutes the first train travels 105 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm. The answer is C. #### C QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is options: A)66Â° B)18Â° C)24Â° D)60Â° E)None of these SOLUTION:In a clock, each minute makes 6Â° âˆ´ 11 minutes will make 6 Ã— 11 = 66Â° Answer A #### A QUESTION:If a certain manager had received a 5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise? options: A)55,000 B)58,806 C)59,290 D)62228.52 E)61,620 SOLUTION:No need of getting involved with decimals ..just work in fractions .. salary(let X) included 5% increase can be written as (1+5/100)X=60500 X=60500/1.05------>57619.05 if there is 8% rise in 57619.05 then the salary now is 8% of 57619.05 857619.05/100=4609.52 then toal salary after increment=57619.05+4609.52----->62228.52 Ans D #### D QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in? options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18 = 4/18 The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs. Answer:B #### B QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rakesh ? options: A)1000 B)1100 C)1125 D)1200 E)1050 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>412 : 54 : 38 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 460012/23 = 2400 Share of Rakesh => 46005/23 = 1000 ANSWER:A #### A QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer:A #### A QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)39.1 E)None SOLUTION:Sol. Therefore correct sum = ( 36 × 50 + 48 – 23) = 1825. Therefore correct mean = 1825 / 50 = 36.5. Answer C #### C QUESTION:If log10 2 = 0.3010, the value of log10 80 is: options: A)1.5252 B)1.903 C)3.9252 D)3.903 E)2.5252 SOLUTION:= log10 8 + log10 10 = log10 (23 ) + 1 = 3 log10 2 + 1 = (3 x 0.3010) + 1 = 1.9030. ANSWER B #### B QUESTION:72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand? options: A)Rs. 3.23 B)Rs. 5.11 C)Rs. 5.51 D)Rs. 7.22 E)None SOLUTION:Explanation : The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7. To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504. It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase . Let us now roughly multiply the decimal values of the options also by 72, e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36. So, option (1) will yield (216 + 14) = 230 (approximately), option(2) will yield (360 + 7) = 367 (approximately), option(3) will yield (360 + 36) = 396 (approximately), and option(4) will yield (504 + 14) = 528 (approximately). Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96. Answer : C #### C QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40x+52x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =2512 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)3 B)7 C)8 D)5 E)1 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? options: A)30days B)35days C)40days D)44days E)45days SOLUTION:Explanation: (A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5 A complete remaining work in 2/550 = 20 Total work = 10+20= 30days Answer: Option A #### A QUESTION:There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd. options: A)8/16 B)9/16 C)10/16 D)11/16 E)7/16 SOLUTION:since, p(odd)=3p(even) and p(odd)+p(even)=1 hence p(odd)=3/4 now only oddodd=odd hence two odd i s p(odd)=3/43/4=9/16 ANSWER:B #### B QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400? options: A)8100 B)3388 C)7767 D)2009 E)22888 SOLUTION:6400* 9/8 * 9/8 = 8100 Answer: A #### A QUESTION:A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack? options: A)106 B)301 C)309 D)400 E)450 SOLUTION:Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301. Answer: B) 301 #### B QUESTION:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean? options: A)a) 43.6 B)b) 60 C)c) 72 D)d) 77.5 E)e) 81 SOLUTION:Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it. Here, we're told two things about a group of numbers: 1) The average of the group is 80 2) The standard deviation of the group is 14 If you go 1 SDupfrom the average, you hit.....80+14 = 94 If you go 1 SDdownfrom the average, you hit.....80-14 = 66 If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108 If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52 Etc. Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean.... 2.60 SDsupwould be.....80 + 2.60(14) = 43.6 A #### A QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:Convert 0.30 in to a vulgar fraction ? options: A)18/50 B)16/50 C)3/10 D)19/50 E)None SOLUTION:Answer 0.30 = 30/100 = 3/10 Correct Option: C #### C QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now? options: A)8 B)12 C)16 D)20 E)24 SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with: 1) Today, Jim is TWICE as old as Fred 2) Today, Sam is 2 years younger than Fred 3) Six years ago, Jim was 7 times as old as Sam. let's TEST Answer D: 20 IF....Jim is currently 20 years old.... Fred is 10 years old Sam is 8 years old 6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer. D #### D QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full. After 28 days, the dish was one quarter full. After 27 days, the dish was one eighth full. After 26 days, the dish was one sixteenth full. After 25 days, the dish was 1/32 full. After 24 days, the dish was 1/64 full. The answer is C. #### C QUESTION:Two dice are rolled. The probability of getting a sum of at least 9 is options: A)13/36 B)5/18 C)35/36 D)11/36 E)15/36 SOLUTION:Sum of 9 = {(3,6) (6,3)} = 2ways. Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways. Sum of 11 = {(6,5) (5,6)} = 2 ways. Sum of 12 = {(6,6) (6,6)} = 2 ways. Therefore, Favourable cases = 10 Total cases = 6 x 6 = 36. Therefore, Probability = 10/36 = 5/18. ANSWER:B #### B QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Important point to notice- 2.5% decrease from the original price 2.5% of 22,000= 550 Total reduction in 6 years= 5506= 3300 Final price= 22,000 +1500 - 3300= 20,200 C is the answer #### C QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected? options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9) SOLUTION:x red balls y green balls x+4+y+5 is the total =x+y+9 x+5 is the number of red balls so (x + 5)/(x + y + 9) the answer is C #### C QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc... The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc... The distances between marks are 3/12, 1/12, and 2/12. The answer is C. #### C QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:Find the value of a from (15)^2 x 8^3 Ã· 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 Ã· 256 = a = 225 x 512 Ã· 256 = 450 E #### E QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)x years. ((2/5)x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 11030=3,300 copies. Answer: C. #### C QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50X + 500 (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)21 B)24 C)88 D)99 E)26 SOLUTION:(1618)/12 = 24 Answer: B #### B QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 16 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 16: 8 :: 12 : x => 12 x 16 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (12 x 16) => x = 5 Answer : B #### B QUESTION:How many ways could two people sit at a table with four seats in which two of the four seats will remain empty? options: A)60 B)12 C)112 D)118 E)120 SOLUTION:ways in which 2 seats out 4 can be selected = 4C2 ways in which 2 people can be arranged in 2 seats = 2! Total ways of arrangement = 4C22! =43 =12 Ans = B #### B QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: DaysRate=Work 51/7+61/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114. options: A)2 or ½ B)2/3 or 3/2 C)¾ or 4/3 D)4 or ¼ E)5 or 1/5 SOLUTION:Let the terms be a/r, a , ar a/r a ar = a 3 =216, a =6 (a/ra )+ (aar) + (ara/r ) =114, a 2/r + a 2 r + a 2 =114 a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114 6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0, On solving, r = 2/3 or 3/2 ANSWER:B #### B QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock options: A)47 B)76 C)28 D)66 E)99 SOLUTION:Explanation: For ticking 6 times, there are 5 intervals. Each interval has time duration of 45/5 = 9 secs At 12 o'clock, there are 11 intervals, So total time for 11 intervals = 11 × 9 = 99 secs. Answer: E #### E QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips? options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32 SOLUTION:(1/2) (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7][8] = ? options: A)[22] B)[44] C)[75] D)[88] E)[90] SOLUTION:[7][8]=(72+1)(8/2+1) =[75]. Ans -C #### C QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is: options: A)364724 B)365387 C)365737 D)366757 E)366767 SOLUTION:Required number= 999366+103 = (1000-1)366+103 = 366000-366+103 = 365737. ANSWER:C #### C QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:If 45-[28-{37-(15-)}]= 56, then * is equal to: options: A)-29 B)-19 C)17 D)29 E)39 SOLUTION:45-[28-{37-(15-)}]= 56 => 45-[28-{37-15+}]=56 45-[28-37+15-]=56 => 45[43-37-]=56 45-[6-]=56 => 45-6+=56 39+=56 => =56-39 = 17 ANSWER:C #### C QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required? options: A)34 B)40 C)68 D)88 E)26 SOLUTION:We have: l = 20 ft and lb = 60 sq. ft. So, b = 3 ft. Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft. ANSWER:E #### E QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)10 D)8 E)9 SOLUTION:US = 15 DS = 35 M = (35 - 15)/2 = 10 Answer: C #### C QUESTION:probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits? options: A)9/27 B)10/27 C)11/27 D)12/27 E)11/26 SOLUTION:(1/31/3)[guy1](1/31/3)[guy2] for 1 hit each: (4 ways) (2/31/3)(2/31/3), (2/31/3)(1/32/3), (1/32/3)(2/31/3), (1/32/3)(1/32/3) for 2 hits each:(1 way) (2/32/3)(2/32/3) Add all these cases, you will get answer as 11/27. ANSWER:C #### C QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog? options: A)16.5 kmph B)16.6 kmph C)16.4 kmph D)16.9 kmph E)16.2 kmph SOLUTION:In an average speed of 22 kmph horse got dog in 6 hours So distance=speedtime distance=226=132km Dog takes 8 hours to travel 132 km. So the speed if dog is speed=distance/time speed=132/8=16.5 kmph Answer: 16.5 kmph Answer A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? options: A)23/35 B)23/38 C)23/18 D)53/18 E)23/22 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A #### A QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)Monday SOLUTION:Explanation: Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer: Option C #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:What is the smallest positive integer x, such that 6000x is a perfect cube? options: A)4 B)6 C)36 D)12 E)18 SOLUTION:Take out the factors of 6000 that will come 2310^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2 C is the answer. #### C QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)14 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m. Answer C #### C QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is options: A)250 B)276 C)280 D)285 E)None SOLUTION:Solution since the month begins with a sunday , so there will be five sundays in the month. Required Average = (510x5+240x25 / 30) = (8550 / 30) = 285 Answer D #### D QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together? options: A)120 B)110 C)105 D)140 E)135 SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8C6 + (8C5 * 2C1) this is 28 + 112=140 Answer : D #### D QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:A car crosses a 720 m long bridge in 2 minutes. What is the speed of car in km per hour? options: A)20.5 km/hr B)21.6 km/hr C)31.6 km/hr D)15.6 km/hr E)22.3 km/hr SOLUTION:Speed = 720 m/sec. 360/60m/s = 6 m/sec. Converting m/sec to km/hr (see important formulas section) =6 x 18/5 km/hr 5 = 21.6 km/hr B #### B QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:What is the SI on Rs.8000 from August 6th to Dec 30th at 5% per annum rate of interest? options: A)Rs 100 B)Rs 120 C)Rs 140 D)Rs 160 E)Rs 200 SOLUTION:Number of days from August 6th to December 30th = 146 days ( we don’t count the given day) Simple Interest= PTR 100 = 8000 x 146 365 x 5 100 = Rs 160 D #### D QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? options: A)0.44 B)0.55 C)0.65 D)0.75 E)0.85 SOLUTION:Number of people whose age is less than 20 is given by 160 - 90 = 70 Probability P that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer A #### A QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:Sum of 42 odd numbers is? options: A)1764 B)1774 C)1784 D)1794 E)1754 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 42 odd numbers = 42^2 = 1764 ANSWER:A #### A QUESTION:Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. options: A)Rs. 610 B)Rs. 612 C)Rs. 614 D)Rs. 616 E)None of these SOLUTION:Explanation: Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112 So compound interest = (8112 - 7500) = 612 Answer: B #### B QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)1752 B)1799 C)1719 D)1750 E)1800 SOLUTION:Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2 = 1800 Answer: E #### E QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)500m C)C)650m D)D)750m E)E)1200m SOLUTION:Relative speed of the policeman = 20-16 = 4 km/hr time taken by policeman to cover 300m = (300/1000)(1/4) = 3/40 hr In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m Answer is E #### E QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg? options: A)72 B)47 C)40 D)28 E)20 SOLUTION:940(30/100) = 282 ---- 6 ? ---- 1 => Rs.47 Answer:B #### B QUESTION:Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)s.225 B)s.288 C)s.485 D)s.279 E)s.282 SOLUTION:Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5 SP = CP[(100 + profit%)/100] = 232.5 * [(100 + 20)/100] = Rs.279. Answer:D #### D QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs.2(1/9) B)Rs.2(2/9) C)Rs.3(1/9) D)Rs.1(1/9) E)Rs.2(2/5) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10100/((100-10 )5) = Rs.2(2/9) B #### B QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged? options: A)6 B)48 C)36 D)24 E)12 SOLUTION:Dhoni have to sit at either of the ends. If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24 David can also sit on the other end, then another 4! ways we can arrange. So total number of ways = 24+24 = 48 Answer : B #### B QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)100]%=50% Answer A) 50. #### A QUESTION:In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 30, find the number? options: A)11201 B)12102 C)12081 D)12108 E)10126 SOLUTION:D 12108 Let the three digit numbers be 100a + 10b + c a = b + 2 c = b - 2 a + b + c = 3b = 30 => b = 10 So a = 12 and b = 8 Hence the three digit number is: 12108 #### D QUESTION:What is the units digit of 32! + 50! + 2! + 4!? