regisss/math_qa huggingface dataset:
Problem: when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 7 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 8
Rationale: i tried plugging in numbers x = 9 q + 5 x = 14 7 x = 98 7 x / 9 = 9 * 10 + 8 remainder is 8 answer is e .
Answer: e
Problem: an alloy weighing 26 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 34 , e ) 48
Rationale: in 24 ounces , gold is 26 * ( 70 / 100 ) = 18.2 ounces . now we add x ounces of pure gold to make it 90 % gold . so 18.2 + x = ( 24 + x ) * 90 / 100 = > x = 34 . answer is d .
Answer: d
Problem: an inspector rejects 10 % of the meters as defective . how many will he examine to reject 15 ?
Options: a ) a ) 100 , b ) b ) 150 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 15 ( 10 / 100 ) x = 15 x = ( 15 * 100 * ) / 10 = 150 answer is b"
Answer: b
Problem: the sale price sarees listed for rs . 400 after successive discount is 25 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 240 , e ) 269
Rationale: "400 * ( 75 / 100 ) * ( 80 / 100 ) = 240 answer : d"
Answer: d
Problem: two trains of length 120 m and 210 m are 80 m apart . they start moving towards each other on parallel tracks , at speeds 69 kmph and 82 kmph . after how much time will the trains meet ?
Options: a ) 15 / 10 , b ) 19 / 10 , c ) 20 / 19 , d ) 16 / 10 , e ) 27 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 69 + 82 ) * 5 / 18 = 41.9 mps . the time required = d / s = 80 / 41.9 = 19 / 10 sec . answer : b"
Answer: b
Problem: a shopkeeper sold 10 articles at the cost price of 8 articles . then find the profit % or lost % ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 30 % , e ) 20 %
Rationale: "here 10 articles selling price = 8 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is e"
Answer: e
Problem: a and b can finish a work in 16 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 16 – 1 / 24 = 1 / 48 = > 48 days answer : b"
Answer: b
Problem: . 009 / ? = . 01
Options: a ) . 9 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 009 / x = . 01 ; then x = . 009 / . 01 = . 9 / 1 = . 9 answer is a"
Answer: a
Problem: a can run a kilometer race in 4 1 / 2 min while b can run same race in 5 min . how many meters start can a give b in a kilometer race , so that the race mat end in a dead heat ?
Options: a ) 200 m , b ) 700 m , c ) 800 m , d ) 100 metre , e ) 1004 m
Rationale: explanation : a can give b ( 5 min - 4 1 / 2 min ) = 30 sec start . the distance covered by b in 5 min = 1000 m . distance covered in 30 sec = ( 1000 * 30 ) / 300 = 100 m . a can give b 100 m start . answer : d
Answer: d
Problem: if 10 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 2.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 12.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "c for me 9 people with 2 $ each - > maximum = 12"
Answer: c
Problem: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 42 , what is the remainder when k is divided by 7 ?
