Cheukting/mathqa huggingface dataset:
Question (physics): 2 persons can finish a job in 8 days . first person alone can finish the work in 24 days . how many days does the second person take to finish the job ?
Options: a ) 10 days , b ) 12 days , c ) 14 days , d ) 16 days , e ) 18 days
Rationale: 2 persons can do work in 1 day = 1 / 8 first person can do work in 1 day = 1 / 24 second person can do work in 1 day = 1 / 8 - 1 / 24 = 1 / 12 so second person can finish work in 12 days answer : b
Answer: b
Question (physics): a cistern is filled by pipe a in 12 hours and the full cistern can be leaked out by an exhaust pipe b in 18 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 36 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 12 - 1 / 18 ) hrs = 1 / 36 = 36 hrs answer : c"
Answer: c
Question (general): | x + 3 | – | 4 - x | = | 8 + x | how many x solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "x = | x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Question (general): of the 100 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 20 answer : option a"
Answer: a
Question (general): a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 3 / 7 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b"
Answer: b
Question (gain): the list price of an article is rs . 70 . 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 ) 10.85 % , b ) 14.85 % , c ) 15.85 % , d ) 16.85 % , e ) 17.85 %
Rationale: "70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 10.85 % answer : a"
Answer: a
Question (physics): a man swims downstream 42 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 6 , e ) 10
Rationale: "42 - - - 3 ds = 14 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : e"
Answer: e
Question (other): a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 15750 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 ã — 12 ) : ( 4 x ) = 2 : 3 â ‡ ’ x = 15750 answer : d"
Answer: d
Question (general): joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 9 , e ) 13
Rationale: joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d )
Answer: d
Question (general): 5 20 380 144020 ?
Options: a ) 20741616380 , b ) 20841616380 , c ) 21741616380 , d ) 22741616380 , e ) 20791616380
Rationale: "if number = n , then next number = n * ( n - 1 ) so 5 , ( 5 * 4 = 20 ) , ( 20 * 19 = 380 ) , ( 380 * 379 = 144020 ) , ( 144020 * 144019 = 20741616380 ) answer : a"
Answer: a
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4538 , b ) s . 6342 , c ) s . 4518 , d ) s . 4530 , e ) s . 4517
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b"
Answer: b
Question (physics): two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) 160 m
Rationale: "relative speed = 81 km / h = 81 x 5 / 18 m / sec = 22.5 m / sec length of slower train = speed x time = 36 x 8 km / hr = 288 x 5 / 18 m / sec = 80 m / sec let length of faster train = b time cross to each other 8 = ( 80 + b ) x 18 / ( 81 x 5 ) = 3240 - 1440 = 18 b 1800 / 18 = b b = 100 m answer : b"
Answer: b
Question (general): if the mean of numbers 28 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 280 , 511 , 1023 and x ?
Options: a ) 395 , b ) 375.8 , c ) 355 , d ) 415 , e ) 365
Rationale: "the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 62 * 5 - - > x = 58 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 280 + 511 + 1023 + 58 ) / 6 = 375.8 . answer : b ."
Answer: b
Question (general): the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?
Options: a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77
Rationale: let x be the number of students in the class . let p be the average of the rest of the class . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d .
Answer: d
Question (gain): the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1260 respectively . what is the rate of interest ?
Options: a ) 5 % , b ) 8 % , c ) 11 % , d ) 14 % , e ) 18 %
Rationale: "1260 - 1200 = 60 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 60 ) / ( 1200 ) = 5 % the answer is a ."
Answer: a
Question (general): a fair 2 sided coin is flipped 7 times . what is the probability that tails will be the result at least twice , but not more than 7 times ?
Options: a ) 119 / 128 , b ) 120 / 113 , c ) 114 / 210 , d ) 121 / 141 , e ) 104 / 117
Rationale: "at least twice , but not more than 7 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 7 c 2 / 2 ^ 7 + 7 c 3 / 2 ^ 7 + 7 c 4 / 2 ^ 7 + 7 c 5 / 2 ^ 7 + 7 c 6 / 2 ^ 7 = 119 / 128 option : 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 q 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 q = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e
Answer: e
Question (gain): the s . i . on a certain sum of money for 2 years at 4 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 5250 , b ) 1267 , c ) 5750 , d ) 2267 , e ) 5262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 5250 answer : a"
Answer: a
Question (geometry): a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 6564
b ) 7372
c ) 8281
d ) 9331
e ) can not be determined
Rationale: let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c .
Answer: c
Question (gain): a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 9.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 8 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.095 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 95 f - - > s = f - - > f / s = 1 / 12 - - > f / ( s + f ) = 1 / ( 1 + 12 ) = 1 / 13 = 0.08 . answer : b ."
Answer: b
Question (general): how many of the positive divisors of 720 are also multiples of 4 not including 720 ?
Options: a ) 11 , b ) 12 , c ) 17 , d ) 18 , e ) 24
Rationale: "720 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 ^ 2 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 2 , and 1 . there are ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 720 . the answer is c ."
Answer: c
Question (general): ( p / q - q / p ) = 21 / 10 . then find 4 p / q + 4 q / p ?
