Cheukting/mathqa huggingface dataset:
Question (geometry): huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 9 inches on a side and costs $ 10 , and a large pizza that measures 14 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches
b ) 10 square inches
c ) 15 square inches
d ) 25 square inches
e ) 34 square inches
Rationale: in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 9 * 9 = 81 ) for the small pizza and ( 14 * 14 = 196 ) for the large pizza . in total sq inches that would be ( 81 + 196 ) * 2 = 554 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 196 = 588 sq inches . hence , the difference is 34 square inches more ( 588 - 554 ) . the correct answer is e
Answer: e
Question (other): which number is a factor of 20 ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 18 , e ) 9
Rationale: a whole number that divides exactly into another whole number is called a factor 20 / 5 = 4 answer b
Answer: b
Question (general): there are 2 sections a and b in a class , consisting of 24 and 16 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 24 * 40 + 16 * 35 = 1520 average weight of the class is = 1520 / 40 = 38 kg answer is d"
Answer: d
Question (general): if n divided by 5 has a remainder of 4 , what is the remainder when 3 times n is divided by 5 ?
Options: a ) 1 , b ) 4 , c ) 3 , d ) 2 , e ) 0
Rationale: "as per question = > n = 5 p + 4 for some integer p hence 3 n = > 15 q + 12 but again , 12 can be divided by 5 to get remainder 2 for some integer q hence d"
Answer: d
Question (physics): a man can row downstream at 18 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 2
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 4 . answer : d"
Answer: d
Question (physics): if four machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 48 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 4 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 8 / 3 = 10 / 3 * x x = 4 / 5 hour so 48 minutes answer : a"
Answer: a
Question (other): the ratio of number of boys and girls in a school is 2 : 5 . if there are 210 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 210 number of girls in the school = 5 * 210 / 7 = 150 answer is a"
Answer: a
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , and 2 * 5 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 = 2520 the answer is d ."
Answer: d
Question (general): there are two positive integers a and b . what is the probability that a + b is odd /
Options: a ) 3 / 2 , b ) 6 / 7 , c ) 1 / 2 , d ) 7 / 2 , e ) 4 / 5
Rationale: s = adding two numbers is ( even + even ) , ( even + odd ) , ( odd + odd ) , ( odd + even ) n ( s ) = 4 e = ( even + odd ) , ( odd + even ) are the points in the event . n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 4 = 1 / 2 answer is option c
Answer: c
Question (general): of the 150 employees at company x , 60 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 = 80 answer : option d"
Answer: d
Question (geometry): if f is the smallest positive integer such that 3,150 multiplied by f is the square of an integer , then f must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by f is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x f = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , y = 7 x 2 = 14 answer is e .
Answer: e
Question (general): what is the least number . which should be added to 0.0355 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0016 , c ) 0.0056 , d ) 0.0066 , e ) 0.0006
Rationale: "0.0355 + 0.0006 = 0.0361 ( 0.19 ) ^ 2 answer : e"
Answer: e
Question (general): if x + 4 y = 5 and 5 x + 6 y = 7 , then 3 x + 5 y = ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: add the left terms and right terms of the two equation to obtain a new equation x + 5 x + 4 y + 6 y = 5 + 7 group and simplify 6 x + 10 y = 12 divide all terms of the above equation by 2 to obtain a new equation 3 x + 5 y = 6 correct answer a
Answer: a
Question (physics): the distance from steve ' s house to work is 10 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 10 km = > speed = 5 kmph a"
Answer: a
Question (general): 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 35 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 35 % = 63 responded as satisfied , so remaining satisfied are 120 - 63 = 57 so 57 is what percentage of 300 - 19 % so the answer should be a
Answer: a
Question (physics): a work can be finished in 30 days by 30 women . the same work can be finished in fifteen days by 15 men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 4 : 1 , e ) 2 : 4
Rationale: "work done by 30 women in 1 day = 1 / 30 work done by 1 woman in 1 day = 1 / ( 30 × 30 ) work done by 15 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 × 15 ) ratio of the capacity of a man and woman = 1 / ( 15 × 15 ) : 1 / ( 30 × 30 ) ) = 1 / 225 : 1 / 900 = 1 / 1 : 1 / 4 = 4 : 1 option d"
Answer: d
Question (general): if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 8 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 8 = 8 c 2 total possible outcomes - 2 ^ 8 ( each child can be either a girl or a boy ) probability = 2 c 1 * 8 c 2 / 2 ^ 8 = 2 * 8 / 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 16 / 256 = 1 / 16 ans = d"
Answer: d
Question (gain): ? % of 360 = 126
Options: a ) 277 , b ) 35 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 126 or , ? = 126 × 100 / 360 = 35 answer b"
Answer: b
Question (geometry): the area of a circle of radius 5 is numerically what percent of its circumference ?