Options: a ) 5 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 42 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29 , 35,41 } ( less than 42 ) 17 is the only common number in both the sets . hence k = 17 answer : b"
Answer: b
Problem: a person borrows rs . 5000 for 2 years at 5 % p . a . simple interest . he immediately lends it to another person at 61 ⁄ 4 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 62.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 5 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 5 × 2 / 100 = 500 he also lends it at 6 1 ⁄ 4 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 25 / 4 × 2 / 100 = 625 his overall gain in 2 years = rs . 625 - rs . 500 = rs . 125 his overall gain in 1 year = 125 / 2 = rs . 62.5 answer : option a"
Answer: a
Problem: a student chose a number , multiplied it by 6 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 40 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 6 ⋅ x − 138 = 102 6 x = 240 x = 40 answer a"
Answer: a
Problem: in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 12 or larger is drawn is 1 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 1 / 3 + p ( set 2 ) - 1 / 6 = 1 p ( set 2 ) = 5 / 6 answer ( e )"
Answer: e
Problem: 10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "explanation : total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be x years . then , age of the elder child = ( x + 2 ) years . so , x + ( x + 2 ) = 8 ⇔ x = 3 age of younger child = 3 years . answer : c"
Answer: c
Problem: if it takes 70 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 ) 7 / 3 , e ) 9 / 7
Rationale: 70 workers = 3 hours then , 1 worker = 3 * 70 hours 30 workers = ( 3 * 70 ) / ( 30 ) = 7 answer : c
Answer: c
Problem: a batsman scored 150 runs which included 5 boundaries and 10 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 46.67 % , c ) 600 / 11 , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 150 − ( 5 × 4 + 10 × 6 ) . = > 150 − 80 = > 70 hence , the required percentage is : - = > 70 / 150 * 100 = > 46.67 % answer : b"
Answer: b
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 390 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 600 , c ) 510 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 390 = 3510 salary of the new supervisor = 3510 â ˆ ’ 3000 = 510 answer : c"
Answer: c
Problem: a invested $ 400 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 80
Rationale: a : b = 400 * 12 : 200 * 6 a : b = 4 : 1 a ' s share = 100 * 4 / 5 = $ 80 answer is e
Answer: e
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 62 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : b ) 38 km
Answer: b
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 10 % of the money for taxi fare and buys 10 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 10 % of 200 = 20 for taxi fare , so he is left with 180 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 80 ( 180 - 100 ) no of oranges he can buy = 80 / 4 = > 20 so , george can buy 10 oranges . c"
Answer: c
Problem: a ’ s speed is 17 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 16 , b ) 2 / 15 , c ) 2 / 17 , d ) 1 / 8 , e ) 1 / 7
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 15 ) = xd / v ( 15 / 17 ) * d / v = x * d / v x = 15 / 17 b should have a head start of 2 / 17 of the full distance . the answer is c ."
Answer: c
Problem: a box contains 8 apples , 7 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 5 times in a row ) = 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 * 3 / 4 = 3 / 8 < 0.5 the answer is c ."
Answer: c
Problem: a factory produces 8000 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 2000 toys , d ) 2354 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 8000 / 4 = 2000 toys correct answer c"
Answer: c
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 2 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 1 / 7 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 21
Rationale: the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 2 bottles of apple juice is 6 c 2 * 4 c 4 = 15 * 1 = 15 p ( selling 2 bottles of apple juice ) = 15 / 210 = 5 / 70 = 1 / 14 the answer is c .
Answer: c
Problem: if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 89 ) = ?
Options: a ) 6150 , b ) 6200 , c ) 6050 , d ) 6075 , e ) 5075
Rationale: "explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 89 = 1 + ( n - 1 ) 2 = > n = 45 use value of n in ( 1 ) then , sn = ( 45 / 2 ) ( 1 + 89 ) = 2025 ans : - 3 ( sn ) = 6075 answer : d"
Answer: d
Problem: in what time will a railway train 120 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 12 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 10 sec
Rationale: "t = 120 / 36 * 18 / 5 = 12 sec answer : a"
Answer: a
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent q of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , q = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."
Answer: d
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1400 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 15,600 , d ) rs . 28,875 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1400 x 20.625 ) = rs . 28875 . answer d"
Answer: d
Problem: find the smallest positive integer n such that 11 n - 1 is divisible by 105 .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the last digit of 11 n − 1 is 0 , so 5 always divides 11 n − 1 . also , checking the remainders when the powers of 11 are divided by 3 and 7 we get that 3 divides 11 n − 1 exactly when n is even , and 7 divides 11 n − 1 exactly when 3 divides n . correct answer d
Answer: d
Problem: there are 89 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 59 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 89 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 89 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 59 answer : d"
Answer: d
Problem: a sum of rs . 2691 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1656 , c ) 1277 , d ) 6298 , e ) 1279
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2691 - x ) * 3 * 5 ) / 100 24 x / 100 = 40365 / 100 - 15 x / 100 39 x = 40365 = > x = 1035 second sum = 2691 â € “ 1035 = 1656 answer : b"
Answer: b
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 155 , b ) $ 225 , c ) $ 510 , d ) $ 850 , e ) $ 1250
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 × $ 0.5 = $ 225 the answer is b ."