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:For all N greater than 4, the units digit of N! is 0. The sum of the four units digits is 0 + 0 + 2 + 4 = 6 The units digit is 6. The answer is D. #### D QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way? options: A)5 sec B)4 sec C)3 sec D)6 sec E)1 sec SOLUTION:T = 30/36 * 18/5 = 3 sec Answer: C #### C QUESTION:If a randomly selected non-negative single digit integer is added to {2, 3, 4, 9}. What is the probability that the median of the set will increase but the range still remains the same? options: A)0.2 B)0.3 C)0.4 D)0.5 E)0.6 SOLUTION:We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes. Hence, the total number of outcomes is 10. We need to find the probability that the median of the set will increase but the range still remains the same. The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater. For the range to remain the same, the number must be between 2 and 9 inclusive. To satisfy both conditions, the number selected must be 4, 5, 6, 7, 8, or 9. The probability is 6/10 = 0.6 The answer is E. #### E QUESTION:The number of positive integer solutions for the equation x +y +z + t = 18 is options: A)640 B)780 C)380 D)540 E)680 SOLUTION:The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k (k-1)C(n-1)- where k is the number and n is number of variable in the equation. 18-1 C 4-1 = 17C3 = 680 Answer : E #### E QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)64% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5(4/5) of the original price, which nets to 0.64 of the original price, or 64%. E #### E QUESTION:The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m. correct answer A)50 #### A QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is options: A)28 B)H C)27 D)29 E)271 SOLUTION:Answer:B #### B QUESTION:The daytime telephone rate between two cities is 50 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is: options: A) 0.4(0.60) + 35c B) 0.4(0.50 + 0.32c) C) 0.4(0.60 + 9c) D) 0.6(0.60 + 32c) E) 0.6(0.60 + 0.35c) SOLUTION:For first three minutes = 50 cents Remaining minutes = 35 -3 = 32 charge for 32 minutes = 32c total cost (if the call was made in daytime) = 0.50 + 32c 60% chargereducedon night calls => 40% charge =>0.4(0.50 + 32c) Hence, Answer is B #### B QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 700/20 S = 35 M/Sec Speed= 3518/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 126 Kmph Answer: A #### A QUESTION:In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is: options: A)4 B)5 C)6 D)7 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 15 : 9 :: 12 : x => 12 x 15 x x = 10 x 8 x 12 => x = 10 x 9 x 12 / (12 x 15) => x = 7 Answer : D #### D QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25 SOLUTION:Explanation : Face value of each share = Rs.20 Dividend per share = 9% of 20 = 9×20/100=9/5 He needs to have an interest of 12% on his money ie, Money Paid for a share 9×12/100=9/5 Money Paid for a share=9/5×100/12=15 ie, Market Value of the share = Rs.15 Answer : Option C #### C QUESTION:If a sum of money doubles itself in 20 years at simple interest, the ratepercent per annum is options: A)12 B)12.5 C)13 D)5 E)14 SOLUTION:Explanation: Let sum = x then Simple Interest = x Rate = (100 x) / (x * 20) = 5 Option D #### D QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price 100/(100+profit) C.P. = 100100/130 = $77(approximately) Answer is D #### D QUESTION:Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March? options: A)5% B)10% C)20% D)25% E)50% SOLUTION:Let J,F,M be the values of the stock in Jan,Feb and March. Thus, per the question, J = 0.9F = 1.2M ----> M =0.75F Thus the % decrease from F to M = (F-M)/(F) 100 = (F-0.75F)/F 100 = 0.25100 = 25 %, D is the correct answer. #### D QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)96 C)100 D)125 E)250 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 5.6 , so radius is 2.8 New area = 7.84π Increase in area is 3.84π % increase in area = 3.84/4100 So, % increase is 96% Answer will be (B) #### B QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? options: A)62% B)69.45% C)70% D)71% E)72% SOLUTION:Required percentage = [ (288 + 98 + 3.00 + 23.4 + 83) x 100 ] % (420 + 142 + 3.96 + 49.4 + 98) = [ 495.4 x 100 ] % 713.36 ~= 69.45%. B) #### B QUESTION:The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ? options: A)15 : 8 : 2 B)19 : 7 : 9 C)7 : 15 : 10 D)12 : 9 : 17 E)None of these SOLUTION:Explanation: Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively. Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y) Now, 6x – 5y = 1/4(6x) 24x – 20y = 6x 18x = 20y x/y = 20/18 = 10 / 9 Savings of P / Savings of Q = 6x – 5y / 8x – 8y = [6(x/y) – 5] / [8(x/y) – 8] = [(6 * 10/9) – 5] / [(8 * 10/9) – 8] = 15/8 Savings of Q / Savings of R = 8x – 8y / 11x – 12y = [8(x/y) – 8] / [11(x/y) – 12] = (8 * 10/9) – 8 / (11* 10/9) – 12 = 8/2 Ratio of savings of P : Q : R = 15 : 8 : 2 ANSWER: A #### A QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D <<<Examples ends QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 9/3 m = 150 m. ANSWER : OPTION D #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally? options: A)475 B)700 C)220 D)400 E)None of these SOLUTION:Explanation : He sells 20% of oranges and still there are 380 oranges remaining => 80% of oranges = 380 ⇒ (80 × Total Oranges)/100 = 380 ⇒ Total Oranges/100 = 4.75 ⇒ Total Oranges = 4.75 × 100 = 475 Answer : Option A #### A QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean? options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5 SOLUTION:The value which is exactly two SD below the mean is: mean-2SD=13.5-20.5=12.5. Answer: E. #### E QUESTION:Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? options: A)76 seconds B)16 seconds C)18 seconds D)27 seconds E)19 seconds SOLUTION:Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds. Answer: D #### D QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is options: A)40 B)49 C)80 D)88 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 22 and x2 + y2 = 386. Now, 2xy = (x+y)2 - (x2 + y2) = (22)2 - 386= 484 - 386= 98 xy = 49. Answer B #### B QUESTION:For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! A #### A QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient = (19 x 41 x a) + (19 x 2) + 9 = 19 x (41a + 2) + 9 = 19 x (New quotient) + 9 \inline \fn_jvn \therefore Required remainder = 9 Answer:A #### A QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4? options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters SOLUTION:4:1 --- 60 1:4 2:8 --------------- 5 5 ----------- 60 5 ----------- ? => 60 liters ANSWER:A #### A QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:8k8 + k88 -------- 1,6w6 If k and w represent non-zero digits within the integers above, what is w? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16w6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8+7=16 or 8+8=16 (k can not be less than 7 or 9, as the result won't be 16*). After that it's easy to get that k=7 and w=6. Answer: A. #### A QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2 6! = 360 = B #### B QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is: options: A)0 B)10 C)20 D)30 E)40 SOLUTION:You can calculate the LCM (10,14) = 70. After that you should check which of the possible X values will result in a number divisible by 70. The only possibility for this is 30 ( because 250 + 30 = 280 = 704) Answer D #### D QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Answer:D #### D QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream? options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 51/3 = 17 kmph ANSWER:E #### E QUESTION:The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7) options: A)80 m2 B)84 m2 C)88 m2 D)86 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 4 = 88 m2 Answer C #### C QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)7 B)9 C)8 D)4 E)5 SOLUTION:25 = E/(1000 - E) 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 8 Answer:C #### C QUESTION:Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is : options: A)a) 4 B)b) 3 C)c) 2 D)d) 1 E)e) 0 SOLUTION:Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 396 99c - 99a = 99(c - a) = 396 396 = 994 = 99(c - a) So c - a = 4 Answer (A #### A QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 18/5 = 60 km/hr. Answer: C #### C QUESTION:The remainder when 1!+2!+3!...+50! divided by 8! will be options: A)21 B)5193 C)77 D)9275 E)19 SOLUTION:The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!. So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!. So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320) So remainder is 5193. Answer:B #### B QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours? options: A)125 miles B)225 miles C)520 miles D)425 miles E)525 miles SOLUTION:During each hour, the car travels 65 miles. For 8 hours it will travel 65 + 65 + 65 + 65 + 65+ 65 + 65 + 65 = 8 × 65 = 520 miles correct answer is C) 520 miles #### C QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:26=12.Answer is B. #### B QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 54 years now, the son's age 8 years back was? options: A)12yr B)19yr C)14yr D)10yr E)20yr SOLUTION:Let the son's present age be x years Then, 54-x = x x = 27 Son's age 8 years back = 27-8= 19years Answer is B #### B QUESTION:In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)170 C)C)190 D)D)210 E)E)1663200 SOLUTION:11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200 Option 'E' #### E QUESTION:How much interest will $8,000 earn in 9 months at an annual rate of 6%? options: A)$250 B)$350 C)$360 D)$550 E)$650 SOLUTION:Soln:- 9 months = 3/4 of year; 6% = 6/100=3/50; $8,000(principal)3/50(interest rate)3/4(time)=$360. ANSWER:C #### C QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6d B) 7/3d C) 10/3d D) 7/2d E) 9/2d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:A square with sides of 15 units each. What would be the area of the square. Consider a square as a combination of two right angled triangles. options: A)100 B)256 C)225 D)81 E)144 SOLUTION:A square can be considered as a set of two right angled triangles joined from the hypotenuse. Since the sides are 10 units each. The height and base of both the triangles is 10 each. Area of a right angled triangle is 1/2 * base * height Area of both the triangles is 2 * 1/2 * base * height. Since both triangles are similar. = base * height = 1515 =225 Ans: C #### C QUESTION:Working together, Jose and Jane can complete an assigned task in 5 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 15 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose options: A)26 days B)15 days C)60 days D)65 days E)36 days SOLUTION:Assume: Jose does 1 job in x days, so Jose does 1/x job in a day Jane does 1 job in y days, so Jane does 1/y job in a day Together, they does (x+y)/xy job in a day. This is equals to 1/20. So (x+y)/xy = 1/5 5(x+y) = xy Next, we're told 1 job takes 15 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half. x/2 + y/2 = 15 x+y = 30 So xy = 150 The answer choices are: 26 days 15 days 60 days 65 days 36 days From the answer choices, So I'll go for 15 days for Jose and 10 days for Jane. Answer : B #### B QUESTION:What should come in place of the question mark (?) in the following equation? 