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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? options: A)A)270 B)B)280 C)C)290 D)D)300 E)E)310 SOLUTION:Let the smaller number be x. Then larger number = (x + 1515). x + 1515 = 6x + 15 5x = 1500 x = 300 Smaller number = 300. D) #### D QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P*20*R)/100 R = 5% ANSWER:E #### E QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? options: A)299 B)277 C)276 D)370 E)281 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 150)/26 = 20 x = 370 m. Answer: D #### D QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)4 C)20 D)25 E)30 SOLUTION:Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20. ANSWER C #### C QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number? options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63 SOLUTION:Let the numbers be 5x, 6x, 8x. Largest number = 8x. Smallest number = 5x. Third number = 6x. 8x + 5x = 6x + 49 7x = 49 =>x=7 6x=42=> third number is 42. Answer:D #### D QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)128% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,16 = 16/100 x= 80*16/100 x= 12.8 12.8/10 = 1,28 = 128%, Answer E #### E QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these SOLUTION:Explanation : 100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/- Answer : D #### D QUESTION:Nirmala gains 10% by selling her bicycle for a certain price. If she sells it at 2 times the price, the percentage of profit will be : options: A)130% B)140% C)160% D)120% E)None of these SOLUTION:Explanation : Solution: Let C.P =Rs. x. then, S.P. = Rs. (110% of x) = Rs. 11x/10. New S.P. = Rs. (2*11x/10) =Rs. 22x/10. profit = Rs. (22x/10 - x) = Rs. 6x/5. .'. Profit% = (6x/5 *1/x * 100) = 120%. Answer : D #### D QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2 SOLUTION:Ans: Very interesting question. As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls Probability of choosing any box is 1/ 2. So probability of taking one red ball = 12×(1)+12(3864)≃0.8 Answer:B #### B QUESTION:At what time between 5.30 and 6 will the hands of a clock be at right angles? options: A)43 7/12 min. past 5. B)43 7/13 min. past 5. C)42 7/11 min. past 5. D)42 7/18 min. past 5. E)43 7/11 min. past 5. SOLUTION:At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60/55 x 40 min = 43 7/11 min. Required time = 43 7/11 min. past 5. Answer: E #### E QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:If 40% of a number is 16, then the number is options: A)number is 60 B)number is 70 C)number is 90 D)number is 40 E)None of these SOLUTION:Solution: Let "a" be the number we seek. We get 40% × a = 16 2 × 40% × a = 2 × 16 = 32 80% × a = 32 10% × a = 32 : 8 = 4 100% × a = 4 × 10 = 40 a = 40 Answer D #### D QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55*800)/100 =>440 15% of his 440 marks is 440*(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? options: A)140 B)99 C)100 D)72 E)12 SOLUTION:Given that the area of the square = 625 sq.units => Side of square = √625 = 25 units The radius of the circle = side of the square = 25 units Length of the rectangle = 2/5 * 25 = 10 units Given that breadth = 10 units Area of the rectangle = lb = 10 * 10 = 100 sq.units Answer: C #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:If 7 is 10 percent of 50 percent of a certain number, what is the number? options: A)150 B)217 C)100 D)90 E)140 SOLUTION:Using elimination method to pick the correct option it will be discovered that option E i.e 140 is the correct option because 50% of 140 is 70 and 10% of 70 is 7. ANSWER:E #### E QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 21% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)63.5% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 63.5%. E #### E QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24*144)= 30. Answer is C. #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:From given equation find the value of x: 2x² + 9x − 5 options: A)−5 B)-4 C)-3 D)3 E)4 SOLUTION:That quadratic is factored as follows: 2x² + 9x − 5 = (2x − 1)(x + 5). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = −5. As for the value of x that will make 2x − 1 = 0, we must solve that little equation. (Lesson 9.) We have: 2x = 1 x = 1 2 The solutions are: x = 1/2 or −5 A #### A QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers. Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. . Answer: A #### A QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point? options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec SOLUTION:Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) } = LCM (90, 60) =180 sec. Answer:D #### D QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pi*r^2*h Volume of a sphere = 4*pi*R^3 / 3 9*4*pi*R^3 / 3 = pi*r^2*h R^3 = r^2*h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 30*1.5 more revolutions is 60*1.5 = 90 seconds. The answer is C. #### C QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100*100 = 132 10% discount Then price = 132 * 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways. Answer: A #### A QUESTION:Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? options: A)3/5 B)2/5 C)1/2 D)4/5 E)19/25 SOLUTION:There can be an odd product only if both integers are odd. P(odd product) = 1/2*2/5 = 1/5 P(even product) = 1 - 1/5 = 4/5 The answer is D. #### D QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)109% B)160% C)100% D)600% E)108% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour? options: A)73 B)83 C)12 D)83 E)11 SOLUTION:Explanation: T = 8/45 * 60 = 11 Answer: Option E #### E QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:If “*” is called “+”, “/” is called “*”, “-” is called “/”, “+” is called “-”. 240*80 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 240*80 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1). options: A)-1 B)-1/2 C)-1/4 D)1/4 E)1/2 SOLUTION:Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore, f(1) = 0 and the answer is 1/4. correct answer D #### D QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? options: A)229 B)270 C)877 D)266 E)281 SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages. Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left. 23⋅x−13⋅x=9023⋅x−13⋅x=90 13⋅x=9013⋅x=90 x=270x=270 So the book is 270 pages long. Answer:B #### B QUESTION:9 - 3 ÷ 1/3 + 4 = ? options: A)4 B)3 C)6 D)9 E)12 SOLUTION:9 - 3 1/3 + 4 =9-3÷1/3+4 =9-(3X3) +4 =9-9+4 =4 CORRECT ANSWER : A #### A QUESTION:In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is : options: A)23 B)37 C)28 D)40 E)50 SOLUTION:Explanation: Formula n(a∪b) = n(a) + n(b) − n(a∩b) Fail in Hindi or English = 25 + 50 – 25 = 50 Therefore students who passed = 100 – 50 = 50. Answer: E #### E QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ? options: A)249 B)498 C)676 D)823 E)274 SOLUTION:slope of 2 and a y-intercept of 2 y-coordinate is 550 y = 2x + 2 548 = 2x x = 274 Answer: E. 274 #### E QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4.... options: A)7 B)6 C)3 D)4 E)1 SOLUTION:First if we count 1223334444. they are 10 In the next term they are 20 Next they are 30 and so on So Using n(n+1)2×10≤2888 For n = 23 we get LHS as 2760. Remaining terms 128. Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's. The 2888 term will be “3”. Answer:B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? options: A)Rs.3944 B)Rs.3948 C)Rs.3988 D)Rs.3949 E)Rs.3923 SOLUTION:Let the side of the square plot be a ft. a2 = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 * 58 = Rs.3944. Answer: A #### A QUESTION:Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets? options: A)60 minutes B)50 minutes C)40 minutes D)30 minutes E)None SOLUTION:Solution: 60 minutes Explanation: Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. Answer A #### A QUESTION:Find the value of y from (12)^3 x 6^4 ÷ 432 = y? options: A)3452 B)2343 C)2435 D)2578 E)5184 SOLUTION:Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 E #### E QUESTION:In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last? options: A)9 B)5 C)6 D)2 E)4 SOLUTION:I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p: In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last? Water required is 200*5=1000 (m*n) Water available is 2000 (p) It will last 2 months (p/m*n) Ans : D #### D QUESTION:A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)22 B)50 C)99 D)288 E)59 SOLUTION:Speed of the train relative to man = (150/10) m/sec = (15) m/sec. [(15) * (18/5)] km/hr = 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 54 ==> x = 59 km/hr.Answer: E #### E QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of the couple and a child, who was born during the interval, is 22Yrs now. How old is the child now ? options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these SOLUTION:(a+b-6-6)/2=26; a+b=64; a+b+c/3=22; solving both c=2 ANSWER:A #### A QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))? options: A)0 B)2 C)1 D)6 E)9 SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1. Thus, the answer is C. #### C QUESTION:1397 x 1397 = ? options: A)1961609 B)1851609 C)1951619 D)1951609 E)1851619 SOLUTION:1397 x 1397 = (1397)^2 = (1400 - 3)^2 = (1400)^2 + (3)^2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer is D. #### D QUESTION:The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is options: A)850 B)900 C)750 D)950 E)800 SOLUTION:Let the price of one apple = a and price of one orange = b Price of 24 apples is equal to that of 28 oranges 24a = 28b => 6a = 7b ⇒b=6a/7 -----(Equation 1) price of 45 apples and 60 oranges together is Rs.1350 => 45a + 60b = 1350 => 3a + 4b = 90 ⇒3a+4(6a)/7=90 (∵ Substituted the value of b from equation 1) ⇒a+4(2a)/7=30 => 7a + 8a = 30 × 7 = 210 => 15a = 210 ⇒a=21015=423=14 b=6a7=(6×14)/7=6×2=12 Total price of 30 apples and 40 oranges = 30a + 45b = (30 × 14) + (40 × 12) = 420 + 480 = 900 Answer is B. #### B QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:If p and q are two different prime numbers, which of the following cannot be true? options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer SOLUTION:A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q). Answer: E. All other options are possible: A. pq is odd --> p=3 and q=5; B. p + q is even --> p=3 and q=5; C. p + q is odd --> p=2 and q=3; D. pq is even --> p=2 and q=3; E #### E QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:5% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning? options: A)2988 B)2776 C)4400 D)4675 E)881 SOLUTION:X * (95/100) * (80/100) = 3553 X = 4675 Answer:D #### D QUESTION:Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes? options: A)1344 B)3360 C)8400 D)5040 E)67200 SOLUTION:8 machines produce 560 in 1 min 8 machines produce 560* 6 in 6 min 12 machine produce 560*6*(12/8) in 6 minutes 560*6*12/8=5040 answer is D. #### D QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP? options: A)56% B)68% C)75% D)85% E)95% SOLUTION:Let the volume of sphere PP be 64 parts. Therefore volume of sphere QQ =64−3764%=64−3764% of 6464 =64−37=27=64−37=27 parts. The volume of RR =27−1927×27=27−1927×27 =27−19=8=27−19=8 parts. Volume ratio: =P:Q:R=64:27:8=P:Q:R=64:27:8 Radius ratio: =P:Q:R=4:3:2=P:Q:R=4:3:2 The surface area will be 16:9:516:9:5 Surface area of RR is less than the surface area of sphere PP 16k−4k=12k16k−4k=12k Now, =12k16k×100=12k16k×100 =75%=75% Thus surface area of sphere RR is less than the surface area of sphere P by 75% C #### C QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 3 years? options: A)5100 B)4096 C)5200 D)5400 E)5500 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8000 × 80/100 × 80/100 x 80/100= 4096 Answer : B #### B QUESTION:A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is options: A)74 B)M=75 C)M=175 D)M=680 E)690 SOLUTION:I solved this question by plugging in numbers from the answer choices. A.) 74 Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5. B.) 75 I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7. 15-7 = 8 so I know the correct answer isB #### B QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (5*4*3!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:1395 x 1395 options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these SOLUTION:1395 x 1395 = (1398)2 = (1400 - 2)2 = (1400)2 + (5)2 - (5 x 1400 x 5) = 1946025. Answer: Option A #### A QUESTION:A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $1050? options: A)$3,000 B)$3,150 C)$4,000 D)$4,150 E)$6,000 SOLUTION:We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $1050. Since the salesperson receives a $150 salary, the remaining $900 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales. Let's TEST Answer C: $4,000 Since 15% of $1,000 = $150 15% of $4,000 = 4($150) = $600 This is TOO HIGH (it's supposed to be $900), so we need a LOWER total sales figure. Let's TEST Answer E: $6,000 Since 15% of $1,000 = $150 15% of $6,000 = 6($150) = $900 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: E #### E QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty? options: A)36 B)39 C)42 D)48 E)24 SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS. We're told 3 facts about the relative ages of 3 people: 1) Carol's age is 4 times Alice's age 2) Carol's age is 2 times Betty's age 3) Carol is 36 years older than Alice We're asked for BETTY'S age. Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first. IF.... Betty = 24 Then Carol = 2(24) = 48 Then Alice = 48 - 36 = 12 AND 48/4 =12 All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24 E #### E QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ? options: A)2 B)7 C)5 D)3 E)6 SOLUTION:Let n=3 (leaves a remainder of 3 when divided by 24) 9n = 9(3) =27, which leaves a remainder of 6 when divided by 7. difference = 6 - 3 = 3. Answer D #### D QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:Tough and Tricky questions: Work/Rate Problems. If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)8 E)9/7 SOLUTION:80 Workers = 3 hours then, 1 Worker = 3*80 Hours 30 Workers = (3*80) /(30) = 8 Answer.D #### D QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 * 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:How many such letter-pairs are there in the word SERVANT having the same no. of letters left between them in the word as they have in the series? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:1 pair is S & V 1 pair is N &S total 2 pair ANSWER: A #### A QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/5 B)2/5 C)3/10 D)3/7 E)1/7 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel? options: A)400 B)450 C)500 D)550 E)600 SOLUTION:The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour. The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours. The answer is A. #### A QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph. answer :C #### C <<<Examples ends QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2*T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated? options: A)24 B)60 C)720 D)520 E)180 SOLUTION:Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle. so its (7-1)! = 6! = 720=C #### C QUESTION:The area of a square is 625 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square. options: A)5 : 12 B)5 : 13 C)2:9 D)1:15 E)1:5 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 625 a = 25 L = 3a and b = a - 20 b : l = a - 20 : 3a = 5 : 75 = 1:15 Answer: D #### D QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4 SOLUTION:5C3 (1/2)^3(1/2)^2 = (5 * 4 * 3!)/2!3! * 1/32 W= 5/16 Answer - C #### C QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of shelves. 11x - 30 = 7(x-1) + 5 4x = 28 x = 7 The answer is C. #### C QUESTION:A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X. Find out the total time taken by the Red and the Black ant to make the journey. options: A)30 and 15 seconds B)10 and 15 seconds C)20 and 15 seconds D)25 and 15 seconds E)5 and 15 seconds SOLUTION:Solution: Let the speed of red ant be R. Speed of Black ant be B. Time at which they cross their paths be T. Now we will apply the basic formula of distance Distance = Speed * Time The Red ant travels R * T distance before meeting and R * 20 after meeting. The Black ant travels B * T distance before meeting and B * 5 after meeting. Now as per the question, The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well. Thus R * T = B * 5 and B * T = R * 20 Using both the quations T = 10 Thus the red ant will require 10 + 20 = 30 seconds to travel the distance. And the black ant will take 10 + 5 = 15 seconds to travel the distance. Answer A #### A QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/16*1/a^2*100)=56.25% Answer is(B) #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 3.5) kg = 35 kg. Weight of new person = (65 + 35) kg = 100 kg. Answer: A #### A QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is? options: A)150 B)133 C)175.5 D)178 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. So, their average price = Rs. 126 + 135 = Rs. 130.50 2 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price Rs. 153 Rs. x (x - 153) 22.50 x - 153 = 1 22.50 x - 153 = 22.50 x = 175.50 C #### C QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 * 12 =420 Answer: D #### D QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? (A) The median of S is prime. Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime. (B) The median of T is prime. Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number. (C) The median of S is equal to the median of T. Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true. (D) The sum of the terms in S is prime. Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime. (E) The sum of the terms in T is prime. Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime. C #### C QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg SOLUTION:let c=coach's avg. weight original total weight=(30 friends)(30 kg avge)=900kg (900+3c)/(30+3)=33 kg avg. c=63 kg Answer B #### B QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit? options: A)10000 B)12000 C)13000 D)14000 E)30000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000 E #### E QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these SOLUTION:Explanation: Error = (25.5 - 25.461) = 0.039 Required percentage = 0.039/ 25.461×100=0.153 Option B #### B QUESTION:A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price. options: A)$1,000 B)$960 C)$240 D)$200 E)$150 SOLUTION:Cost price=1000 Profit=20% =20% of 1000=200 selling price=CP+ Profit SP=1200 a Discount of 20% to employees means 20% off on 1200 so 20% of 1200= 240 so a employee thinks he saved 240.. Answer: C #### C QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P*20*R)/100 R = 5% ANSWER:E #### E QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? options: A)20 B)60 C)100 D)120 E)150 SOLUTION:y = 0.5*0.5*x = x/4 y%*x = 9 (y/100)*x = 9 (x/400)*x = 9 x^2 = 9*400 x = 60 The answer is B. #### B QUESTION:Ravi's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ravi's average score on the 5 tests to be 80? options: A) 80 B) 82 C) 84 D) 86 E) 88 SOLUTION:E. 88 Ravi must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88. #### E QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:Evaluate 25% of 450 + 45% of 250 options: A)225 B)242 C)252 D)262 E)272 SOLUTION:Explanation: = (25/100) * 450 + (45/100) * 250 = 225 Option A #### A QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother. options: A)24 years B)25 years C)26 years D)27 years E)28 years SOLUTION:At the present, Sara's age is x. Sara's mother's age is y=6x. Next year, Sara's age will be x+1. Sara's mother's age will be y+1=5(x+1). From the two equations, we can calculate Sara's age: y=6x y+1=5 (x+1) 6x+1=5x+5 6x-5x=5-1 x=4 If Sara is currently 4 years old, and her mother is 6 times older, then her age is 6x=6×4=24. ANSWER: A #### A QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:The following sets each have a mean of 10 and the standard deviations are given in variable form. Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q Set III = {10, 10, 10, 10, 10, 10}, standard deviation = R Rank these three standard deviations from least to greatest. options: A)P, Q, R B)P, R, Q C)Q, P, R D)Q, R, P E)R, P, Q SOLUTION:SD is minimum when the terms are closer to the mean. In set 3, we have all terms equal to mean. hence, its SD is 0.(The Lowest) Comparing Set 1 and Set 2, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest. So, Answer is E #### E QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =25*16=400 Answer: E #### E QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm SOLUTION:r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 ANSWER:C #### C QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission? options: A)4% B)0.4% C)0.04% D)0.004% E)0.0004% SOLUTION:% of sales amount of commission = (Commission/Total Value) *100 = (0.8/2000) * 100 = 0.04% The answer is C. #### C QUESTION:A jeep takes 7 hours to cover a distance of 420 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? options: A)48 Kmph B)52 Kmph C)40 Kmph D)63 Kmph E)65 Kmph SOLUTION:Time = 7 Distance = 420 3/2 of 7 hours = 7 * 3/2 = 10.5 Hours Required speed = 420/10.5 = 40 Kmph C) #### C QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book? options: A)20 B)18 C)16 D)15 E)15.39 SOLUTION:Actually u can set up 2 equation P--stands for the pages D--stands for the days 1) P*D=480 (we want to find the Days, soP=480/D) 2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000 as the 1) stated u can put 1) into 2) => 1000-5P+15D-75=1000 => 15D-5P=75 put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16) => D^2-5D-160=0 so D=15.39days. Ans: (E) #### E QUESTION:What is the difference between the local values of 4 in the number 54404? options: A)2992 B)3996 C)2877 D)2077 E)1211 SOLUTION:Explanation: 4000 – 4 = 3996 Answer:B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 3*40 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 41*3 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent E of the list price is the lowest possible sale price? options: A)20 B)25 C)30 D)40 E)50 SOLUTION:Let the list price be 2x for min sale price, the first discount given should be 50%, 2x becomes x here now, during summer sale additional 20% off is given ie sale price becomes 0.8x it is given lise price is $80 => 2x = 80 => x = 40 and 0.8x = 32 so lowest sale price is 32, which E is 40% of 80 hence, D is the answer #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C5*5C3 = 42 * 5 = 210 ANS:C #### C QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:8k8 + k88 -------- 1,6t6 If k and t represent non-zero digits within the integers above, what is t? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16t6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and t=6. Answer: A. #### A QUESTION:If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true? (i) x is prime (ii) y is even (iii) xy is positive options: A)ii only B)iii only C)i and iii only D)ii and iii only E)i, ii and iii SOLUTION:Effectively y = 36x/41 (i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime. (ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN. (iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:B #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:Find the odd man out 4, 15, 40, 121, 364, 1093, 3280 options: A)4 B)15 C)121 D)364 E)3280 SOLUTION:1*3+1 = 4 4*3+1 = 13 13*3+1 = 40 40*3+1 = 121 121*3+1 = 364 364*3+1 = 1093 1093*3+1= 3280 ANSWER:B #### B QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:The product of two numbers a and b equals one-quarter their average. What is a in terms of b? options: A)a= b/(8b-1) B)a= b/(7b-1) C)a= b/(8b) D)a= b/(8b-4) E)a= 2b/(8b-1) SOLUTION:a*b = ( a+b)/8 8ab =a+b a= b/(8b-1) ANSWER:A #### A QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together? options: A)81 B)81.5 C)82 D)84.5 E)None of these SOLUTION:Explanation : Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a Total of Y = 76b Total of Z = 85c And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b. Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b. Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a. Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c). => 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a . => 978/12 => 81.5 Answer : B #### B QUESTION:A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)28 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=224/32=28/4=7 m/sDistance covered by B in 4 seconds = Speed × time =7×4=28 metre i.e., A beat B by 28 metre Answer is B #### B QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P ; grows as a linear function of time t, where t is the number of years after 2003. a) How many students will be enrolled in the school in 2010? options: A)1800 B)1900 C)1700 D)1500 E)1600 SOLUTION:a) The given information may be written as ordered pairs (t , P). The year 2003 correspond to t = 0 and the year 2006 corresponds to t = 3, hence the 2 ordered pairs (0, 1200) and (3, 1500) Since the population grows linearly with the time t, we use the two ordered pairs to find the slope m of the graph of P as follows m = (1500 - 1200) / (6 - 3) = 100 students / year The slope m = 100 means that the students population grows by 100 students every year. From 2003 to 2010 there are 7 years and the students population in 2010 will be P(2010) = P(2003) + 7 * 100 = 1200 + 700 = 1900 students Answer B #### B QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km? options: A)22754.3 B)22254.2 C)25754.2 D)22753.2 E)22254.2 SOLUTION:2 * 22/7 * 3.62 * x = 22754.3 x = 1000 Answer: A #### A QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n? I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true. Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D QUESTION:A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly? options: A)55 B)60 C)93 D)82 E)91 SOLUTION:let the number of correct responses be x then the number of incorrect responses =100-x according to question x-2(100-x)=79 (subtracting twice of incorrect from correct) 3x=279 x=93 ANSWER:C #### C QUESTION:The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen? options: A)Rs.32 B)Rs.28 C)Rs.36 D)Rs.25 E)None of these SOLUTION:Let the cost of each pen and pencil be 'p' and 'q' respectively. 16p + 8q = 352 --- (1) 4p + 4q = 96 8p + 8q = 192 --- (2) (1) - (2) => 8p = 160 => p = 20 ANSWER:E #### E QUESTION:Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20 options: A)15 ÷ 3 x 3 - 5 = 20 B)15 + 3 ÷ 3 + 5 = 20 C)15 x 3 + 3 + 5 = 20 D)15 x 3 ÷ 3 + 6 = 20 E)15 x 3 ÷ 3 + 5 = 20 SOLUTION:Answer : E #### E QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pi*r^2*h Volume of a sphere = 4*pi*R^3 / 3 9*4*pi*R^3 / 3 = pi*r^2*h R^3 = r^2*h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job? options: A)98 days B)21 days C)48 days D)18 days E)19 days SOLUTION:WC = 1:2 2x + x = 1/32 => x = 1/96 2x = 1/96 => 48 days Answer:C #### C QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)9 1/2 SOLUTION:Son's 1day work = 1/3 - 1/5 = 2/15 Son alone can do the work in 15/2days = 7 1/2 days Answer is C #### C QUESTION:log3 N+log12 N what is 3 digit number N that will be whole number options: A)6291 B)7292 C)1728 D)1929 E)1727 SOLUTION:No of values N can take is 1 12^3=1728 ANSWER:C #### C QUESTION:A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? options: A)0.09 B)0.15 C)0.54 D)0.75 E)0.91 SOLUTION:According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 5)/60 = 45/60 = 0.75. Answer: D. #### D QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P*10*5)/100 P = 6200 Answer: A #### A QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:Find a sum for first 12 prime no's from number series? options: A)190 B)178 C)197 D)189 E)100 SOLUTION:Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197 Note: 1 is not a prime number Option C #### C QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Let 2x be the number of spinsters. Then 7x is the number of cats. 7x-2x=40 x=8 and the number of spinsters is 2(8)=16. The answer is B. #### B QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer:D #### D QUESTION:The salaries of A and B together amount to $2000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary? options: A)$1000 B)$1250 C)$2500 D)$1500 E)$1200 SOLUTION:Let A's salary is x B's salary = 2000-x (100-95)% of x = (100-85)% of (2000-x) x = $1500 Answer is D #### D QUESTION:Which is greater than -1? options: A)-5 B)-4 C)-3 D)-2 E)0 SOLUTION:-1 greater than 0. Answer: E #### E QUESTION:Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? options: A)5/6 B)5/9 C)5/3 D)5/0 E)5/1 SOLUTION:No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4 = 120 favourable cases. The total cases are 6 * 6 * 6 = 216. The probability = 120/216 = 5/9. Answer: B #### B QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)0.07 B)0.049 C)0.7 D)0.49 E)4.9 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 490/10,000 = 49/1000 = 0.049 ft The answer is B. #### B QUESTION:A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games? options: A) 7 B) 6 C) 5 D) 4 E) 3 SOLUTION:18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most. Answer (C) #### C QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is? options: A)1/0 B)1/3 C)1/5 D)1/2 E)1/1 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train? options: A)23 m B)23 (2/9)m C)38 (8/9)m D)29 m E)28 m SOLUTION:Relative speed = (40 - 20) km/hr = (20 x(5/18))m/sec = (50/9)m/sec. Therefore Length of faster train = ((50/9) x 7) m = (350/9)m = 38 (8/9) m. C #### C QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1996 has to be the ring finger Answer is (D) #### D QUESTION:A committee of 7 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? options: A)308 B)700 C)1404 D)2620 E)3510 SOLUTION:The only cases possible are : 1. 2 men and 5 women : 8C2 * 5C5 = 28 2. 4 men and 3 women: 8C4*5C3 = 280 Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed) Total possible combinations = 28+280 = 308. Thus A is the correct answer. #### A QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:P,Q and R enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B’s share in the profit is: options: A)Rs.2100 B)Rs 2400 C)Rs.3600 D)Rs.4000 E)Rs.3000 SOLUTION:Ratio of initial investments = 105 : 40 : 36. Let the initial investments be 105x, 40x & 36x. Therefore, P : Q : R = 105x * 4 + 150/100 x 105x * 8 : 40x * 12 : 36x * 12 = 1680x : 480x : 432x = 35 : 10 : 9. Therefore, Q’s share = Rs. 21600 * 10/54 = Rs.4000. ANSWER:D #### D QUESTION:Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex? options: A)15 B)13 C)20 D)21 E)26 SOLUTION:Let Alex's present age be x Alex's age after 17 years = x+17 Alex's age 10 years back = x-10 x+17= 10(x-10) x = 13 Rajeev's present age = 13 years Answer is B #### B QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race? options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec SOLUTION:Time taken by B run 1000 meters = (1000 * 10)/16 = 625 sec. Time taken by A = 625 - 10 = 615 sec. Answer:E #### E QUESTION:The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is : options: A)1 : 3 : 4 B)1 : 3 : 6 C)1 : 2 : 6 D)1 : 3 : 5 E)1 : 4 : 6 SOLUTION:Ratio of time taken : 1/12 :1/4 : 1/2 = 1 : 3 : 6 ANSWER:B #### B QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5% B)7% C)3% D)9% E)1% SOLUTION:160 = (180*4*R)/100 R = 5% Answer:A #### A QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =2*50=100m ANSWER:D #### D QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)4! B)8! C)9! D)10! E)12! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)45% C)32% D)40% E)28% SOLUTION:answer b male-employed - 64% female-employed-19% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 19/64 =28 E #### E QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball? options: A)10 cm B)12 cm C)14 cm D)16 cm E)18 cm SOLUTION:similar triangle properties.. 