Options: a ) 58 / 9 , b ) 58 / 5 , c ) 58 / 7 , d ) 58 / 2 , e ) 58 / 1
Rationale: let p / q = a , then ( a - 1 / a ) = 21 / 10 ⇒ a 2 − 1 = a . 2110 ⇒ a 2 − 1 = a . 2110 ⇒ 10 a 2 − 21 a − 10 ⇒ 10 a 2 − 21 a − 10 = 0 roots of the equation = − b ± b 2 − 4 ac − − − − − − − √ 2 a − b ± b 2 − 4 ac 2 a a = 21 ± 441 + 400 − − − − − − − − √ 2021 ± 441 + 40020 a = 21 ± 292021 ± 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b
Answer: b
Question (gain): a jar was full with honey . a person used to draw out 20 % of the honey from the jar and replaced it with sugar solution . he has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar , the rest part of the jar was filled with the sugar solution . the initial amount of honey in the jar was filled with the sugar solution . the initial amount of honey in the jar was :
Options: a ) 1.25 kg , b ) 1.29 kg , c ) 1.85 kg , d ) 3.25 kg , e ) 1.23 kg
Rationale: answer : a ) 1.25 kg
Answer: a
Question (general): a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b"
Answer: b
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 8,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 1600
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 8,000 = $ 1600 as our answer . but since , the interest is compounded , it will be a bit more than $ 1600 . option ( e ) looks correct ."
Answer: e
Question (general): the ratio of two numbers is 2 / 3 , and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1 / 2 , then the numbers are .
Options: a ) 6 and 9 , b ) 6 and 10 , c ) 6 and 8 , d ) 6 and 7 , e ) 6 and 11
Rationale: a : b = 2 : 3 b = 3 / 2 a a - 1 / b + 1 = 1 / 2 solving this we get a = 6 and b = 9 answer : a
Answer: a
Question (other): the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 280 , c ) 322 , d ) 345 , e ) 354
Rationale: "clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b"
Answer: b
Question (geometry): two cubes of their volumes in the ratio 64 : 125 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 64 : 125 4 : 5 answer is e ."
Answer: e
Question (general): if the average of 16 x and 8 y is greater than 80 , and x is twice y , what is the least integer value of x ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 16 x and 4 x is greater than 80 . average of 16 x and 4 x is 10 x . so , 10 x > 80 x > 8 answer : a"
Answer: a
Question (other): what is the square root of 168,921 ?
Options: a ) 476 , b ) 389 , c ) 497 , d ) 411 , e ) 524
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) b = 389 ^ 2 and d = 411 ^ 2 b = ( 400 - 11 ) ^ 2 and d = ( 400 + 11 ) ^ 2 since we need the answer less than 160000 = > b is out . thus we have d as the ans ."
Answer: d
Question (general): if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 24 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d"
Answer: d
Question (general): a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 26 , e ) 10
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d"
Answer: d
Question (general): in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 56 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 30 + 42 â € “ 28 = 44 therefore students who passed = 100 â € “ 44 = 56 . answer : c"
Answer: c
Question (gain): a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is : ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 67 , e ) 30
Rationale: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"
Answer: c
Question (physics): two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1 / 2 minute . if the length of the first train is 125 m , what is the length of the second train ?
Options: a ) 300 m , b ) 287 m , c ) 125 m , d ) 250 m , e ) 167 m
Rationale: rs = 50 â € “ 40 = 10 * 5 / 18 = 25 / 9 mps t = 90 sec d = 25 / 9 * 90 = 250 m 125 - - - - - - - - 125 m answer : c
Answer: c
Question (physics): a man can row upstream at 25 kmph and downstream at 31 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 28 , c ) 30 , d ) 27 , e ) 18
Rationale: "us = 25 ds = 31 m = ( 31 + 25 ) / 2 = 28 answer : b"
Answer: b
Question (physics): a , b , c can complete a piece of work in 24 , 8,12 days . working together , they complete the same work in how many days ?
Options: a ) 4 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 24 + 1 / 8 + 1 / 12 = 6 / 24 = 1 / 4 a , b , c together will complete the job in 4 days answer is a"
Answer: a
Question (general): a cricket player whose bowling average was 23.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 131 , d ) 456 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 23.5 w + 52 total wickets after last match = w + 5 ( 23.5 w + 52 ) / ( w + 5 ) = 23.5 - 0.5 = 23 w = 126 so total wickets aftr last match = w + 5 = 131 answer : c"
Answer: c
Question (general): on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )"
Answer: b
Question (other): how many different positive integers are factors of 20 ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 10 , e ) 12
Rationale: "2 * 10 4 * 5 answer : c"
Answer: c
Question (general): jim â € ™ s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.65 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d"
Answer: d
Question (geometry): if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?
Options: a ) 225 square inches
b ) 45 square inches
c ) 25 square inches
d ) 15 square inches
e ) 10 square inches
Rationale: definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d
Answer: d
Question (gain): at a certain university , 66 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 60 , d ) 62.5 , e ) 75
Rationale: "answer is 75 % total women = 66 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 24 % but question wants to know the percent of men that are tenured 24 % / 40 % = 60 % c"
Answer: c
Question (gain): a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 50 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 49 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.5 = $ 14 - - > x = $ 28 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 28 + 21 = $ 49 . answer : b .
Answer: b
Question (physics): excluding stoppages , the speed of a bus is 58 kmph and including stoppages , it is 40 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 19 , b ) 19.13 , c ) 10.5 , d ) 11.35 , e ) none of these
Rationale: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( ( 18 / 58 ) ã — 60 ) = 19 min . option ( a ) is correct"
Answer: a
Question (general): the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 465 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b"
Answer: b
Question (general): what is the 149 th digit to the right of the decimal point in the decimal form of 30 / 33 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 0 , e ) 1
Rationale: to solve , we first have to use some long division . long division allows us to get 30 / 33 in decimal form , which is 0.909090 … where “ 90 ” is repeating . we see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 9 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 0 . in other words , each odd - positioned digit is a 9 , and each even - positioned digit is a 0 . then the 149 th digit to the right of the decimal point and we see that 149 is odd , then 149 th digit is a 9 . answer c .
Answer: c