45789+ 34567 = 610+ ? options: A)96543 B)13678 C)23456 D)56789 E)79746 SOLUTION:45789+ 34567 = 610+ ? 45789+ 34567 – 610 = 79746 Answer E #### E QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)5 C)8 D)13 E)15 SOLUTION:Total # of students = 40 Avg # of books per student = 2 Total # of books = 402 = 80 # of student borrowed at least 3 books = 40-2-12-10 = 16 # of books borrowed by above 16 students = 80-(121)-(102) = 48 Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 153 = 45 So maximum # of books borrowed by any single student = 48-45 = 3 option A #### A QUESTION:A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.9 km C)3.4 km D)1.9 km E)5.6 km SOLUTION:Explanation: Speed in still water = 4 kmph Speed of the current = 1 kmph Speed downstream = (4+1) = 5 kmph Speed upstream = (4-1) = 3 kmph Let the required distance be x km Total time taken = 1 hour â‡’ x/5+x/3=1 â‡’3x+5x=15 â‡’8x=15 â‡’x=1.9 km Answer: Option D #### D QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18(K+(K+1)+...+(K+N-1)) = 18(N(2K+N-1)/2). So the average is 153=[18(N(2K+N-1)/2)]/N = 18(2K+N-1)/2 = 9 (2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---*). By ), *) we have K=2, N=14. Since 153/18 = 8.5, 188<153<189. So the number of terms R which are smaller than the average is 182, 183, ..... ,188 ---> 7. The answer is C. #### C QUESTION:What is the value of x if (64^2)-(36^2)=20x? options: A)120 B)100 C)140 D)130 E)115 SOLUTION:20x=(64+36)(64-36) 20x=10028 x=(10028)/20 x=528 x=140 Option C #### C QUESTION:Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is: options: A)8 B)4 C)12 D)16 E)14 SOLUTION:Explanation : Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4. Number of Knives = 3x = 12. Answer : C #### C QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in options: A)6 days B)2 days C)3 days D)5 days E)4 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. C #### C QUESTION:The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/91% B)18 2/11% C)27 3/11% D)18 2/91% E)12 2/11% SOLUTION:14 CP = 11 SP 11 --- 2 CP 100 --- ? =>27 3/11% Answer:C #### C QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square options: A)337 B)297 C)266 D)116 E)130 SOLUTION:Explanation: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 Required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square. Answer: E #### E QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Sandy can do 1/12 of the job each day. Molly can do 1/24 of the job each day. The combined rate is 1/12 + 1/24 = 1/8 of the job each day. The job will take 8 days. The answer is C. #### C QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:A woman swims downstream 54 km and upstream 6 km taking 6 hours each time, what is the speed of the woman in still water? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:54 --- 6 DS = 9 ? ---- 1 6 ---- 6 US = 1 ? ---- 1 M = ? M = (9 + 1)/2 = 5 Answer:D #### D QUESTION:Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together? options: A)300 B)325 C)350 D)375 E)400 SOLUTION:At 6:45, the first train is 75 km ahead. The second train gains 25 km each hour. The time it takes the second train to catch the first train is 75 / 25 = 3 hours. In this time, the second train travels 3125=375 km. The answer is D. #### D QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work? options: A)6 days B)7.2 days C)9.5 days D)12 days E)13 days SOLUTION:EXPLANATION: Hint: A's one day work = 1/12 B's one day work = 1/18 (A + B)'s one day work = 1/12 + 1/18 = (18 + 12)/(12 x 18)= 30/216= 1/7.2 Together, A & B will finish the work in 7.2 days. ANSWER IS B #### B QUESTION:The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers? options: A)2/3 B)1/12 C)2/9 D)1/2 E)1/24 SOLUTION:Probability of first member an English teacher = 3/9 Probability of second member an English teacher = 2/8 Probability of both being english teacher = 3/9 x 2/8 =1/12 (B) #### B QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:Find the total number of divisors of 1728(including 1 and 1728) options: A)28 B)29 C)30 D)31 E)32 SOLUTION:1728=2^63^3 no. of divisors = (6+1)(3+1)=28 ANSWER:A #### A QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 (2/25) = 44 seconds Answer: E #### E QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond? options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525 SOLUTION:Solution Let S be the sample space. Then, n(S) = 52C3 = 22100 Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 26 =13C1 * 13C2= 1372 = 936 P(E) = n(E) / n(S) = 936 / 22100 = 234/5525 = 234/5525. Answer D #### D QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Let the number of men be m and so the number of women = 15-m Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start. Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days). Let the total work be 360 units (LCM of 180 and 120). 1 man does 360/120 = 3 units per day 1 woman does 360/180 = 2 units per day Based on above facts, Total work by men + women in these 17 days = 360 units m93 + (15-m)62 = 360, 27m + 180 -12m = 360, Solving m=12. Num of men = 12 and number of women = 15-12 = 3 ANSWER:C #### C QUESTION:If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ? options: A)4 B)7 C)5 D)3 E)6 SOLUTION:Answer Dividing numerator as well as denominator by b, we get Given Exp. = (5a + 4b) / (5a - 4b) = (5a/b + 4) / (5a/b - 4) Since a/b = 6/5 this implies that =[(56)/5 +4]/[(56)/5 -4)] = (6 + 4) / (6 - 4) = 5 Option: C #### C QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:One train is traveling 72 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)2:1 D)5:4 E)5:1 SOLUTION:72 5/18 = 10 20:10 => 2:1 Answer: C #### C QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 98900 E)Rs. 10000 SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:If P represents the product of the first 16 positive integers, then P is not a multiple of: options: A)a) 99 B)b) 84 C)c) 72 D)d) 65 E)e) 57 SOLUTION:a) 99 = 911 b) 84 = 473 c) 72 =98 d) 65 = 513 e) 45 =95 since 11 is not there in first 15 positive numbers it is the only possibility A #### A QUESTION:How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? options: A)48 B)12 C)72 D)100 E)720 SOLUTION:So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 24!=48. Answer A. #### A QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 1/5. The probability that none of them will be alive for 10 more yrs, is options: A)1/2 B)1 C)2/3 D)1/5 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/5 Ans.(D) #### D QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? options: A)2.04% B)6.12% C)8% D)8.25% E)10% SOLUTION:Per quarter, interest = 2% So for a year, interest = 8% Due to quarter cumulation, effective yield (YTM) would be slight higher than 8% Answer = 8.25% =ANSWER:D #### D QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:Find the odd man out 4, 16, 25, 36, 42, 64 options: A)36 B)25 C)42 D)95 E)4 SOLUTION:2^2 = 4 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 ANSWER:C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60100)/36) %=285% Answer E #### E QUESTION:Positive Integer A gives the remainder of 9 when divided by another positive Integer B. If A/B = 47.45, what is the value of B? options: A)96 B)75 C)48 D)20 E)12 SOLUTION:I think the answer should be 25. This is how i solved. .45 of B = Remainder .45 of B = 9 B = (9 100) / 45 = 20. D #### D QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years? options: A)0.400 tons B)0.200 tons C)0.175 tons D)0.160 tons E)0.185 tons SOLUTION:X is the quantity of gold reserves of the mine After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining. So we have: X1=95/100 X X2=95/100 X1 X3=95/100 X2 X4=95/100 X3 By multiplying both ends of the equations we get: X1X2X3X4 = (95/100)^4 XX1X2X3 Simplification leaves us with: X4 = (95/100)^4 X X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4) In this case, given X was: X=2 tons So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton Answer E. #### E QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B QUESTION:In how many ways can the integer 120 be expressed as a product of two different positive integers? options: A)10 B)8 C)5 D)4 E)2 SOLUTION:120=(2^3)35 Since 120 is not a perfect square, no of ways=5 Answer C #### C QUESTION:a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? options: A)30.5 B)31.0 C)32.0 D)33.0 E)34.5 SOLUTION:CP = 206+254+303+351=345 SP = 1.4345=483 Total no.of kgs=6+4+3+1=14 SP per kg=483/14 = 34.50 ANSWER:E #### E QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? options: A)s.4000 B)s.5000 C)s.4500 D)s.4800 E)s.8000 SOLUTION:CI=8820,R=5,N=2 CI=P[1+R/100]^2 =P[1+5/100]^2 8820=P[21/20]^2 8820[20/21]^2 8000 ANSWER:E #### E QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:What is the remainder when 103 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =441=16/9==> Remainder=7 Answer: E #### E QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games? options: A) 7 B) 6 C) 5 D) 4 E) 3 SOLUTION:18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most. Answer (C) #### C QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7 SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively. Then, (4.5x - 4)/(3x + 4) = 1/1 1.5x = 8 => x = 5.33 Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:200002+8x=1566510 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French? options: A)9 B)10 C)11 D)12 E)8 SOLUTION:let no.of persons who speeks booth latin and french = x so, no.of persons who speeks only latin = 13-x no.of persons who speeks only french= 15-x no.of persons who speeks dont speek any lag = 6 therefore (13-x)+(15-x)+x+6=25 34-x=25 x=9 ANSWER:A #### A QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)1/2 D)5/6 E)2/3 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/41/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/42/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: E. #### E QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)None of these SOLUTION:Explanation : The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5. and all these letters are different. Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120 All The 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6 Hence, required number of ways = 120 x 6 = 720. Answer : Option B #### B QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%? options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33% SOLUTION:10 CP = 15 SP 15 --- 5 100 --- ? => 33.33% (Loss) Answer:E #### E QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 6 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)3/16 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 6 = 6C2 Total possible outcomes - 2^6 (each child can be either a girl or a boy) Probability=2C16C2/2^6= 26/222222=12/64=3/16 Ans=D #### D QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay? options: A)m/(5d) B)20d C)5d D)5dm E)20d/m SOLUTION:Total income of Sara in a month = d5m dollars. = d5m = 5dm Answer is D #### D QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 12.. so total who won N = 11+12 = 23.. B #### B QUESTION:The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ? options: A)11 B)13 C)14 D)16 E)10 SOLUTION:Explanation : Let Somu's age be x and that of his father be 3x. So, x - 8 = 3x - 8/5 = x = 16 Answer : Option D #### D QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? options: A)129 B)128 C)189 D)187 E)112 SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135 SP = CP[(100 + profit%)/100] = 135 [(100 + 40)/100] = Rs. 189. Answer: C #### C QUESTION:Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed. options: A)s. 5266 B)s. 5396 C)s. 5228 D)s. 5218 E)s. 52192 SOLUTION:Explanation: Let us assume Mr. Karan borrowed amount is Rs. A. (the principal) By formula of simple interest, S.I. = PRT / 100 Where P = The principal, R = Rate of interest as a %, T = Time in years S.I. = (P * 6 * 9)/100 = 54 P/100 Amount = Principal + S.I. 8310 = P + (54P/100) 8310 = (100P + 54P)/100 8310 = 154P/100 P = (8310 * 100)/154 = Rs. 5396.104 ANSWER: B #### B QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)635.50 B)635.53 C)635.57 D)635.52 E)635.51 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer: A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. âˆ´ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence. options: A)21 B)20 C)40 D)42 E)19 SOLUTION:n for cyclic hand shake and n-1 for linear handshake. so here no of hand shake is 20. ANSWER:B #### B QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 220500 + 18000 = 59000 Answer: D #### D QUESTION:Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit? options: A)$8100 B)$8820 C)$8800 D)$8810 E)$8825 SOLUTION:Amount = 8000 x (1 + 5/100)^2) = 8000 x 21/20 x 21/20 =8820. Answer B)$8820 #### B QUESTION:How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length? options: A)18.9 sec B)88.9 sec C)22.9 sec D)30.00 sec E)72.0 sec SOLUTION:D = 110 + 390 = 500 m S = 60 5/18 = 50/3 T = 500 * 3/50 = 30 sec Answer: D #### D QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:The average height of 60 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ? options: A)287 cm B)150.8 cm C)276 cm D)287 cm E)297 cm SOLUTION:Total height = 150 * 60 = 9000 cm. New average = [9000 - 5 * 146 + 5 * 156 ] / 60 = 150.8 cm. Answer:B #### B QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)a^2 = (3/2)a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to bsqrt2 so, b sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)a^2 so, a^2 = (2/3)b^2 = (2/3)*18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A <<<Examples ends QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION:If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ? options: A)55 B)45 C)33 D)60 E)40 SOLUTION:Explanation: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26 GREEN = 7 + 18 + 5 + 5 + 14 = 49 Thus we get, VIOLET = 22 +9 +15+12 + 5 + 20 = 83 PINK = 16 + 9 + 14 + 11 = 50 Thus, difference is 83 – 50 = 33. ANSWER C #### C QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joined them. How many days will they take to complete the remaining work? options: A)3days B)4days C)2days D)8days E)5days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 days work = 6/9 = 2/3 remaining work = 1 – 2/3 = 1/3 18 men's 1 days work = 18/108 = 1/6 1/6 work is done by them in 1 day therefore, 1/3 work is done by them in 6/3 = 2 days. ANSWER C 2days #### C QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ? options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8 SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed) let E is the event of getting at least 1 head and 1 tail n(E) = TTH , HTT, THT, HHT, HTH, THH = 6 P(E) = n(E) / n(s) = 6/8 = 3/4 Ans- C #### C QUESTION:Car A runs at the speed of 60 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 70 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B? options: A)3 : 7 B)4 : 9 C)12 : 7 D)5 : 7 E)6 : 11 SOLUTION:Car A travels 60 × 8 = 480 km Car B travels 70 × 4 = 280 km The ratio is 480 : 280 = 48 : 28 = 12 : 7 The answer is C. #### C QUESTION:850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 17 E)e) 12 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 850 = 17 Answer: D #### D QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 610 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 1080)/60 = 18 Hence option (E). #### E QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:Mary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? options: A) 124% B) 102% C) 96% D) 80% E) 64% SOLUTION:Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 102 (70 percent more than Tim's income). Thus, Mary's income (102) is 102% of Juan's income (100). Answer: B. #### B QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed. options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above SOLUTION:My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 57 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 #### D QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)52% E)None of these SOLUTION:Explanation: cost price = (225 + 15) = 240 sell price = 300 gain = (60/240)100 = 25%. Answer: C #### C QUESTION:If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by options: A)15% B)20% C)25% D)30% E)40% SOLUTION:Sol. Let the original consumption = 100 kg and new consumption = x kg. So, 100 x 3 = x × 5 = x = 60 kg. ∴ Reduction in consumption = 40%. Answer E #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make? options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss SOLUTION:81 ---- 17 100 ----- ? è 20.98%loss Answer: B #### B QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:In how many ways can the integer 120 be expressed as a product of two different positive integers? options: A)10 B)8 C)5 D)4 E)2 SOLUTION:120=(2^3)35 Since 120 is not a perfect square, no of ways=5 Answer C #### C QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. â€¹=â€º 61. Answer C #### C QUESTION:There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen? options: A)2 B)3 C)14 D)16 E)20 SOLUTION:60% of 30 = 18. So, there are 18 red socks and there are 12 blue socks. Check out this possible cases once we have selected TWO socks: case a: 2 red socks, in which case we have a pair of matching socks. DONE! case b: 2 blue socks, in which case we have a pair of matching socks. DONE! case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet. Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock. If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock. In both cases, we are guaranteed to have a pair of matching socks. So, selecting 3 socks guarantees that we have a pair of matching socks. ANSWER:B #### B QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? options: A)229 B)270 C)877 D)266 E)281 SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages. Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left. 23⋅x−13⋅x=9023⋅x−13⋅x=90 13⋅x=9013⋅x=90 x=270x=270 So the book is 270 pages long. Answer:B #### B QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? options: A)990 B)495 C)1980 D)none E)Cannot be determined SOLUTION:Explanation : For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals. Answer : B #### B QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be options: A) 478,823 B) 511,913 C) 531,875 D) 538,424 E) 569,114 SOLUTION:To know the unit digit you can multiply both digit number: 5 x 5 = 25 This eliminates A, B, D, and E, because the number must end with a 5 So the answer is C #### C QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get? options: A)57% B)57.3% C)65% D)90% E)80% SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates) percentage of the total votes recd by the winning candidate = 10011620/20280 = 57.3% ANSWER:B #### B QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 30000(1 + 2/100)^4 = 30000 51/50 * 51/50 * 51/50 * 51/50 = $32472.96 C.I. = 32472.96-10000 = $2472.96 Answer is D #### D QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 918 = 162. Answer: Option A #### A QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)2388 B)2380 C)2888 D)2663 E)2922 SOLUTION:Kamal : Sameer = (9000 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs. 2380. Answer: B #### B QUESTION:With out any halt a train travels a certain distance with an average speed of 66 km ph , and with halts it covers the same distance at an average speed of 33 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ? options: A)48 min. B)12min. C)60min. D)18min. E)19min. SOLUTION:With halt in 1 hour the train travels 60km With out halt for traveling same distance it take 66/33= 2/1 = 120 minutes :. 60 minutes is the halting time per hour ANSWER:C #### C QUESTION:What is the remainder when 1274 * 1275 * 1277 1285 is divided by 12? options: A) 0 B) 6 C) 11 D) 9 E) 7 SOLUTION:1271127512771285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1) Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6. Answer: B #### B QUESTION:If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss. options: A)50 B)60 C)70 D)20 E)90 SOLUTION:Cost of 10 lollipops = $80 Sold each lollipop for $6 So he sold 10 lollipops for $(10 × 6) = $60 Loss = $(80 – 60) = $20 answer :D Therefore, loss = $ 20. #### D QUESTION:Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums? options: A)30 B)36 C)70 D)80 E)150 SOLUTION:Method I: the rates solution “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time: T = A/R = 15/(5/12) = 15(12/5) = (15/5)12 = 312 = 36 BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums. Answer = B. #### B QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? options: A)4 B)5 C)56 D)12 E)7 SOLUTION:Explanation: Let the price be = Rs.100, and number of units sold = 100 Then, sale value = Rs.(100 × 100) = Rs.10000 New sale value = Rs.(140 × 80) = Rs.11200 Increase% = 1200/10000 × 100 = 12% Answer: D #### D QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800Ã—1200 /12Ã—6)=30000 Option D #### D QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 15 = 45 => x = 60 km/hr. Answer:A #### A QUESTION:A club wants to mix 15 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Let number of pounds of 5$ candy to be used be w 6 = (158 + 5w)/(15 +w) =>90 + 6w = 120 + 5w => w = 30 Answer B #### B QUESTION:Two coins are tossed, find the probability that two Tails are obtained options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3 SOLUTION:The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(T,T)} P(E) = n(E) / n(S) = 1/4 B #### B QUESTION:A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple? options: A)1/5 B)2/7 C)2/9 D)3/5 E)4/11 SOLUTION:The total number of ways to choose 2 apples is 7C2 = 21 The number of ways that include the spoiled apple is 6C1 = 6 P(the spoiled apple is included) = 6/21 = 2/7 The answer is B. #### B QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------\|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (3540)/3 Hence Car2 will cover total distance in (3540)/(315) = 31.11 sec approx. Answer D #### D QUESTION:If you add all the numbers on your mobile phone , what is the answer? options: A)45 B)50 C)55 D)100 E)60 SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone. Therefore 0+1+2+3+4+5+6+7+8+9=45 Answer is A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 2) = 30 years. (A+B), now = (30+52)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:33 1/3% OF 330? options: A)80 B)90 C)110 D)120 E)130 SOLUTION:33 1/3 % = 1/3 1/3 × 330 = 110 C) #### C QUESTION:If the sum of the interior angles of a regular polygon measures up to 1440 degrees, then how many sides does the polygon have? options: A)10 B)16 C)12 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1440 180n - 360 = 1440 180n = 1800 n = 1800/180 = 10 ANSWER:A #### A QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)288 B)165 C)881 D)1277 E)121 SOLUTION:Speed = 54 5/18 = 15 m/sec. Length of the train = 15 * 25 = 375 m. Let the length of the platform be x m . Then, (x + 375)/36 = 15 => x = 165 m. Answer: B #### B QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)50 B)88 C)77 D)55 E)23 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is options: A)Rs.48,000 B)Rs.45,000 C)Rs.30,000 D)Rs.50,000 E)None of the above SOLUTION:investment by B=(590000)/(4+5) =50000 ANSWER:D #### D QUESTION:Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled? options: A)6 hrs 43 min B)2 hrs 25 min C)7 hrs 30 min D)6 hrs 32 min E)7 hrs 10 min SOLUTION:tank filled in 1 hr = 1/10 + 1/12 - 1/20 = 8/60 = 2/15 part so full tank is filled in 15/2 hrs = 7 hr 30 min.. ANSWER:C #### C QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? options: A)600 B)640 C)680 D)720 E)760 SOLUTION:The number of seats in the theater is 15 + (15+2) + ...+ (15+38)= 20(15) + 2(1+2+...+19)= 20(15) + 2(19)(20)/2= 20(15+19) = 20(34) = 680 The answer is C. #### C QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2 SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations. Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8. The right answer is choice (C). #### C QUESTION:In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons? options: A)17 B)18 C)56 D)21 E)23 SOLUTION:8p2 = 8 x 7 = 56 Answer: C #### C QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 8011/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 40 =20 hours Answer is D #### D QUESTION:How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ? options: A)6 B)3 C)2 D)1 E)5 SOLUTION:There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options. So, we start with a=1, we get b as -ve. out a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions) a=3, we get b as 3. Yes (Now we have 3 possible solutions) a=4, we get b as fraction. Out a=5, we get b again as some fraction. Out a=6 already taken. We have A,B options left. C,D,E are out. A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b. When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible. So, answer will be E. #### E QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? options: A)5:4 B)1:4 C)3:1 D)3:5 E)3:4 SOLUTION:12:16 = 3:4 ANSWER:E #### E QUESTION:After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is? options: A)Rs.2989 B)Rs.5029 C)Rs.5000 D)Rs.5197 E)Rs.5029 SOLUTION:Given SP = Rs. 6800 Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000 If SP = Rs. 8000, profit 60% CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs.5000 Answer: C #### C QUESTION:A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage? options: A)116% B)166.66% C)60% D)100% E)150% SOLUTION:Explanation: Let the cost price of 1 litre pure milk be Re.1, then {6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only and 8 litre mixture ->SP -> 8 x 2 = Rs.16 Profit %= [16/6 -6]x100=100/6=166.66% ANSWER IS B #### B QUESTION:At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? options: A)7 B)7/15 C)5/8 D)9/2 E)4/6 SOLUTION:Yellow: Blue = 3:2 Let Yellow = 3x and Blue = 2x 1/3 of Yellow are left handed => 1/3 * 3x = 3x/3 Yellow left handed 2/3 of Blue are left handed => 2/3 2x = 4x/3 blue left handed fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15 Answer : B #### B QUESTION:The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? options: A)40 B)41 C)46 D)42 E)49 SOLUTION:Total age of all students =23Ã—22 Total age of all students + Age of the teacher =24Ã—23 Age of the teacher =24Ã—23âˆ’23Ã—22=23(24âˆ’22)=23Ã—2=46 Answer is C. #### C QUESTION:How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? options: A)03 B)4 C)5 D)1 E)7 SOLUTION:You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines. AB , AC BA , BC CA , CB There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB. The lines are: AB, BC and AC ; 3 lines only. So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important. Answer:A #### A QUESTION:The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? options: A)45 B)65 C)75 D)78 E)90 SOLUTION:A + B + C = 3 84 = 252 A + B + C + D = 4 * 80 = 320 ---- (i) So, D = 68& E = 68 + 6 = 74 B + C + D +E = 79 * 4 = 316 --- (ii) From Eq. (i) & (ii) A-E = 320 – 316 = 4 A = E +4 = 74 + 4 = 78 D #### D QUESTION:A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members? options: A)182 B)208 C)224 D)229 E)302 SOLUTION:If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x but we are given .85x = 195 x = 229 So the original number of faculty members is 229 Correct Answer - D #### D QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ? options: A)28years B)29years C)30years D)31years E)32years SOLUTION:Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 25) years = 35 years. Ayush's father's present age = (35+ 5) years = 40 years. Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years. Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years. Answer: A) 28 year #### A QUESTION:Which of the following MUST yield an integer when divided by 11? options: A)The sum of eleven consecutive positive integers. B)The square of a prime number. C)The sum of two odd integers. D)The product of three consecutive odd numbers. E)The difference between a multiple of 8 and a multiple of 3. SOLUTION:For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, Ans(A). #### A QUESTION:If eight machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job? options: A)45 B)60 C)75 D)96 E)100 SOLUTION:using the std formula m1d1h1/w1=m2d2h2/w2 substituting the values we have 81/24/3=25/3x (converted 30 min into hours =1/2) 16/3=10/3x x=8/5 hour so 96 minutes ANSWER:D #### D QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)s. 99.75 B)s. 89.75 C)s. 72.75 D)s. 58.75 E)s. 49.75 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1 or, 35x + 42 = 39x – 39 or, x = 20.25 Thus the original expenditure of the mess = 35 x 20.25=708.75 Therefore x-1 = 19.25 hence 42 x 19.25 = 808.50 808.50 - 708.75 = Rs. 99.75 A #### A QUESTION:If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true? I. a + b + c > a^3 II. a × b × c < a^3 III. 5b > bc options: A)I only B)II only C)III only D)II and III E)I, II, and III SOLUTION:Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4 Putting the values in the answers only 'A' seems valid. #### A QUESTION:If p/q = 5/4 , then 2p+q= ? options: A)12 B)14 C)13 D)15 E)16 SOLUTION:let p=5, q=4 then 25+4=14 so 2p+q=14. ANSWER:B #### B QUESTION:The ages of two person differ by 12 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively options: A)30, 10 B)25, 5 C)29, 9 D)50, 30 E)20, 8 SOLUTION:Let their ages be x and (x + 12) years. Then, 5(x - 5) = (x + 12 - 5) => 4x = 32 =>x =8 Their present ages are 20 years and 8 year. ANSWER:E #### E QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? options: A)576 metres B)589 metres C)600 metres D)700 metres E)None SOLUTION:Solution Let the length of the outer edges be x metres. Then, length of the inner edge = ( x - 6)m. ∴ x2 - (x-6)2 = 1764 ‹=› x2-(x2-12x+36)= 1764 ‹=›12x = 1800 ‹=›x = 150. ∴ Required perimeter = (4x)m ‹=› (4 x 150)m = 600m. Answer C #### C QUESTION:In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998? options: A)80% B)105% C)120% D)112% E)138% SOLUTION:0,112R = x/1000.1R Answer D #### D QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 532=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 3^2 * 5 * n = 37K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2235 = 60. So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 607 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 602 or 6032 or 605 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has. Answer (C) #### C QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above SOLUTION:5510 = 550 665 = 330 880/15 = 58.66 ANSWER:C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000. 36/7 has a remainder of 1. Jan. 8th is: Friday + 1 day = Saturday The answer is D. #### D QUESTION:A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)22 days B)12 days C)67 days D)17 days E)18 days SOLUTION:C = 1/2 - 1/6 - 1/4 = 1/12 => 12 days Answer:B #### B QUESTION:A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? options: A)50 B)8 C)60 D)42 E)32 SOLUTION:in the first case the lady takes up 32 red colour then he takes up 24 y (cause he should take up pair) then he takes up 1y+1blue then 2blue(cause to make sure he has a pair of each color in hand) 32+24+2+2=60 ANSWER:C #### C QUESTION:A grocer has a sale of Rs. 3435, Rs. 3920, Rs. 3855, Rs. 4230 and Rs. 3560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? options: A)500 B)1000 C)6000 D)7000 E)2000 SOLUTION:Total sale for 5 months = Rs. (3435 + 3920 + 3855 + 4230 + 3560) = Rs. 19000. Required sale = Rs. [ (3500 x 6) - 19000 ] = Rs. (21000 - 19000) = Rs. 2000 Answer: Option E #### E QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/24=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is options: A)360 B)240 C)2520 D)480 E)None of these SOLUTION:Solution Order of vowels of fixed âˆ´ required number of ways are 7!/2!. Answer C #### C QUESTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y 1997- x1---- y1-- x1+y1 x1= ax .....(P) y1= 1.07y...(Q) x1+y1/x+y = 1.01 solve using P and Q and find x/y #### A QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 64 litres of milk = (1⁄4 × 64) litres = 16 litres. Answer A #### A QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:If 6a = 7b = 20, then 84ab = options: A)50 B)100 C)625 D)800 E)1250 SOLUTION:6a * 7b = 20 * 20 = 400 42 ab = 400 i.e. 84 ab = 800 Answer: Option D #### D QUESTION:In a certain store, the profit is 1150% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)30% B)70% C)900% D)250% E)120% SOLUTION:Let C.P. = Rs. 100. Then, profit = Rs. 1150, S.P. = Rs. 1250 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 1250 Profit = 1250 - 125 = Rs. 1125 Required percentage = 1125/1250 * 100 = 900% ANSWER:C #### C QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)20, 35, 48 E)None of these SOLUTION:Let the present ages are 4x, 7x, 9x. => (4x-8) + (7x-8) + (9x-8) = 56 => 20x = 80 => x = 4 So their present ages are: 16,28,36 ANSWER:B #### B QUESTION:The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : options: A)22.75 B)33.25 C)22.25 D)11.75 E)18.75 SOLUTION:Explanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48=18.75 Answer:E #### E QUESTION:A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 85 on the S scale? options: A)39 B)41 C)43 D)45 E)47 SOLUTION:A change of +18 on the R scale is a change of +30 on the S scale. R = (18/30)S + K = 3S/5 + K 6 = 3(30)/5 + K K = -12 R = 3S/5 - 12 R = 3(85)/5 - 12 = 51-12 = 39 The answer is A. #### A QUESTION:In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? options: A)150 B)750 C)1,250 D)1,500 E)2,500 SOLUTION:Given 150 deers were caught and they are tagged in the first slot. In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged. Given this 10% approximates the percentage of tagged deer in the forest..here number is 150.. then 100% is 1500.. is the number of deers population in the forest.. Answer: D is correct answer.. #### D QUESTION:The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is? options: A)8 B)3 C)9 D)4 E)2 SOLUTION:S.I. = (1600 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D #### D QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 9 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? options: A)72% B)80% C)100% D)120% E)125% SOLUTION:For A, r=8/2pi. Its capacity = (4pi)^2 * 9= 144pi For B, r=10/pi. Its capacity = (5pi)^2 8 = 200pi A/B = 144pi/200pi = 0.72 A #### A QUESTION:John bought 2 shares and sold them for $90 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had options: A) a profit of $10 B) a profit of $8 C) a loss of $8 D) a loss of $20 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-90 20-? $10 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-90 20-? $30 loss on the sale of 1 share. 10-30=Loss of $20 Answer: D #### D QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 23x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 44000 = 16,000 Answer (E) #### E QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:What number should replace the question mark? 105, 87, 70, 52, ? options: A)49 B)35 C)70 D)55 E)83 SOLUTION:B 35 The sequence progresses -18, -17, -18, -17. #### B QUESTION:If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit? options: A) 50/349 B) 1/313 C) 1/49 D) 1/100 E) 1/50 SOLUTION:Hundreds digit has to be 3 . So units digit needs to 3 as well And both Hundreds and Units digit needs to be 2 more than ten's digit The number is 313 Total numbers between 300 and 349 = (349-300)+1 = 50 Probability = 1/50 Answer E #### E QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true? I. c - a = 2 II. abc is an odd integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and III only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: C. #### C QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram? options: A)90° B)75° C)60° D)45° E)30° SOLUTION:let smaller be x ,larger becomes x+90... total of all angles=360 so 4x+180=360 and x=45 ANSWER:D #### D QUESTION:If 24 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)45 hours C)50 hours D)55 hours E)60 hours SOLUTION:Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40 Hence, 15 men can do it in 60 hours Answer is A. #### A QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195 = 495 m Required time = 495 * 2/55 = 18 sec Answer: B #### B QUESTION:The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers? options: A)9x + 8 B)3x + 3 C)5x + 1 D)5x + 4 E)15x + 12 SOLUTION:If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8. Answer is A. #### A QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours Answer: Option D #### D QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:The number of livestock in a farm at the beginning of year 2000 was 110,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 110,000. Which of the following expressions is correct? options: A)q>p B)p > q C)p = q D)With the exception of 1 instance, p will be equal to q E)There is no relation between p and q SOLUTION:Number plugging in will be best strategy for this question. Let p = 5%, Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence B is the correct answer. #### B QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:Tough and Tricky questions: Mixture Problems. A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture? options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5 SOLUTION:Answer = B) 5:15 ........................ Rum ..................... Coke ................. Total First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2) Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3) Total .................. 10 ............................. 28 .................... 38 Ratio = 10:30 = 5:15 B #### B QUESTION:If there are 10 apples and 20 oranges, what is the ratio of apples to oranges? options: A)10:20 B)2:4 C)1:2 D)4:8 E)It cannot be determined from the information given SOLUTION:A ratio should be reduced to the lowest common denominator. 10:20 means 10x:20x which can be written as 1(10):2(10)... ANSWER:C #### C QUESTION:The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is: options: A)377 B)267 C)268 D)750 E)271 SOLUTION:Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D #### D QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women? options: A)63 B)67 C)70 D)90 E)80 SOLUTION:We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this = 6C4 × 4C2 90 D) #### D <<<Examples ends QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two squares are chosen at random on a chessboard. What is the probability that they have a side in common? options: A)1/18 B)64/4032 C)63/64 D)1/9 E)1/4 SOLUTION:Explanation : No of ways of selecting two squares from 64 squares on the chess board is 64C2. Three cases arise: case 1: when first square is any of the four corner ones In this case second square can be chosen in 2 ways no of ways of selecting two squares: 42 = 8 case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones the second square can be chosen in 3 ways no of ways of selecting two squares: 243 = 72 case 3: the first square is any of the 36 remaining squares the second square can be chosen in 4 ways no of ways of selecting two squares: 364 = 144 Total no of ways of selecting two adjacent squares = 8 + 72 + 144 = 224 So required probability = 224/64C2 = 224/4032 = 1/18 Answer : A #### A QUESTION:If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2? options: A)1 B)3 C)5 D)6 E)14 SOLUTION:For unit digit of a^2 to be 9...unit digit of a has to be 3 or 7... Now for unit digit of (a+1)^2 to be 4..unit digit of a has to be 1 or 7.... From the above two conditions, unit value of a has to be 7, which will satisfy both the conditions... Now id unit digit of a is 7, unit digit of (a+2)^2 hast to be 1. ANSWER:A #### A QUESTION:(a/2)/(b/c) In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6 SOLUTION:(a/2)/(b/c) = (ac)/2b The expression will have the largest value when numerator (ac) is the largest. = (24)/21 =8/2 Answer A #### A QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:E = 30! 