2/r+4 = 4/r-4 giving r = 14. Answer: C #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B <<<Examples ends QUESTION:Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? options: A)3, 8, 24 B)7, 9, 17 C)6, 9, 12 D)5, 15, 18 E)9, 10, 13 SOLUTION:I didnt get your point on eliminating A. The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps. I choose this and marked A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)135 m B)786 m C)566 m D)546 m E)445 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec Length of the train = speed * time = 15 * 9 = 135 m Answer: A #### A QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1500. What is their H.C.F.? options: A)5 B)15 C)25 D)35 E)45 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 1500 x = 25 The numbers are (3 x 25), (4 x 25) and (5 x 25). The H.C.F. is 25. The answer is C. #### C QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ? options: A)4 / 7 B)34 C)1 D)2 E)3 SOLUTION:Answer Given Exp. = 4 / 7 + {(2q - p) / (2q + p)} Dividing numerator as well as denominator by q, Exp = 1/7 + {2-p/q) / (2 + p/q)} = 1/7 + {(2 - 4/5) / (2 + 4/5)} = 1/7 + 6/14 = 1/7 + 3/7 =4/7 Correct Option: A #### A QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in ? options: A)3 days B)1 day C)9 days D)11 days E)15 days SOLUTION:That is, 1 person can do one time of the work in 1 day. Therefore, 7 persons can do 7 times work in the same 1 day itself. Option 'B' #### B QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? options: A)322 B)342 C)344 D)328 E)320 SOLUTION:Average mark scored by all the three boys = [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3 300+456+276= 344 Answer: C #### C QUESTION:A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display? options: A)15/56 B)3/28 C)1/28 D)1/56 E)3/55 SOLUTION:Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator. Total no of ways we can choose 3 from 11 is 11c3, which is the denominator. So, the probability: 9c1/11c3= 3/28 ans is E. #### E QUESTION:You have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs. options: A)163 B)166 C)162 D)164 E)165 SOLUTION:67 + 52 + 47 = 166 Answer: E #### E QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 2*3x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000 Answer (E) #### E QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:In how many Q ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12N E)15N SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 +2x$500 = $500 + $1000 =$1500 This is 15 times the 1992 number, so the correct answer is 15N. #### E QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5*700 = Rs.3500 ANSWER:D #### D QUESTION:A basket contains 3 blue, 3 red and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted? options: A)2/21 B)3/25 C)1/6 D)9/28 E)11/24 SOLUTION:Probability of getting each color marble = (3C1*3C1*3C1)/9C3 = (3*3*3)/84 = 27/84 = 9/28 So answer is D #### D QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (125*23+162*25)/125+162 = 24 years Answer is D #### D QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs? options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5% SOLUTION:Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed. Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed. The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5% The answer is C. #### C QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is - options: A)1/5 B)1/3 C)1/4 D)118/2 E)21/4 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B? options: A)100 B)120 C)140 D)160 E)180 SOLUTION:After two hours, Train A is ahead by 60 miles. Train B can catch up at a rate of 15 miles per hour. The time to catch up is 60/15 = 4 hours. In 4 hours, train A travels another 30*4 = 120 miles for a total of 180 miles. The answer is E. #### E QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 80 and n is not prime, what is the greatest possible value of f(n)? options: A)75 B)69 C)60 D)55 E)63 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 75 = 3*5*5. This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? options: A)150 B)750 C)1,250 D)1,500 E)2,500 SOLUTION:Given 150 deers were caught and they are tagged in the first slot. In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged. Given this 10% approximates the percentage of tagged deer in the forest..here number is 150.. then 100% is 1500.. is the number of deers population in the forest.. Answer: D is correct answer.. #### D QUESTION:Which of the following numbers is divisible by 4? options: A)27767 B)10224 C)26778 D)26679 E)26711 SOLUTION:10224. This is the only option with last two digits divisible by 4 Answer:B #### B QUESTION:If each digit in the set of A = {1,2,3,4,5,6,7,8} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent? options: A)8! / 7! B)8! - 7! C)6*7! D)8!/2! E)7! SOLUTION:The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent). The number of ways to arrange 8 units is 8! If we think of 2 and 5 as one single unit, the number of arrangements is 7! Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*7! The total number of valid arrangements is 8! - 2*7! = 8*7! - 2*7! = 6*7! The answer is C. #### C QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? options: A)6.33 B)7.5 C)10 D)15 E)24 SOLUTION:If there is one bacteria colony, then it will reach the limit of its habitat in 25 days. If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times. Answer: E. Similar questions to practice: Hope it helps. #### E QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $400 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)3000 B)5000 C)2000 D)4000 E)6000 SOLUTION:So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $200, thus 0.2x = $200 --> x = $1,000. Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000. Answer:C #### C QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)76% B)58% C)68% D)89% E)49% SOLUTION:let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100=49 and 30* 30/100=9 so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58% ANSWER:B #### B QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.05 D)2.16 E)2.35 SOLUTION:(34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845 = 2.16 ANSWER:D #### D QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None SOLUTION:Solution Perimeter of the rhombus = 56 m Each side of the rhombus = 56 / 4 m = 14 m. Height of the rhombus = 5 m Area = (14 x 5) m² = 70 m² Answer B #### B QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:The password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and characters can be repeated. Given these rules, how many different passwords are possible? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:The area of the maximum size of the circle described from the 10 inch square? options: A)75.5 sq inch B)76.5 sq inch C)77.5 sq inch D)78.5 sq inch E)79.5 sq inch SOLUTION:10 inch square means sides of sq are 10inch then circle is within square so diameter would be 10 inch maximum and radius is 5inch so area of the circle is = pi*r*r=3.14*5*5=78.5 sq inch ANSWER:D #### D QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26×72×5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E QUESTION:The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9.33% B)9.44% C)9.45% D)9.56% E)9.67% SOLUTION:69*(90/100)*((100-x)/100) = 56.16 x = 9.56% ANSWER:D #### D QUESTION:If n is the product of three consecutive integers, and n is divisible by 6, which of the following is not necessarily a divisor of n ? options: A)242 B)4 C)6.8 D)5 E)0. SOLUTION:IF ONE NO. IS 6 THEN OTHER CONSEQUTIVE NO. ARE 4*5*6 =120 , 5*6*7=210 , 6*7*8 =336 NO NUMBER WILL NO BE DIVISOR OF N E #### E QUESTION:Which of the following describes all values of x for which 4–x^2 >= 0? options: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –2 <= x <= 2 SOLUTION:4 - x^2 >=0 means x^2 - 4 <=0 => (x-2)(x+2) <= 0 => -2 <= x <= 2 Answer - E #### E QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:Two numbers N and 16 have LCM = 48 and GCF = 8. Find N. options: A)11 B)32 C)24 D)48 E)50 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 16 * N = 48 * 8 N = 48 * 8 / 16 = 24 correct answer C #### C QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?. options: A)540 m B)178 m C)936 m D)234 m E)713 m SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m. When B covers 960 m, C covers 936 m Option C #### C QUESTION:Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is: options: A)10/21 B)20/22 C)32/45 D)13/98 E)43/21 SOLUTION:Number of ways of choosing 4 persons out of 9 =9c4 =126 No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2) =60 P(E)=60/126 =10/21 ANSWER A #### A QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is options: A)3° B)18° C)24° D)90° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 15 minutes will make 6 × 15 = 90° Answer D #### D QUESTION:5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are? options: A)6 B)5 C)2 D)7 E)2 SOLUTION:5M = xW = 8B 5M + xW + 8B ----- 90 Rs. 5M + 5M + 5M ----- 90 Rs. 15M ------ 90 Rs. => 1M = 6Rs. Answer: A #### A QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3*x ANSWER:D #### D QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 * 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:A swimmer can swim in still water at 4 km/h. If the speed of the water current is 1 km/h, how many hours will the swimmer take to swim against the current for 6 km? options: A)1.2 B)1.4 C)1.6 D)1.8 E)2 SOLUTION:The swimmer can swim against the current at a speed of 4-1 = 3 km/h. The time it will take is 6/3 = 2 hours. The answer is E. #### E QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:Set A: {1, 3, 4, 6, 9, 12, 15} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3? options: A)3/14 B)2/7 C)9/14 D)5/7 E)11/14 SOLUTION:Probability of an event = (# of favorable outcomes) / (total # of outcomes). There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so P=C35C37=27P=C53C73=27. Answer: B. #### B QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total? options: A)220 B)250 C)280 D)300 E)340 SOLUTION:Let the total number of ounces in the drink be x. % of orange = 25% % of watermelon = 40% % of grape = 100% - 65% = 35% 0.35x = 105 x = 300 Therefore there are a total of 300 ounces in the drink. The answer is D. #### D QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average? options: A)69 B)70 C)71 D)72 E)75 SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D #### D QUESTION:For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *4 + 3 and *4 + 4, inclusive? options: A) None B) One C) Two D) Three E) Four SOLUTION:Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *4 would be divisible by all numbers from 1 to 4. => *4+3 would give me a number which is a multiple of 3 and therefore divisible (since *4 is divisible by 3) In fact adding anyprimenumber between 1 to 4 to *4 will definitely be divisible. So the answer is none (A)! Supposing if the question had asked for prime numbers between *4 + 3 and *4 + 11 then the answer would be 1. For *4 +3 and *4 + 13, it is 2 and so on... A #### A QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A QUESTION:By selling 66 bags, a shopkeeper gains the price of 33 bags. His gain per cent is options: A)91% B)100% C)95% D)98% E)93% SOLUTION:Suppose S.P of 66 bags = Rs 66 Therefore, Gain = Rs 33 => C.P = Rs 33 Gain % = 33/33 x 100 = 100% Gain = 100% ANSWER:B #### B QUESTION:The H.C.F. of two numbers is 12 and their difference is 12. The numbers are : options: A)66, 78 B)70, 82 C)94, 106 D)84, 96 E)None of these SOLUTION:Explanation: Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96. ANSWER IS D #### D QUESTION:How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)40 sec B)50 sec C)60 sec D)70 sec E)80 sec SOLUTION:The distance to be covered = Sum of their lengths = 400 + 300 = 700 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 700/10 = 70 sec. ANSWER:D #### D QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150 required percentage = (2800/8150)*100=33.35% C #### C QUESTION:The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas. options: A)5:25 B)4:25 C)3:15 D)7:15 E)6:15 SOLUTION:Let the diagonals of the squares be 2x and 5x respectively. Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2 = 4x2: 25x2 = 4 : 25. ANSWER B 4:25 #### B QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x))) 2=5%*(13+x)-------->x=27 Ans B #### B QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The distance between the nest and the ditch is 250 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 250 = 7500. D = ST 7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km) D) #### D QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)23% B)56% C)70% D)35% E)20% SOLUTION:C C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 420 - 125 = Rs. 295 Required percentage = 295/420 * 100 = 1475/21 = 70% #### C QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:If 50 percent of the members of a certain organization are women and 5/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)I B)II C)III D)I,II & III E)I,II SOLUTION:5/10 (50%) of the members are women and 5/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 5/10*80 = 40 women; 80 - 40 = 40 men; 5/8*40 = 25 married men; 40 - 25 = 15 unmarried men. So, option I,II is true. Answer: E #### E QUESTION:A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)20 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=20%. Answer: E. #### E QUESTION:John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? options: A)6 days B)8 days C)10 days D)12 days E)14 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 × 40/50 = 8 days B) #### B QUESTION:Find the value of 72519 x 9999 = m. options: A)233243413 B)354545451 C)343435451 D)565656767 E)725117481 SOLUTION:72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 E #### E QUESTION:If x < y < 0, which of the following must be true? options: A)x/y is a negative integer B)xy is a negative integer C)x+y is a negative integer D)x-y is a positive integer E)(-x)+ (-y) is positive integer SOLUTION:Given x, y are less than 0. So both will be negative integers negative + negative = negative negative * negative = positive negative / negative = positive x-y is false since x<y eg. x=-2, y=-1 then -2-(-1)=-1 So, option E is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers) Answer : E #### E QUESTION:Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations R are there for the children? options: A)240 B)480 C)720 D)1440 E)3600 SOLUTION:MAGOOSHOFFICIAL SOLUTION: First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats? X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10. Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats. Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations R of 24*10 = 240. Answer = A #### A QUESTION:How many of the positive factors of 17 are not factors of 34? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 17 - 1, 17 factors of 34- 1, 2, 17, 34, Comparing both, we have three factors of 17which are not factors of 34- no factors The answer is A #### A QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:Two taps can separately fill a cistern 8 minutes and 12 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? options: A)7 B)8 C)6.5 D)9 E)5 SOLUTION:1/8 + 1/12 - 1/x = 1/18 x = 72/11 = 6.5 Answer: C #### C QUESTION:How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 options: A)3 B)4 C)5 D)6 E)7 SOLUTION:B 4 By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. #### B QUESTION:A marketing firm determined that, of 200 households surveyed, 80 used neither Brand W nor Brand B soap, 60 used only Brand W soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? options: A) 15 B) 20 C) 30 D) 40 E) 45 SOLUTION:SOLUTION FOR SOAP W AND SOAP B (D) 40 #### D QUESTION:If x^2+4x+3 is odd, then which one of the following could be the value of x. options: A)3 B)4 C)5 D)6 E)9 SOLUTION:for any x, 4x+3->odd so x^2 should be even, means x should be even; only ans we have 4 as even. ANSWER:B #### B QUESTION:A Baker decides to make a cake of 5 layers, one of strawberry, chocolate, butterscoch, vanila and pista. Baker decides not to put the layers of butterscoch and vanila next to each other as they both are white in colour. How many different type of such cakes can he make? options: A)5! - (4!×2!) B)4! - (6!×2!) C)3! - (2!×4!) D)4! - (4!×2!) E)5! × (4!×3!) SOLUTION:We can find the answer by substracting the number of arrangements in which V and B comes together from the total number of arrangements of 5 layers. Arrangements in which V and B comes next to each other: We can consider V and B as a single object having 2! Variations(VB and BV). VB, S, C, P can be arranged in 4! Ways. In total there are 4!×2! Ways of arranging 5 layers with B and V layers coming next to each other. Required answer = A. 5! - (4!×2!) #### A QUESTION:If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Let length of rectangle = L 8^2 = L*4 => L = 64/4 = 16 Answer D #### D QUESTION:1!+2!+3!+4!+5!+.100! is divided by 24. Find the remainder from this? options: A)4 B)6 C)9 D)10 E)11 SOLUTION:By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24. So the remainder = 1 + 2 + 6 + 0 + 0....... = C #### C QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48 SOLUTION:First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4) So now as above we have three events A,BC. 1st method(This is lengthy method) Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1.ABC= 1/2*5/6*3/4 OR 2.ABC= 1/2*1/6*3/4 OR 3.ABC= 1/2*5/6*1/4 OR 4.ABC= 1/2*1/6*3/4 OR 5.ABC= 1/2*5/6*1/4 OR 6.ABC= 1/2*5/6*1/4 OR 7.ABC= 1/2*1/6*1/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 Answer : B #### B QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? options: A)72 B)83 C)45 D)53 E)64 SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Answer:A #### A QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is: options: A)1:3 B)2:4 C)9:3 D)7:8 E)3:4 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y= 8 1/x + 4/y = 1/15 ....(i) And, 200/x + 400/y = 25/3 1/x + 2/y = 1/24 ....(ii) Solving (i) and (ii), we get: x = 60 and y = 80. Ratio of speeds = 60 : 80 = 3 : 4. answer :E #### E QUESTION:If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase? options: A)21% B)42% C)80% D)96% E)120% SOLUTION:Let B be the base and H be the height of the original triangle. The original area is (1/2)BH. The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH The answer is A. #### A QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 *x = 9 * 6 * 1000 or x = 9*6*1000/ 4*10 = 1350 Answer : B #### B QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. Answer:B #### B QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ? options: A)11 B)13 C)14 D)16 E)10 SOLUTION:Explanation : Let Somu's age be x and that of his father be 3x. So, x - 8 = 3x - 8/5 = x = 16 Answer : Option D #### D QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (750*6+ 770 *20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:In how many ways can the letters of the word STATE be arranged? options: A)60 B)1348 C)2520 D)3000 E)3478 SOLUTION:STATE has 5 words, but T is repeated two times. Thus ways = 5! / 2! = 60 ways A #### A <<<Examples ends QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C

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