Answer: b
Problem: a can do a piece of work in 15 days and b in 20 days . they began the work together but 5 days before the completion of the work , a leaves . the work was completed in ?
Options: a ) 8 days , b ) 10 days , c ) 15 days , d ) 11 3 / 7 days , e ) none of these
Rationale: "explanation : ( x â € “ 5 ) / 15 + x / 20 = 1 x = 11 3 / 7 days answer is d"
Answer: d
Problem: a is half good a work man as b and together they finish a job in 10 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 15 , d ) 36 , e ) 48
Rationale: "c 15 wc = 1 : 2 2 x + x = 1 / 10 = > x = 1 / 30 2 x = 1 / 15 = > 15 days"
Answer: c
Problem: rohit walked 25 m towards south . then he turned to his left and walked 20 m . he then turned to his left and walked 25 m . he again turned to his right and walked 15 m . at what distance is he from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m east , e ) 55 m east
Rationale: ! 20 ! - - - > 15 ! ! ! - - - > ! 20 + 15 = 35 answer : a
Answer: a
Problem: a mixture contains milk and water in the ratio 6 : 3 . on adding 10 litters of water , the ratio of milk to water becomes 6 : 5 . the quantity of milk in the original mixture is ?
Options: a ) 90 , b ) 45 , c ) 110 , d ) 40 , e ) 50
Rationale: "explanation : milk : water = 6 : 3 6 x : 3 x + 10 = 6 : 5 5 [ 6 x ] = 6 [ 3 x + 10 ] 30 x = 18 x + 60 30 x - 18 x = 60 12 x = 60 x = 5 the quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9 x = 45 short cut method - 2 : for only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio - - - - - - - > 10 liters 9 part of ratio - - - - - - - > 45 liters answer : option b"
Answer: b
Problem: if the numerator of a fraction be increased by 20 % and its denominator be diminished by 10 % , the value of the fraction is 20 / 21 . find the original fraction ?
Options: a ) 1 / 2 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 7 , e ) 7 / 9
Rationale: "let the original fraction be x / y then , 120 % of x / 90 % of y = 20 / 21 120 x / 90 y = 20 / 21 x / y = 5 / 7 answer is d"
Answer: d
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?
Options: a ) 1 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 5 / 4 ) * 4 = 1 / 5 the answer is a ."
Answer: a
Problem: a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 200 per month . what is his monthly salary ?
Options: a ) rs . 22,000 , b ) rs . 21,000 , c ) rs . 20,000 , d ) rs . 23,000 , e ) rs . 24,000
Rationale: "income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 10 / 100 ) = rs . 99 present savings = 100 – 99 = rs . 1 if savings is rs . 1 , salary = rs . 100 if savings is rs . 200 , salary = 100 / 1 * 200 = 20000 answer : c"
Answer: c
Problem: the median annual household income in a certain community of 21 households is $ 50000 . if the mean w income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ?
Options: a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined
Rationale: answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean w is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified .
Answer: e
Problem: 4 different children have jelly beans : aaron has 5 , bianca has 7 , callie has 8 , and dante has 9 . how many jelly beans must dante give to aaron to ensure that no child has more than 1 fewer jelly beans than any other child ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: since bianca and callie are both within 1 jelly bean of each other and aaron has 5 , dante must provide 3 of his 9 jelly beans so each child has no more than 1 fewer jelly bean than any other child . dante + aaron = 9 + 5 = 14 / 2 = 7 9 - 8 = 1 so dante must provide 3 jelly beans to aaron . answer ( a )
Answer: a
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 12 - meter platform and caught it after it had traveled 35.65 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 12 + 12 + 6 + 3 + 1.5 + . 75 + 0.4 ans b"
Answer: b
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 10 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 18 , b ) 27 , c ) 26 , d ) 16 , e ) 12
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 10 days , a can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 10 = 16 . the answer is d ."