8 E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 So we have a total of 14 three's ... Therefore the maximum value of K can be 14 (C) #### C QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27 SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30 We can write 30 as product of two numbers in following ways 130 215 310 56 4 cases = 42 i.e. 8 factors (including 1) Factors greater than 1 = 7 Answer: Option D #### D QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ? options: A)22,550 B)32,550 C)52,550 D)62,550 E)12,550 SOLUTION:Total money spent on food and house rent = 5,040+5,000 = 10,040 Which is 100 - 20 = 80% of his monthly salary ∴ His salary = 10040x100/80 = 12550 Answer : E #### E QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:If n = 2.0254 and n is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153 SOLUTION:n=2.03 n-n=2.03-2.0254 0.0046 Answer: D #### D QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4332211 = 144 ways E #### E QUESTION:Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged? options: A)6 B)48 C)36 D)24 E)12 SOLUTION:Dhoni have to sit at either of the ends. If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24 David can also sit on the other end, then another 4! ways we can arrange. So total number of ways = 24+24 = 48 Answer : B #### B QUESTION:Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is: options: A)10/21 B)20/22 C)32/45 D)13/98 E)43/21 SOLUTION:Number of ways of choosing 4 persons out of 9 =9c4 =126 No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2) =60 P(E)=60/126 =10/21 ANSWER A #### A QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(8003) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (80083)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 sec B)16 sec C)19 sec D)7.2 sec E)13 sec SOLUTION:RS = 60 -40 = 20 5/18 = 100/18 T = 36 D = 36 * 100/18 = 200 RS = 60 + 40 = 100 * 5/18 T = 200 * 18/500 = 7.2 sec Answer: D #### D QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 1000.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration 10 + 7b =560 7b = 290 b= 41 The total number of iterations --> 41+1 = 42 and 43rd iteration will be completed at 304seconds which is above 5 minutes ANSWER: B #### B QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer: B #### B QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:What is the rate percent when the simple interest on Rs.1600 amount to Rs.200 in 4 Years? options: A)4% B)3.125% C)5% D)6% E)7% SOLUTION:Interest for 1 year = 200/4 = 50 Interest on Rs 1600 p/a = 50 interest rate = 50/1600100 = 3.125% Answer : B #### B QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.? options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454 SOLUTION:it is given that last 3 digits are randomly dialed Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability = 1/(10)3 = 1/1000 C #### C QUESTION:By how much is 50% of 250 greater than 25% of 400. options: A)25 B)26 C)29 D)39 E)26 SOLUTION:(50/100) 250 â€“ (25/100) * 400 125 - 100 = 25 Answer:B #### B QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/- SOLUTION:Loss = 50010/100 = 50 S.P = C.P - Loss = 500- 50 =Rs.450/- Answer : A #### A QUESTION:Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? options: A)8 B)10 C)12 D)14 E)16 SOLUTION:Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump. Both pumps together can fill 1/6 of the pool each hour. 2.5x = 1/6 x = 1/15 1.5x = 1.5/15 = 1/10 The faster pump could fill the pool in 10 hours. The answer is B. #### B QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 987656!/2!=5443200. Answer: C. #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)165 B)771 C)245 D)177 E)121 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer: C #### C QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:Arjun started a business with Rs. 40,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 40000 * 12 = 80000 * (12 – x) => x = 6. ANSWER:D #### D QUESTION:$500 will become $1000 in 6 years find the rate of interest? options: A)A)16.67% B)B)20% C)C)25% D)D)30% E)E)50% SOLUTION:SI = simple interest = A-P = 1000-500 = $500 R = 100SI/PT = 100500/5006 =16.67% Answer is A #### A QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail? options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail. = {HHT, HTH, THH, TTH, THT, HTT} C #### C QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/45 B)1/42 C)1/46 D)1/48 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer:B #### B QUESTION:Each of the positive integers a and c is a four-digit integer. If each of the digits 0 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a and c? options: A)18695 B)18325 C)18365 D)18395 E)18485 SOLUTION:According to the stem we should use the digits 0 through 9 to construct 2 four-digit integers, so that their sum is as big as possible. To maximize the sum, maximize the thousands digits of a and c, so make them 9 and 8. Next, maximize hundreds digits. Make them 7 and 6 . Next maximize 10's digit place by 5 and 4 Use the remaining digits (3,and 2) for units digits. So, a would be 9753,and c would be 8642. 9753 + 8642 = 18395 Answer: D. #### D QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/1006000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positivenegative = negative. Thus option C is always negative. #### C QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? options: A)6 B)7 C)8 D)2 E)9 SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class. We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24 x+9(24−x)=3⋅24x+9(24−x)=3⋅24 x+216−9x=72x+216−9x=72 216−72=8x216−72=8x 1448=x1448=x x=18x=18 So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. Answer:A #### A QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)3 Total Earnings = $8x + ($3x+$2xy)3 = 17x+6xy Answer: option E #### E QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 14555 + 3555 = 2375 ANSWER:C #### C QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (120R)/100 R = 40% Answer:D #### D QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 71+1 (71+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages? options: A)(12/x)y B)(5/x)y C)(10/x)y D)(10x)y E)(13/x)y SOLUTION:x page in 10 mins i.e. 1 page in 10/x mins i.e. y pages in (10/x)y Answer: option C #### C QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A #### A QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)32 E)40 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40. Thus E is the correct answer choice #### E QUESTION:If 144/0.144 = 14.4/x, then the value of x is: options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144 SOLUTION:=144/0.144 = 14.4/x =144 x 1000/144 =14.4/x =x = 14.4/1000 = 0.0144 Answer is C. #### C QUESTION:Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number? options: A)1/2 B)2/5 C)3/5 D)2/7 E)3/10 SOLUTION:There are 5 numbers higher than 5 and 3 of them are even. The probability is 3/5. The answer is C. #### C QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 235711131719 to some power of 10. # of different approximations are possible. Approach #1: 25=10; 37=~20 (actually more than 20); 1119=~200 (actually more than 200); 1317=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 25=10 317=~50 (actually more than 50); 713=~100 (actually less than 100); 1119=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800 100 = 75% ANSWER:B #### B QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =2516=400 Answer: E #### E QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ? options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these SOLUTION:Explanation: Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24) =12:15:16=12:15:16. ANSWER IS D #### D QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? options: A)576 metres B)589 metres C)600 metres D)700 metres E)None SOLUTION:Solution Let the length of the outer edges be x metres. Then, length of the inner edge = ( x - 6)m. ∴ x2 - (x-6)2 = 1764 ‹=› x2-(x2-12x+36)= 1764 ‹=›12x = 1800 ‹=›x = 150. ∴ Required perimeter = (4x)m ‹=› (4 x 150)m = 600m. Answer C #### C QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? options: A)287 B)27 C)28 D)25 E)28 SOLUTION:[50/x + 50/(x/2)] – 100/x = 2 x = 25 Answer: D #### D QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat? options: A)3! B)8! C)11! D)12! E)14! SOLUTION:Ans.(A) Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A QUESTION:Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is even C)AB is even options: A)I only B)II only C)III only D)II,III only E)None of the above SOLUTION:If AB is Odd then C will not even. O+E = O If B is even AB is even always. But If C is Odd E+O = O None of the above are true #### E QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:There are 3 people A,B & C. Rs.700 is divided among A,B & C so that A receives 1/2 as much as B and B 1/2 as much as C. What is the C's share is? options: A)Rs.100 B)Rs.200 C)Rs.400 D)Rs.500 E)Rs.550 SOLUTION:Let C's share = Rs.x. Then B's share = Rs.x2 And, A's share = Rs.x4 A:B:C = x4:x2:x=1:2:4 Hence, C's share = Rs.(700×47) = Rs.400 C #### C QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.8 C)4 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 Â½ sec B)6 Â½ sec C)9 Â½ sec D)8 sec E)7 Â½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:Which of the following numbers is a perfect square? options: A)1266 B)1444 C)2022 D)4034 E)8122 SOLUTION:perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022. 3838 = 1444 ANSWER:B #### B QUESTION:1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4.... options: A)7 B)6 C)3 D)4 E)1 SOLUTION:First if we count 1223334444. they are 10 In the next term they are 20 Next they are 30 and so on So Using n(n+1)2×10≤2888 For n = 23 we get LHS as 2760. Remaining terms 128. Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's. The 2888 term will be “3”. Answer:B #### B QUESTION:The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half? options: A)44.2 B)47.8 C)50.5 D)53.6 E)56.9 SOLUTION:The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. #### B QUESTION:A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230m B)240m C)250m D)260m E)270m SOLUTION:speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s time= 9sec let the lenght of second train is x total distance covered= 260 + x therefore, D= speedtime thus 260 + x = 500/9 * 9 x= 500-260=240 m ANSWER:B #### B QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is? options: A)7 B)7.67 C)8.75 D)8.98 E)8.28 SOLUTION:(4 * 3.5)/2 = 7 Answer:A #### A QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.03N + 8,000 SOLUTION:I will go with option E According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 * 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option E #### E QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow? options: A)11000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220 18x + 45x + 39x = (11220 * 100) 102x = 1122000 => x = 11000. Answer:A #### A QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden options: A)has increased by 20 percent B)has increased by 12 percent C)has increased by 8 percent D)is exactly the same as the old area E)cannot be expressed in percentage terms without actual numbers SOLUTION:Let L be the original length and let W be the original width. The original area was LW. The new area is 0.9W1.2L = (0.9)(1.2)LW = 1.08LW The answer is C. #### C QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520 SOLUTION:P - 340 = (P48)/100 P = 500 Answer:D #### D QUESTION:If P Q implies (P2 + Q2), 8 * (3 * 2) = ? options: A)239 B)278 C)233 D)2697 E)771 SOLUTION:Explanation: We have, P * Q = (P2 + Q2) ......... Given 8 * (3 * 2) = ? 