Cheukting/mathqa huggingface dataset:
Question (general): positive integers from 1 to 45 , inclusive are placed in 5 groups of 9 each . what is the highest possible average of the medians of these 5 groups ?
Options: a ) 25 , b ) 31 , c ) 15 , d ) 26 , e ) 23
Rationale: answer we need to maximize the median in each group in order to maximize the average of all the medians . the highest possible median is 41 as there should be 4 numbers higher than the median in a group of 9 . so , if we have a group that has a , b , c , d , 41 , 42 , 43 , 44 , 45 , the median will be 41 . in this set , it is essential not to expend any more high values on a , b , c , or d as these do not affect the median . the median of a group that comprises 1 , 2 , 3 , 4 , 41 , 42 , 43 , 44 , 45 will be 41 . the next group can be 5 , 6 , 7 , 8 , 36 , 37 , 38 , 39 , 40 . the median will be 36 . extrapolating the findings in the two sets listed above , to maximize medians in all the 5 groups , the medians of the 5 groups will have to be 21 , 26 , 31 , 36 and 41 . the average of the highest possible medians will be the average of these 5 numbers = 31 . answer b
Answer: b
Question (general): for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 40 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 40 / 100 ) * 300 = 100 + 120 = 220 % comission = ( 220 / 800 ) * 100 = 27.5 ~ 28 % answer is e"
Answer: e
Question (general): a salt manufacturing company produced a total of 5000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 195 , e ) 200
Rationale: "total production of salt by the company in that year = 5000 + 5100 + 5200 + . . . . + 6100 = 66600 . average monthly production of salt for that year = 66600 / 365 = 185 answer : b"
Answer: b
Question (general): the average weight of 9 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 88.5 , e ) 89.5
Rationale: "total increase in weight = 9 × 2.5 = 22.5 if x is the weight of the new person , total increase in weight = x − 65 = > 22.5 = x - 65 = > x = 22.5 + 65 = 87.5 answer : c"
Answer: c
Question (physics): a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 5 miles per hour for 3 hours . how many miles in total did she walk ?
Options: a ) 53 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 3 hours - 15 miles total 18 + 20 + 15 = 53 answer : option a ."
Answer: a
Question (physics): a can do a job 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 ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 5 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"
Answer: d
Question (other): how many zeros are the end of 380 ! ?
Options: a ) 90 , b ) 91 , c ) 94 , d ) none , e ) 95
Rationale: 380 ! has 380 / 5 + 380 / 5 ^ 2 + 380 / 5 ^ 3 = 76 + 15 + 3 = 94 trailing zeros ( take only the quotient into account ) . answer : c .
Answer: c
Question (general): find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case .
Options: a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e"
Answer: e
Question (general): in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the seventh row ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d .
Answer: d
Question (general): q ' = 3 q - 3 , what is the value of ( 5 ' ) ' ?
Options: a ) 96 , b ) 108 , c ) 120 , d ) 132 , e ) 144
Rationale: "( 5 ' ) ' = ( 3 * 5 - 3 ) ' = 12 ' = 12 * 12 - 12 = 132 answer d"
Answer: d
Question (physics): a person can row at 9 kmph and still water . he takes 3 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 54 , e ) 16
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 3.5 = > x / 10 + x / 8 = 7 / 2 = > ( 4 x + 5 x ) / 40 = 7 / 2 = > x = 16 km . answer : e"
Answer: e
Question (physics): the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 210 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 210 = 330 answer is a ."