Answer: d
Problem: a present value of a machine is $ 128000 . its value depletiation rate is 25 % per annum then find the machine value after 3 years ?
Options: a ) $ 54000 , b ) $ 48000 , c ) $ 36520 , d ) $ 32450 , e ) $ 42500
Rationale: "p = $ 128000 r = 25 % t = 3 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 128000 * 3 / 4 * 3 / 4 * 3 / 4 = $ 54000 answer is a"
Answer: a
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus f = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Problem: when 1 / 20 % of 8000 is subtracted from 1 / 10 of 8000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400
Rationale: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d
Answer: d
Problem: what is the remainder when 47 * 50 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 13 , d ) 5 , e ) 14
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 47 * 50 ) / 8 } } = remainder of ( 47 / 8 ) * remainder of ( 50 / 8 ) = 7 * 2 = 14 answer : e"
Answer: e
Problem: there are 100 students in a class . if 14 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 86 , d ) 129 , e ) 11
Rationale: number of students absent on a particular day = 14 % of 100 i . e . , 14 / 100 × 100 = 14 therefore , the number of students present = 100 - 14 = 86 students . answer : c
Answer: c
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 72 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: "72 ° divided by 360 ° equals 0.2 , therefore the sector is equal to 20 % of the total answer : a"
Answer: a
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 25 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 19 , 24 , 26 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 24 , 26 , 28 . . the median of these numbers = center of 24 and 26 = 25 d"
Answer: d
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.5 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 90 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.015 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced × density of water = ( 0.09 × 1000 ) kg = 90 kg . answer b"
Answer: b
Problem: three numbers are in the ratio 1 : 3 : 6 and their average is 100 . the largest number is :
Options: a ) 180 , b ) 98 , c ) 27 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be x , 3 x and 6 x , then , ( x + 3 x + 6 x ) / 3 = 100 = > 10 x = 100 * 3 = > x = 30 largest number 6 x = 6 * 30 = 180 answer : a"
Answer: a
Problem: how many 3 digit positive integers r exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Problem: a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7
Rationale: "let there be g geese , of which 0.3 g are male and 0.7 g are female lets say m geese migrated , 0.2 m are male and 0.8 m are female migration rate male = 0.2 m / 0.3 g = ( 2 / 3 ) * ( m / g ) migration rate female = 0.8 m / 0.7 g = ( 8 / 7 ) * ( m / g ) ratio of migration rates = ( 2 / 3 ) / ( 8 / 7 ) = 7 / 12 answer is ( b )"
Answer: b
Problem: the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 88 kg and 93 kg join the group . find the initial number of members in the group ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "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 , 48 n + 88 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 79 = > n = 26 therefore there were 26 members in the group initially . answer : d"
Answer: d
Problem: what percent of 60 is 25 ?
Options: a ) 60 % , b ) 50 % , c ) 42 % , d ) 25 % , e ) 10 %
Rationale: "the phrasing of the question is difficult for some students . ` ` what percent of 60 is 25 ? ' ' is the same question as ` ` 25 is what percent of 60 ? ' ' many students find this later way of phrasing the question easier to work with . if x is y percent of z , then x / z = y / 100 ; for example , 10 is 50 % of 20 ; x = 10 , y = 50 , and z = 20 similarly , if you wanted to know what percent of 100 is 50 , you would intuitively know that it is 50 % since it is 50 / 100 or 50 per cent ( literally , per 100 ) . applying this logic to the problem at hand : 25 / 60 = . 42 = 42 % thus , 25 is 42 % of 60 if this way of solving the problem is difficult to conceptualize , consider another approach . it should be clear that 30 is 50 % ( or 1 / 2 ) or 60 . since 25 is less than 30 , 25 must be less than 50 % of 60 . this means that any answer that is not less than 50 % is wrong . since 25 % is 1 / 4 and 1 / 4 of 60 is 15 ( since 15 * 4 = 60 ) , 25 % is too small . by process of elimination , the answer is 42 % answer c"
Answer: c
Problem: two trains 121 meters and 153 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 6.8 , c ) 7.2 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 121 + 153 ) / ( 80 + 65 ) * 18 / 5 t = 6.8 answer : b"
Answer: b
Problem: find the average of first 4 multiples of 15 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 37.5
Rationale: "average = ( 15 + 30 + 45 + 60 ) / 4 = 37.5 answer is e"
Answer: e
Problem: the price of 3 chudi and 6 tops is rs . 1500 . with the same money one can buy 1 chudi and 12 tops . if one wants to buy 5 tops , how much shall she have to pay ?