8 * 13 = (64 +169) = 233 ANSWER: C #### C QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:Find the unit digit in the product 274318577313 options: A)5 B)2 C)10 D)26 E)89 SOLUTION:Explanation: Required digit=Unit digit is in(4873)=2 Answer B #### B QUESTION:A small company reduced its faculty by approximately 15 percent to 195 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)229 E)E)302 SOLUTION:If x is the original number of employees, then after 15% reduction in employees number is .85x but we are given .85x = 195 x = 229 So the original number of employees is 229 Correct Answer - D #### D QUESTION:In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers? options: A)25 B)26 C)27 D)28 E)29 SOLUTION:Sum of the 12 numbers=1+2+3+......+12=1213/2=78 So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be: 3+4+5+6+7=25 8+9+10=27 11+12+1+2=26 ANSWER:B #### B QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D QUESTION:Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? options: A)$506.00 B)$726.24 C)$900.00 D)$920.24 E)$926.24 SOLUTION:If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away. Interest earned after the first time interval: $10,0002%=$200; Interest earned after the second time interval: ($10,000+$200)3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$926. Answer: E. #### E QUESTION:The average height of 50 pupils in a class is250 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________ . options: A)151 cm B)351 cm C)241 cm D)251 cm E)261 cm SOLUTION:Total height = 250 * 50 = 12500 cm. New average = [12500 - 5 * 146 + 5 * 156 ] / 50 =251 cm. ANSWER:D #### D QUESTION:Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 7 days? options: A)2/5 B)7/18 C)1/4 D)1/9 E)2/6 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/45 (A + B)'s one day's work = 1/30 + 1/45 = 1/18 The part of the work completed in 7 days = 7 (1/18) = 7/18. ANSWER B #### B QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in options: A)1 13/17 hours B)2 8/11 hours C)3 9/17 hours D)5 5/11 hours E)None SOLUTION:Solution Net part filled in 1 hour = (1/10 + 1/6 -1/12) = 11/60. Therefore, the tank will be full in 60/11 hrs. â€¹=â€º 5 5/11 hrs. Answer D #### D QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h The answer is D. #### D QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. options: A)121km B)242km C)224km D)112km E)115km SOLUTION:Explanation: Average Speed =2Ã—21Ã—24/21+24=22.4 km/hr Total distance =22.4Ã—10=224 km ANSWER IS C #### C QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)288 B)240 C)267 D)299 E)162 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) options: A)200π B)240π C)300π D)480π E)1,200π SOLUTION:Distance traveled in 1 revolution = 2πr= 2π10/5280 Revolutions in one second= 1320 Revolutions in 60 seconds (one minute)= 132060 Total distance traveled= total revolutions distance traveled in one revolution 132060 2π10/5280= 300π C is the answer #### C QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow. options: A)32 B)36 C)40 D)44 E)50 SOLUTION:Explanation : Explation: Let length of bridge is X then middle of bridge is X/2. and Cow is standing at X/2-5 from the end so After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side. So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10 so remaining distance is 10m the cow is hit before 2m i.e cow covers 8m and train will cover 32 m. Answer : A #### A QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:What is the area of a square with perimeter 12P ? options: A) 16p^2 B) 4P C) 9P^2 D) P/16 E) P^2/16 SOLUTION:Each side is 3p A = (3p)^2 = 9p^2 Answer C #### C QUESTION:85 80 25 70 55 25 35 ? ? options: A)10 25 B)25 85 C)35 25 D)85 35 E)25 75 SOLUTION:85-5=80 again 25 80-10=70 70-15=55 again 25 55-20=35 35-25=10 again 25 then answer is 10 ,25 ANSWER:A #### A QUESTION:On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters? options: A)515 B)500 C)525 D)530 E)535 SOLUTION:1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35/8.89127= 500 miles Answer : B #### B QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother. options: A)24 years B)25 years C)26 years D)27 years E)28 years SOLUTION:At the present, Sara's age is x. Sara's mother's age is y=6x. Next year, Sara's age will be x+1. Sara's mother's age will be y+1=5(x+1). From the two equations, we can calculate Sara's age: y=6x y+1=5 (x+1) 6x+1=5x+5 6x-5x=5-1 x=4 If Sara is currently 4 years old, and her mother is 6 times older, then her age is 6x=6×4=24. ANSWER: A #### A QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles? options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26 SOLUTION:let the radius of circle is 'r' area of the circle which is at corner = (22/7r^2)/4 hence the area of all four circles are = 22/7r^2 areaof circle which is made on center of suare is = 22/7r^2 total area of all circles are = 222/7r^2...........................(1) if we construct the diagram we get the relation 4r = 2sqrt2 r = 1/sqrt2 put the value of r in eqn 1 and we get 222/71/2 = 22/7 = 3.14 area of suare = 2^2 = 4 area of remaining part = 4-3.14 = 0.86 ANSWER:B #### B QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ? options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5 SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7 = 2 (2^7) + 3 (3^7) = 2^1 (2^7) + 3^1 (3^7) = 2^(1+7) + 3^(1+7) = 2^8 + 3^8 Ans: A #### A QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9) SOLUTION:The number of possible 4-digit codes is 36^4. The number of possible 5-digit codes is 36^5. The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4) The answer is A. #### A QUESTION:A group of five people are weighed with the results as follows (in pounds): 135, 140, 165, 178, 199. If the weight of the heaviest person is increased by 9 pounds, which of the following statements best describes the change in the mean and the median of the weights? options: A) The mean and the median will remain unchanged. B) The mean will remain unchanged but the median will increase. C) The mean will increase but the median will remain unchanged. D) The mean and the median will increase by the same amount. E) The mean and the median will increase by different amounts. SOLUTION:Old set = {135, 140, 165, 178, 199}. New set = {135, 140, 165, 178, 208} --> the median (middle term) will remain the same and the mean will increase. Answer: C. #### C QUESTION:At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples? options: A)1/12 B)5/14 C)4/9 D)1/2 E)2/3 SOLUTION:"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind). C23∗C46C49=514C32∗C64C94=514. C23C32 - # of ways to choose which 2 samples will be tasted; C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples3 cups each = 6 cups); C49C94 - total # of ways to choose 4 cups out of 9. Answer: B #### B QUESTION:Find the next term in series - 25, 37, 49, 61, ? options: A)71 B)72 C)73 D)74 E)75 SOLUTION:Series is Increased by 12. 25 +12 =37 37 +12 =49 49 +12 =61 61 +12 =73 ANSWER:C #### C QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1? options: A)5 kg B)6.5 kg C)7.5 kg D)8 kg E)9 kg SOLUTION:Milk in 85 kg of mix = 85 (27/34) = 135/2 kg. Water in it = 85-135/2 = 35/2 kg. Let x kg of water be added to it. Then, (135/2)/(35/2 + x) = 3/1; 135/(35 +2x) = 3/1; 105 + 6x = 135 ; 6x = 30; x = 5 The quantity of water to be added = 5 kg ANSWER:A #### A QUESTION:The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July? options: A)$4 B)$0.1 C)$1 D)$3 E)$1.65 SOLUTION:Lets assume price of Coffee in June =100x Price of green Tea in June =100x Price of Coffee in July = 200x (because of 100% increase in price) Price of green Tea in July = 10x (because of 90% Decrease in price) Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x As per question 315x= 3.15$ x = 0.01S So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound Answer B #### B QUESTION:Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is? options: A)98% B)56% C)96% D)964% E)16% SOLUTION:I II III 120 125 100 125----------120 100-----------? => 96% Answer:C #### C QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D <<<Examples ends QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n? options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2 SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2. In an AP, Last term = First term + (n-1)common difference w = First term + (n-1)2 First term = w - 2(n-1) ANSWER:C #### C
Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is? options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1 SOLUTION:100(80/100)(85/100)(92/100) = 62.6 100 - 62.6 = 37.4 Answer:A #### A QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these SOLUTION:Explanation: 2(l+b)/b=5/1 2l + 2b = 5b 3b = 2l b = 2/3 l Then, Area = 216 cm2 l x b = 216 l x (2/3)l = 216 l2 = 324. l = 18 cm. Answer: B #### B QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ? options: A)5 B)-45 C)45 D)50 E)60 SOLUTION:Explanation: => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)] = 5 - (50) = - 45 Answer: Option B #### B QUESTION:A man is 30 years older than his son. In four years, his age will be twice the age of his son. The present age of this son is options: A)22 years B)23 years C)24 years D)25 years E)26 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+30. => 2(x+4) = (x+30+4) => 2x+8 = x+34 => x = 26 years Answer: Option E #### E QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)22 B)287 C)48 D)277 E)21 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: C #### C QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple? options: A)225 B)228 C)230 D)231 E)235 SOLUTION:CP = 1402+1503+1604+1701=1540 SP = 1.51540=2310 Total no.of kgs=2+3+4+1=10 SP per kg=2310/10=231 ANSWER:D #### D QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105. options: A)18 B)8 C)12 D)16 E)None of these SOLUTION:105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 The H.C.F of 32, 48 and 80 is 16. ANSWER:D #### D QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? options: A)776 B)864 C)299 D)257 E)125 SOLUTION:W = 60% L = 40% 60% - 40% = 20% 20% -------- 288 60% -------- ? => 864 Answer:B #### B QUESTION:Smitty Farm picks 9866 cherries a day. If Smitty distributes their apples evenly across 9 different retail shops, how many cherries would remain with him. options: A)1 cherry B)7 cherry C)2 cherry D)4 cherry E)5 cherry SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs before 9,866. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 9+8+6+6 = 29. If we add 7, then it is divisible by 9. Hence, we need to add 7 to this number for it to be divisible by 9 Correct Option : B #### B QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B? options: A)96 B)75 C)48 D)25 E)12 SOLUTION:.24 of B = Remainder .24 of B = 18 B = (18100) / 24 = 75. B #### B QUESTION:The greatest number by which the product of three consecutive multiples of 5 is always divisible is options: A)54 B)750 C)152 D)162 E)None of these SOLUTION:Solution Required number = Product of first three multiplies of 3 = (5 Ã— 10 Ã— 15)= 750. Answer B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 10 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.66 feet C)3.3 feet D)3.4 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+10=40 44/12=3.66 feet ANSWER:B #### B QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is options: A)210 B)212 C)214 D)216 E)None of these SOLUTION:Solution P.W = Rs.(1080 - 180) = Rs. 900 S.I on Rs. 1080 =Rs.