Answer: a
Question (general): the smallest number when increased by ` ` 1 ` ` is exactly divisible by 12 , 18 , 24 , 32 and 40 is :
Options: a ) 1439 , b ) 1440 , c ) 1459 , d ) 1449 , e ) 1500
Rationale: lcm = 1440 1440 - 1 = 1439 answer : a
Answer: a
Question (general): if ( 2 ^ 17 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 17
Rationale: "given 2 ^ 17 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 17 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans e on comparing the power of 2 = > m = 17"
Answer: e
Question (general): of the 720 students at a certain university , 25 percent are seniors . if x seniors were to graduate early and leave the university and no additional students entered or left the university , what value of x would reduce the number of seniors at the university to 20 percent ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 48
Rationale: sol : 180 - x = 20 % of ( 720 - x ) 4 x = 180 x = 45 answer : d
Answer: d
Question (general): from given equation find the value of x : 2 x ² + 9 x − 5
Options: a ) 1 / 2 , b ) 1 , c ) 3 , d ) 4 , e ) 5
Rationale: that quadratic is factored as follows : 2 x ² + 9 x − 5 = ( 2 x − 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 2 x − 1 = 0 , we must solve that little equation . ( lesson 9 . ) we have : 2 x = 1 x = 1 2 the solutions are : x = 1 / 2 or − 5 a
Answer: a
Question (physics): a can do a job in 15 days and b in 20 days . if they work on it together for 3 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 13 / 20 , d ) 1 / 12 , e ) 6 / 13
Rationale: a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 3 days work = 7 / 60 * 3 = 7 / 20 remaining work = 1 - 7 / 20 = 13 / 20 answer is c
Answer: c
Question (general): how many positive integers between 100 and 500 are there such that they are multiples of 19 ?
Options: a ) 10 , b ) 15 , c ) 21 , d ) 18 , e ) 19
Rationale: multiples of 19 = 114 , 133,152 , - - - - - , 494 number of multiples of 19 = > 494 - 114 / 19 + 1 = 21 answer is c
Answer: c
Question (general): p says to q ` ` i am thrice as old as you were when i was as old as you are ' ' . if the sum of their present age is 100 years , then the present age of q ?
Options: a ) 35.5 , b ) 36.5 , c ) 37.5 , d ) 38.5 , e ) 39.5
Rationale: let the present age of q be x the age of q years back ( to be defined ) is x / 3 as the age of p will be x by then . years passed = x - x / 3 = 2 x / 3 ( subtracting age of q ) so p acurrent age is x + 2 x / 3 and q current age is x adding them to 100 we get x = 37.5 answer : c
Answer: c
Question (physics): annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 15 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . in the next 15 minutes , sam rides 3 km so sam will be 1 km ahead . it will take annie 20 minutes to catch sam . the answer is a ."
Answer: a
Question (gain): what percent of 75 is 45 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 60 %
Rationale: "75 * x / 100 = 45 x = 4 * 45 / 3 x = 60 ans : e"
Answer: e
Question (general): a car was driving at 50 km / h for 30 minutes , and then at 90 km / h for another 40 minutes . what was its average speed ?
Options: a ) 102 , b ) 80 , c ) 75 , d ) 70 , e ) 65
Rationale: "driving at 50 km / h for 30 minutes , distance covered = 50 * 1 / 2 = 25 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 85 / 5 / 6 = 102 km / h answer : a"
Answer: a
Question (general): in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent w of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march w = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Question (general): a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction r of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose r = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Question (general): 1234 + 123 + 12 + x = 1221 . find the value of x .
Options: a ) 10 , b ) 148 , c ) 12 , d ) 13 , e ) 189
Rationale: "x = 1234 + 123 + 12 - 1221 x = 148 correct answer : b"
Answer: b
Question (physics): in 110 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 110 / 45 x 9 m = 22 m . a beats b by 20 metres . answer : option c"
Answer: c
Question (general): at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 16.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 13.0 , b ) 13.3 , c ) 13.6 , d ) 13.9 , e ) 14.2
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 16.9 x ^ 2 = 1.69 x = 1.3 at 4 : 00 pm , the amount of bacteria was 10 ( 1.3 ) = 13 grams . the answer is a ."
Answer: a
Question (gain): a certain tax rate is $ 65 per $ 100.00 . what is the rate , expressed as a percent ?
Options: a ) 82 % , b ) 6.5 % , c ) 0.82 % , d ) 65 % , e ) 0.0065 %
Rationale: here in question it is asking $ 65 is what percent of $ 100 . suppose $ 65 is x % of 100 means 100 * ( x / 100 ) = 65 hence x = 65 so answer is d
Answer: d
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 27 kmph and 21 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 ) 457 km , b ) 444 km , c ) 547 km , d ) 645 km , e ) 576 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 27 + 21 = 48 t = 12 d = 48 * 12 = 576 answer : e"
Answer: e
Question (general): what is the sum of the multiples of 4 between 53 and 145 inclusive ?