Options: a ) 500 , b ) 1000 , c ) 1200 , d ) 1300 , e ) 1500
Rationale: let the price of a chudi and a top be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 5 tops = 5 * 100 = 500 answer : a
Answer: a
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 10 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 17 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 10 % then output equals 121 to restore new holidy demand output to original 100 . final - initial / final * 100 = 21 / 121 * 100 = 8 / 33 * 100 = 17 % approxiamately . option a is correct ."
Answer: a
Problem: a bag contains 3 red , 4 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 3 / 55 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 3 c 211 c 2 = 3 c 211 c 2 = 3 / 55 c"
Answer: c
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 39 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 06 , at what time will they be reading the same page ?
Options: a ) 6 : 06 , b ) 6 : 36 , c ) 7 : 06 , d ) 7 : 36 , e ) 8 : 06
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 18 pages in the first 36 minutes . jan can catch tom at a rate of 9 pages per hour , so it will take 2 hours to catch tom . the answer is c ."
Answer: c
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 24 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 21
Rationale: "the question is finding y such that ( 24 - y ) ! is a multiple of 24 . that means we need to have 2 ^ 3 * 3 in ( 24 - y ) ! 4 ! is the smallest factorial number with 2 ^ 3 * 3 as a factor . 24 - y = 4 y = 20 the answer is d ."
Answer: d
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 15.7 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 = 6 * 0 + 2 * 7.2 + 8 - 6.5 = 0 + 14.4 + 1.5 15.7 answer d"
Answer: d
Problem: 15 girls can complete a rangoli in 12 days , and 10 boys can complete the same work in 15 days . to complete the work earlier 10 boys and 15 girls are employed , in how many days will this work get completed ?
Options: a ) 6 , b ) 7 , c ) 6.5 , d ) 6 2 / 3 , e ) 6 1 / 4
Rationale: work done by 15 girls per day = 1 / 12 work done by 10 boys per day = 1 / 15 work done by 15 girls and 10 boys per day = 1 / 12 + 1 / 15 = 3 / 20 = 6 2 / 3 10 boys and 15 girls will complete the work in = 6 2 / 3 days d
Answer: d
Problem: when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ? putting a value say x = 27 we get remainder as 27 when divided by 63 . when 27 divided by 8 we get 3 as remainder . b is the answer ."
Answer: b
Problem: on dividing 100 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "d = ( d - r ) / q = ( 100 - 1 ) / 9 = 99 / 9 = 11 b )"
Answer: b
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is :
Options: a ) 1 / 3 , b ) 7 / 12 , c ) 5 / 12 , d ) 2 / 3 , e ) 1 / 2
Rationale: "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 5 day ' s work = ( 7 / 60 * 5 ) = 7 / 12 therefore , remaining work = ( 1 - 7 / 12 ) = 5 / 12 . answer : c"
Answer: c
Problem: a monkey ascends a greased pole 6 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 9 th minute , b ) 21 st minute , c ) 11 th minute , d ) 22 nd minute , e ) 13 th minute
Rationale: "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 4 meters . i mean this will continue for first 4 * 2 = 8 mins . he would have reached 4 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 8 + 1 = 9 mins . so , asnwer will be a"
Answer: a
Problem: what will be the reminder when ( 67 ^ 67 + 67 ) is divided by 68 ?