(180/900 x 1080) = Rs. 216. Answer D #### D QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to options: A)22 B)14 C)6 D)8 E)16 SOLUTION:Given J > P J + P = 7, only options are (6, 1), (5, 2), (4, 3) From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14 Answer:B #### B QUESTION:In a bag there are a certain number of black balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of black balls to blue balls in the bag options: A)1:2 B)1:4 C)1:1 D)1:5 E)1:6 SOLUTION:since the probability of drawing a blue ball out of two picks is 1/2. the ratio of the blue ball to black balls should be 1:1 Answer : C #### C QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/95=250/9=27 7/9m ANSWER:D #### D QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)34 B)97 C)37 D)80 E)22 SOLUTION:1/2 d (10 + 6) = 640 d = 80 Answer: D #### D QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:The area of a triangle is with base 4m and height 6m? options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 4 * 6 = 12 m2 Answer: E #### E QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:A train 150 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)108 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [150/5] m/sec = [30 * 18/5] km/hr = 108 km/hr. Answer B #### B QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. options: A)6 B)6.5 C)7 D)7.5 E)5 SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total) Hour miles/hour Total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 It takes a total of nine hours to cover the 210 mile distance. ANSWER: A 6 #### A QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 85, what is the value of c âˆ’ a? options: A)25 B)80 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=170 --2 subtracting 1 from 2 we have c-a=80; ANSWER:B #### B QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 245= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 245 + 2y =124 then y=2 244 + 2y = 124 then y=14 243 +2y = 124 then y= 26 242 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 46 x = 12 Answer is B #### B QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 259x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together. options: A)181440 B)191440 C)171440 D)182440 E)185440 SOLUTION:Methods to arrange all the letters leaving A = 87654321/(21)(21)(21)= 5040 Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 98/21 = 36 thus total methods are 504036 = 181440 ANSWER:A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: . options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720 SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? options: A)7 B)14 C)21 D)28 E)35 SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice. With 36 liters of milk, we need a total of 48 liters of juice to make drink B. We need to add 21 liters of juice. The answer is C. #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:If n is a positive integer, which of the following is a possible value of \|36 - 5n\|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then \|36- 5n\| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then \|36- 5n\| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)84 = 36. The answer is E. #### E QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%? options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33% SOLUTION:10 CP = 15 SP 15 --- 5 100 --- ? => 33.33% (Loss) Answer:E #### E QUESTION:The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages. options: A)20, 28 B)28, 36 C)35, 45 D)56, 72 E)of these SOLUTION:Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 136 20x = 160 => x = 8 Their present ages are 32, 56 and 72 years respectively. ANSWER:D #### D QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 182 cm. Wrong total height of 35 boys = 182 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm = 182 cm - 1.71 cm = 180.29 cm. Answer: B #### B QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:E = 30! 8 E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 So we have a total of 14 three's ... Therefore the maximum value of K can be 14 (C) #### C QUESTION:A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ? options: A)1000 B)800 C)1400 D)1200 E)None of them SOLUTION:Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x A’s capital = Rs. (3 x (2/3).x) = Rs. 2x. Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3. Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000. Answer is A #### A QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width? options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3 SOLUTION:2x+2y=50 x+y=25 x+4x=25 5x=25 x=5 Answer C #### C QUESTION:An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)53 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:B #### B QUESTION:REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $15per set. They can sell the sets $40. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit? options: A)$2100 B)$2000 C)$2050 D)$2070 E)$2500 SOLUTION:Total Manufacturing cost = 10500+50015 = 18000 Total Selling cost = 50040= 20000 Profit = 20000-18000 = 2000 Answer : B #### B QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.2 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer: D #### D QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table? options: A)120 B)480 C)960 D)2520 E)5080 SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h The answer is D. #### D QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is options: A)9 years B)11 years C)17 years D)21 years E)25 years SOLUTION:Solution Age of the 15th student =[15x15-(14x8+16x6)] = (225 - 208) = 17 years. Answer C #### C QUESTION:Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once? options: A)9/100 B)1/10 C)11/100 D)19/100 E)1/5 SOLUTION:Probability = No of balls with exactly one 1 / total number of balls = {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100 = 19/100 Answer is D #### D QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)23 days B)16 days C)11 days D)24 days E)35 days SOLUTION:D 24 days 2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days #### D QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1 options: A)(i)0.20(ii)6.31 B)(i)0.21(ii)5.30 C)(i)0.21(ii)6.30 D)(i)1.21(ii)6.50 E)None of these SOLUTION:Explanation : Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10. Without decimal places, these numbers are 63, 105 and 210. Now, H.C.F. of 63, 105 and 210 is 21. H.C.F. of 0.63, 1.05 and 2.1 is 0.21. L.C.M. of 63, 105 and 210 is 630. L.C.M. of 0.63, 1.05 and 2.1 is 6.30. ANSWER IS C #### C QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)2200 miles. B)2300 miles. C)1900 miles. D)2500 miles. E)2100 miles. SOLUTION:E 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 #### E QUESTION:Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? options: A)300 B)800 C)1500 D)1200 E)1900 SOLUTION:(1/5)2500 = 500 Remaining = 2500-500 = 2000 (1/4) of remaining = (1/4)2000 = 500 Remaining now = 2000-500 = 1500 Answer: Option C #### C QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Ans: 6 Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B #### B QUESTION:At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped? options: A)30% B)60% C)50% D)70% E)80% SOLUTION:Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RT/S = 30% notRT/T = 40% => 100% - 40% => RT/T = 60% T/S = (30)/(60)% = 50% Answer: C #### C QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/161/a^2100)=56.25% Answer is(B) #### B QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232? options: A)1000 B)2217 C)1100 D)2777 E)2991 SOLUTION:1232 = P [1 + (512/5)/100] P= 1100 Answer: C #### C QUESTION:John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? options: A)$10,100.25 B)$10,101.50 C)$10,200.75 D)$10,201.00 E)$10,400.35 SOLUTION:2 percent annual interest compounded quarterly --> 0.5% in 3 moths. For the first 3 moths interest was 0.5% of $10,000, so $50; For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25; Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25. Answer: A. #### A QUESTION:A local bank that has 8 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 8 codes? options: A)4 B)6 C)5 D)3 E)7 SOLUTION:Pick any two integer. Integers: 12 Code: 11, 12, 21, 22 = 4 Codes Add one more integer: 3 13, 31, 33, 23, 32 = 5 Codes Total = 9 Codes. Enough. Answer: D #### D QUESTION:At 15:00 there were 22 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ? options: A)7 B)14 C)25 D)27 E)32 SOLUTION:Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) - 8 (1 + No of possible 10 minute intervals between 15:10 and 15:44) 20 + 314 -8 * 4 = 32 E #### E QUESTION:10^(600) Ã· 10^(580) = ? options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24 SOLUTION:10^(600) Ã· 10^(580) = 10^ (600-580) = 10^20 Answer : B #### B QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 66 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:there are two cubes with ratio between volume is 125:64. then what is the value of length of each cube? options: A)25:16 B)16:25 C)4:5 D)5:4 E)150:96 SOLUTION:given 6a12:a22=150:96 then a12:a22=25:16 a1:a2=5:4 so the answer is D #### D QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)-2 D)2 E)-3 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 1. If 1 < m < 200, what is the greatest possible value of m? options: A)47 B)65 C)103 D)117 E)170 SOLUTION:Looking at the choices, options BD can be eliminated as they are divisible by 13 Starting from the highest number 164; 170 = 162 + 8 (162 divisible by 9) 170 = 169 + 1 (169 divisible by 13) it fits the result Answer = E #### E QUESTION:A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is options: A)10√2 m B)100 m C)100√2 m D)200 m E)None SOLUTION:Solution Let the altitude of the triangle be hïand base of each be b. Then , (½ ×b× h1) where h2 = 100 m. = h1 = 2h2 = ( 2 x 100) m = 200 m. Answer D #### D QUESTION:A train 124 m long running at 68 kmph crosses a platform in 19 sec. What is the length of the platform? options: A)338 B)234 C)240 D)881 E)271 SOLUTION:D = 68 * 5/18 = 19 = 358 – 124 = 234 Answer: B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 71 min C)6 hrs 28 min D)6 hrs 21 min E)2 hrs 21 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer: A #### A QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q\|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q\|Q) = 3/51 P(A\|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A\|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q\|Q) P(A\|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:If you add all the numbers on your mobile phone , what is the answer? options: A)45 B)50 C)55 D)100 E)60 SOLUTION:0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone. Therefore 0+1+2+3+4+5+6+7+8+9=45 Answer is A #### A QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)None of these SOLUTION:Explanation : Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer : Option C #### C QUESTION:A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate? options: A)12 Â½ years B)62 Â½ years C)18 Â½ years D)72 Â½ years E)12 Â½ years SOLUTION:100 ---- 200 ---- 5 200 ---- 5 100 ---- 2 1/2 ------------------ 900 ---- 18 Â½ years Answer:C #### C QUESTION:A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes? options: A)100000 B)85236 C)89562 D)90083 E)95842 SOLUTION:winners votes = 100-45 = 55% invalid votes = 83 polled votes = [(1009000)/(255-100)]+83 = 90083 Answer is D #### D QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:A marketing firm determined that, of 200 households surveyed, 80 used neither Brand W nor Brand B soap, 60 used only Brand W soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? options: A) 15 B) 20 C) 30 D) 40 E) 45 SOLUTION:SOLUTION FOR SOAP W AND SOAP B (D) 40 #### D QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%? options: A)20% B)29% C)10% D)35% E)90% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 90 2/3 SP1 = 90 SP1 = 135 100 --- 35 => 35% Answer: D #### D QUESTION:A boy has eight trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)80 ways B)86 ways C)88 ways D)108 ways E)89 ways SOLUTION:The boy can select one trouser in eight ways. The boy can select one shirt in 10 ways. The number of ways in which he can select one trouser and one shirt is 8 * 10 = 80 ways. Answer:A #### A QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[24+(50-1)2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/155297 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:If the number 517 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:(5+1+7+A+3+2+4)=(22+A)MUST BE DIVISIBLE BY 3. HENCE THE SMALLEST WHOLE No. must be 2 ANSWER:B #### B QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is options: A)28 B)H C)27 D)29 E)271 SOLUTION:Answer:B #### B QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the cent tossed is also a head. options: A)4/5 B)3/5 C)2/5 D)3/4 E)1/2 SOLUTION:There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent) How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin) Therefore probability = 4/5 Option A #### A QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact? options: A)16/35 B)16/37 C)16/39 D)16/33 E)16/31 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 2/7 + 2/5 * 5/7 = 16/35 Answer:A #### A QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes? options: A)6 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 11 - 1 = 10 rounds per hour. Time taken to complete one round at this speed = 1/10 hr = 6 min. A #### A QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? options: A)2/33 B)4/33 C)2/165 D)4/165 E)7/165 SOLUTION:The number of ways to choose three people is 11C3=165. The number of ways to choose three girls is 5C3=10. P(only girls are chosen)=10/165=2/33 The answer is A. #### A QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? options: A)30% B)30.77% C)36% D)37% E)38% SOLUTION:Pick numbers. Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100; This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77 Increase in the number of computers purchased = 30.77%. Answer: B. #### B QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)0.125% D)0.2083% E)none SOLUTION:This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/60) = 20.833% and the answer is not there in the options. The correct answer is (E). #### E QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year? options: A)5% B)6% C)7% D)2% E)8% SOLUTION:increase = 262500 - 175000 = 87500 % increase in 10 yrs = 87500/175000100 = 50% avg = 50/10 = 5% ANSWER A #### A QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/- SOLUTION:Loss = 50010/100 = 50 S.P = C.P - Loss = 500- 50 =Rs.450/- Answer : A #### A <<<Examples ends QUESTION:A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500? options: A)5000 B)5500 C)4991 D)5600 E)5700 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991 C #### C