Options: a ) 2000 , b ) 2200 , c ) 2300 , d ) 2450 , e ) 2500
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 53 and 145 , the smallest multiple of 4 is 56 and largest = 144 . . average = ( 56 + 144 ) / 2 = 100 . . total numbers = ( 144 - 56 ) / 4 + 1 = 22 + 1 = 23 . . sum = 23 * 100 = 2300 ans c"
Answer: c
Question (gain): the simple interest on a certain sum of money at the rate of 4 % p . a . for 5 years is rs . 1680 . at what rate of interest the same amount of interest can be received on the same sum after 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: s . i . = 1680 , r = 4 % t = 5 years principal = ( 100 * 1680 ) / ( 5 * 4 ) = 8400 so p = 8400 rate = ( 100 * 1680 ) / ( 8400 * 4 ) = 5 % answer : a
Answer: a
Question (geometry): the edge of a cube is 6 a cm . find its surface ?
Options: a ) 216 a 2 , b ) 24 a 4 , c ) 24 a 1 , d ) 24 a 2 , e ) 24 a 7
Rationale: "6 a 2 = 6 * 6 a * 6 a = 216 a 2 answer : a"
Answer: a
Question (general): if ( 1 / 2 ) ^ 25 ( 1 / 81 ) ^ k = 1 / 18 ^ 25 , then k =
Options: a ) 8 , b ) 12.5 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 25 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 25 ) . ( 3 ^ 2 ) ^ 25 hence 4 k = 50 k = 12,5 answer b i hope it ' s quite clear"
Answer: b
Question (general): a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 4 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 100 , b ) 150 , c ) 140 , d ) 120 , e ) 110
Rationale: "a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 100 ) . 750 = 400 + x + 200 x = 150 b"
Answer: b
Question (physics): 180 metres long yard , 11 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 18 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "11 trees have 10 gaps between them , required distance ( 180 / 10 ) = 18 a"
Answer: a
Question (physics): a can do a work in 4 days . b can do the same work in 6 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 4 : 6 ratio of their wages a : b = 3 : 2 a ' s share = ( 3 / 5 ) 1000 = 600 b ' s share = ( 2 / 5 ) 1000 = 400 correct option is a"
Answer: a
Question (gain): if it is assumed that 70 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 428.5 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 70 % = 300 / 0.7 = 428.5 option b"
Answer: b
Question (general): the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is ?
Options: a ) 4 / 5 , b ) 4 / 7 , c ) 5 , d ) 5 / 7 , e ) none
Rationale: "let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 option a"
Answer: a
Question (general): a man can swim in still water at 1.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 0.5 , c ) 1.1 , d ) 1.5 , e ) 1.9
Rationale: "m = 1.5 s = x ds = 1.5 + x us = 1.5 + x 1.5 + x = ( 1.5 - x ) 2 1.5 + x = 3 - 2 x 3 x = 1.5 x = 0.5 answer : b"
Answer: b
Question (general): by using the numbers 1 , 2 , 3 , 7 and 9 only once , how many 5 digit numbers can be made that are divisible by 25 ?
Options: a ) 5 , b ) 4 , c ) not possible , d ) 3 , e ) 6
Rationale: a number to be divisible by 25 must end with 00 , 25 , 50 , or 75 . so , not possible . answer : c .
Answer: c
Question (gain): double of quarter of 5 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.025 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 5 % = 0.025 answer : c"
Answer: c
Question (gain): a car is purchased on hire - purchase . the cash price is $ 25 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 500 , b ) $ 504 , c ) $ 505 , d ) $ 560 , e ) $ 600
Rationale: "explanation : cash price = $ 25 000 deposit = 10 % ã — $ 25 000 = $ 2500 loan amount = $ 25000 â ˆ ’ $ 2500 number of payments = 60 = $ 22500 i = p * r * t / 100 i = 13500 total amount = 22500 + 13500 = $ 36000 regular payment = total amount / number of payments = 600 answer : e"
Answer: e
Question (general): the average salary of 15 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 15,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 19,100 , e ) $ 12,300
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 25 k = 125 k 4 emp @ 15 k = 60 k remaing 6 emp sal = 300 k - 125 k - 60 k = 115 k average = 115 k / 6 = 19100 ans : d"
Answer: d
Question (probability): a jar contains 5 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 21 , c ) 4 / 21 , d ) 3 / 7 , e ) 1 / 2
Rationale: p ( 1 st black , 2 nd white ) = 5 / 7 * 2 / 6 = 10 / 42 ; p ( 1 st white , 2 nd black ) = 2 / 7 * 5 / 6 = 10 / 42 . p = 10 / 42 + 10 / 42 = 20 / 84 = 10 / 42 = 5 / 21 answer : b .