Options: a ) 1 , b ) 63 , c ) 66 , d ) 67 , e ) none of these
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ; ( 67 ^ 67 + 1 ) + 66 when divided by 68 will give 66 as remainder . correct option : c"
Answer: c
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 140 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "l + k = 140 and so k = 140 - l l + 10 = 1.5 k = 1.5 ( 140 - l ) 2.5 l = 200 l = 80 the answer is a ."
Answer: a
Problem: aunt marge is giving candy to each of her nephews and nieces . she has 20 pieces of candy and she gives all the candy to the children according to her wish . if robert gets 2 more pieces than kate , bill gets 6 less than mary , mary gets 2 more pieces than robert , and kate gets 2 more pieces than bill , how many pieces of candy does kate get ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: use the initial letter of each name as a variable : r = k + 2 b = m − 6 m = r + 2 k = 2 + bk = = r − 2 b = k − 2 = ( r − 2 ) − 2 = r − 4 m = r + 2 r + b + m + k = 20 r + r − 4 + r + 2 + r − 2 = 20 r = 6 k = r − 2 = 6 − 2 = 4 answer : b
Answer: b
Problem: in the list 3 , 3 , 4 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?
Options: a ) 2 / 9 , b ) 1 / 3 , c ) 4 / 11 , d ) 2 / 3 , e ) 7 / 9
Rationale: mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 3 , 4 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option c
Answer: c
Problem: how many multiples of 4 are less than 3200 , and also multiples of 16 ?
Options: a ) 104 , b ) 200 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 4 and 16 is 16 . divide 3200 / 16 = 200 . xxx . so b is your answer .
Answer: b
Problem: a man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph . what is then time taken to row a distance of 90 km down the stream ?
Options: a ) 8 hrs , b ) 5 hrs , c ) 15 hrs , d ) 15 hrs , e ) 20 hrs
Rationale: speed in down stream = 10 + 8 = 18 time taken to cover 90 km down stream = 90 / 18 = 5 hrs . answer : b
Answer: b
Problem: the sum of two consecutive number is 109 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 55
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 109 2 x + 1 = 109 2 x = 108 x = 54 therefore larger number is x + 1 = 55 answer : e"
Answer: e
Problem: what is the least number to be added to 1480 to make it a perfect square ?
Options: a ) 105 , b ) 160 , c ) 200 , d ) 71 , e ) 120
Rationale: "the numbers greater than 1480 and are square of number is 1600 . the least number that should be added 1480 to make it perfect square = 1600 - 1480 = 120 . answer : e"
Answer: e
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.00 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,100 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 7.5 $ then total value is 300 * 7.0 = 2100 . imo option d is correct answer . ."
Answer: d
Problem: in order to obtain an income of rs . 15000 from 80 % stock at rs . 200 , one must make an investment of
Options: a ) rs . 30000 , b ) rs . 37000 , c ) rs . 37500 , d ) rs . 40000 , e ) rs . 40500
Rationale: "explanation : market value = rs . 200 . required income = rs . 15000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 80 ( ie , 80 % of the face value 100 ) , investment = rs . 200 to obtain rs . 15000 , investment = 200 / 80 ã — 15000 = rs . 37500 answer : option c"
Answer: c
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 40 ° is ?
Options: a ) 53 m 2 , b ) 51 m 2 , c ) 50.2 m 2 , d ) 45 m 2 , e ) 40 m 2
Rationale: "40 / 360 * 22 / 7 * 12 * 12 = 50.2 m 2 answer : c"
Answer: c
Problem: the average runs scored by a batsman in 22 matches is 28 . in the next 13 matches the batsman scored an average of 15 runs . find his average in all the 35 matches ?
Options: a ) 31.23 , b ) 25.12 , c ) 36.25 , d ) 23.17 , e ) 27.66
Rationale: total score of the batsman in 22 matches = 616 . total score of the batsman in the next 13 matches = 195 . total score of the batsman in the 35 matches = 811 . average score of the batsman = 811 / 35 = 23.17 . answer : d
Answer: d
Problem: the sum of the numbers is 330 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 90
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 330 11 x / 3 = 330 x = 90 answer : e"
Answer: e
Problem: a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 150 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 750 , e ) 375
Rationale: "max no . of crates = 5 . max weight = 150 kg max . weight carried = 5 * 150 = 750 kg = d"
Answer: d
Problem: the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ."