Answer: b
Question (general): there are 2 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 7 / 9 , e ) 4 / 10
Rationale: "w = m + 2 w + m = 16 m + 2 + m = 16 2 m = 14 m = 7 w = 9 ratio : 7 : 9 ans : d"
Answer: d
Question (gain): the regular price per can of a certain brand of soda is $ 0.40 . if the regular price per can is discounted 15 percent when the soda is purchased in 24 - can cases , what is the price of 100 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 34 , e ) $ 28.80
Rationale: "the discounted price of one can of soda is ( 0.85 ) ( $ 0.40 ) , or $ 0.34 . therefore , the price of 72 cans of soda at the discounted price would be ( 100 ) ( $ 0.34 ) = 34 answer : d ."
Answer: d
Question (general): a lady has fine gloves and hats in her closet - 18 blue , 32 red , and 25 yellow . the lights are out and it is totally dark . in spite of the darkness , she can make out the difference between a hat and a glove . she takes out an item out of the closet only if she is sure that if it is a glove . how many gloves must she take out to make sure she has a pair of each color ?
Options: a ) 50 , b ) 8 , c ) 60 , d ) 42 , e ) 32
Rationale: in the first case the lady takes up 32 red colour then he takes up 24 y ( cause he should take up pair ) then he takes up 1 y + 1 blue then 2 blue ( cause to make sure he has a pair of each color in hand ) 32 + 24 + 2 + 2 = 60 answer : c
Answer: c
Question (other): in a 2000 census , 51.27 % of the population are male , and 48.73 % are female . what is the ratio of men to every 100 women ?
Options: a ) 110 : 100 , b ) 105 : 100 , c ) 95 : 100 , d ) 85 : 100 , e ) 120 : 100
Rationale: the ratio of a to b , where a = the percent of males , and b = the percent of females . a = 51.27 b = 48.73 a : b = 51.27 : 48.73 so , 100 ( 5,127 / 4,873 ) : 100 giving a male to female ratio of 105.20 men for every 100 women . answer is b
Answer: b
Question (physics): the radius of a semi circle is 14 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 72 , d ) 32.2 , e ) 32.9
Rationale: "diameter = 28 cm 1 / 2 * 22 / 7 * 28 + 28 = 72 answer : c"
Answer: c
Question (general): a large field of 900 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 435 hectares . , b ) 425 hectares . , c ) 445 hectares . , d ) 415 hectares . , e ) 405 hectares .
Rationale: "let the areas of the parts be x hectares and ( 900 - x ) hectares . difference of the areas of the two parts = x - ( 900 - x ) = 2 x - 900 one - fifth of the average of the two areas = 1 / 5 [ x + ( 900 − x ) ] / 2 = 1 / 5 × ( 900 / 2 ) = 450 / 5 = 90 given that difference of the areas of the two parts = one - fifth of the average of the two areas = > 2 x - 900 = 90 = > 2 x = 990 ⇒ x = 990 / 2 = 495 hence , area of smaller part = ( 900 - x ) = ( 900 – 495 ) = 405 hectares . answer is e ."
Answer: e
Question (physics): a train passes a station platform in 60 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 420 m , c ) 168 m , d ) 197 m , e ) 691 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 36 = 15 = > x = 420 m answer : b"
Answer: b
Question (physics): 15 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?
Options: a ) 10 days , b ) 11 days , c ) 9 days , d ) 8 days , e ) 12 days
Rationale: "that is , 1 work done = 15 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 15 × 8 × 10 / 15 × 8 = 10 days a )"
Answer: a