Answer: d
Problem: the diagonals of a rhombus are 16 cm and 20 cm . find its area ?
Options: a ) 160 , b ) 288 , c ) 150 , d ) 238 , e ) 31
Rationale: "1 / 2 * 16 * 20 = 160 answer : a"
Answer: a
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 1 , 2 a + 4 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 80 , b ) 75 , c ) 70 , d ) 60 , e ) 65
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 4 ) now 4 a - 5 = 2 a + 4 2 a = 9 therefore , a ( 0,0 ) ; b ( 0,13 ) ; c ( 10,13 ) 1 / 2 * 10 * 13 = 65 answer : e"
Answer: e
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 6 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 6 = 40 40 / 12 = 3.3 feet answer : c"
Answer: c
Problem: xy = 2 then what is ( 2 ^ ( x + y ) ^ 2 ) / ( 2 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 256
Rationale: ( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 8 2 ^ 8 = 256 answer e
Answer: e
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ?
Options: a ) 56
b ) 88
c ) 112
d ) 116
e ) 120
Rationale: ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer
Answer: b
Problem: a sum of money becomes 7 / 6 of itself in 5 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 20 / 7 , b ) 20 / 3 , c ) 23 / 6 , d ) 10 / 3 , e ) 10 / 7
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 5 years . rate = ( 100 * x ) / ( x * 6 * 5 ) = 10 / 3 % . answer : d"
Answer: d
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d"
Answer: d
Problem: all the students of class are told to sit in circle shape . here the boy at the 6 th position is exactly opposite to 16 th boy . total number of boys in the class ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: as half the circle shape consist of 16 - 6 = 10 boys , so total number of boys in full circle = 2 * 10 = 20 answer : c
Answer: c
Problem: the area of a square is 4624 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 11 : 34
Rationale: "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 . a 2 = 4624 a 68 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 44 : 136 = 11 : 34 answer : e"
Answer: e
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 162 km / hr
Options: a ) 8.5 seconds , b ) 2.22 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 162 * ( 5 / 18 ) = 45 m / sec time = distance / speed = 100 / 45 = 2.22 seconds answer : b"
Answer: b
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint t , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 2120 ?
Options: a ) rs . 1000.15 , b ) rs . 1100.95 , c ) rs . 1892.85 , d ) rs . 1050.85 , e ) rs . 1200.25
Rationale: "2120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1892.85 answer : c"
Answer: c
Problem: the average age of an adult class is 40 years . 8 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 8 x 32 = ( y + 8 ) x 36 â ‡ ’ 40 y + 256 = 36 y + 288 â ‡ ’ 4 y = 32 â ˆ ´ y = 8 a"
Answer: a
Problem: what is the ratio of two no . 5 xy and 8 xy .
Options: a ) 2 : 5 , b ) 3 : 4 , c ) 5 : 8 , d ) 2 : 3 , e ) 1 : 2
Rationale: "5 xy / 8 xy = 5 : 8 answer c"
Answer: c
Problem: how many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the number = 2 a + 3 b < 17 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 - > the number = 5 , 8 , 11 , 14 - - > 4 numbers when a = 2 , b = 1,2 , 3,4 - > . . . . - - > 4 numbers when a = 3 , b = 1 , 2,3 - - > . . . . - - > 3 numbers total number is already 11 . look at the answer there is no number greater than 11 - - > we dont need to try any more answer must be d"
Answer: d
Problem: what least number should be added to 1056 , so that the sum is completely divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "that is 1056 / 23 = 45 remainder = 21 = > 21 + 2 = 23 hence 2 should be added to 1056 so that the sum will be divisible by 23 answer is option b"
Answer: b