Options: a ) 200
b ) 225
c ) 240
d ) 250
e ) none
Rationale: solution required % = [ π x ( 5 ) 2 / 2 π x 5 x 100 ] % ‹ = › 250 % . answer d
Answer: d
Question (physics): jony walks along sunrise boulevard daily . he starts walking at 07 : 00 from block 10 and walks to block 90 where he turns around and walks back to block 70 , where he stops at 07 : 40 . the blocks along the boulevard are numbered sequentially ( 1 , 2,3 ) , and each block measures 40 meters . what is jony ' s speed in meters per minute ?
Options: a ) 88 , b ) 100 , c ) 198 , d ) 216 , e ) 252
Rationale: total distance from 10 to 90 = 80 + from 90 to 70 = 20 so the dist is 100 × 40 ( per block dist ) speed = 4000 mts / 40 min = 100 m / min b is the answer
Answer: b
Question (physics): car a is 40 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 5.5 , e ) 6.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 40 miles and drive 8 miles ahead so to drive 48 miles it ' ll need 48 / 8 = 6 hours . answer : b"
Answer: b
Question (general): in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options: a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 8 - 5 ) / ( 4 - 2 ) = - 6.5 imo option a is correct answer ."
Answer: a
Question (physics): two fill taps a and b can separately fill a cistern in 45 and 40 minutes respectively . they started to fill a cistern together but tap a is turned off after few minutes and tap b fills the rest part of cistern in 23 minutes . after how many minutes , was tap a turned - off ?
Options: a ) 9 min , b ) 10 min , c ) 12 min , d ) 7 min , e ) none of these
Rationale: let a was turned off after x min . then , cistern filled by a in x min + cistern filled by b in ( x + 23 ) min = 1 ⇒ x / 45 + x + 23 / 40 = 1 ⇒ 17 x + 207 = 360 ⇒ x = 9 min . answer a
Answer: a
Question (gain): find the compound interest on $ 1200 for 4 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1288 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 4 = $ 2488 ci = $ 1288 answer is c"
Answer: c
Question (other): in a company 10 % of male staff are same in number as 1 / 4 th of the female staff . what is the ratio of male staff to female staff
Options: a ) 3 : 2 , b ) 5 : 2 , c ) 2 : 1 , d ) 4 : 3 , e ) 1 : 2
Rationale: 10 % of ms = 1 / 4 th of fs - > 10 ms / 100 = 1 / 4 fs - > ms = 5 / 2 fs : . ms / fs = 5 / 2 = ms : fs = 5 : 2 answer : b
Answer: b
Question (other): the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 25 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 75 / 2 , e ) 35
Rationale: "b : d : w = 2 : 25 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 25 ) = ( 2 / 75 ) dnew / wnew = ( 1 / 2 ) * ( 25 / 100 ) = ( 1 / 8 ) wnew = 300 dnew = wnew / 5 = 300 / 8 = 75 / 2 so , answer will be d"
Answer: d
Question (general): the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg
Rationale: "solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e"
Answer: e
Question (general): a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number t of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average t sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Question (physics): the speed of a car is 98 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 79 kmph , e ) 86 kmph
Rationale: "s = ( 98 + 60 ) / 2 = 79 kmph answer : d"
Answer: d
Question (general): what is the least whole number that should be added to 625573 if it is to be divisible by 3 ?
Options: a ) 6 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: a number is divisible by 3 if the sum of the digits is divisible by 3 . . here , 6 + 2 + 5 + 5 + 7 + 3 = 28 , the next multiple of 3 is 30 . 2 must be added to 625574 to make it divisible by 3 e
Answer: e
Question (general): what least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
Options: a ) 9 , b ) 8 , c ) 5 , d ) 11 , e ) 15
Rationale: "on dividing 2000 by 17 , we get 11 as remainder . required number to be subtracted = 11 answer d"
Answer: d
Question (geometry): v is the volume of a cylinder ; the radius r is 3.4 . the height is 350 % more than the radius . which of the following is true ?
Options: a ) 100 < v < 300
b ) 300 < v < 500
c ) 500 < v < 700
d ) 700 < v < 900
e ) 900 < v < 1100
Rationale: as we see the answers are in form of range we can use approximation volume of cylinder is π r ^ 2 h given π = 22 / 7 and r = 3.4 so r ^ 2 ~ 12 and h = 4.5 * 3.4 ~ 15 so 22 / 7 * 12 * 15 = 566 so answer should be c . 500 < v < 700 answer : c
Answer: c
Question (general): how many 7 in between 1 to 120 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 , 87,97 , 107,117 22 7 ' s between 1 to 120 answer : c"
Answer: c
Question (general): in 1990 the budgets for projects q and v were $ 620,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 620 + 30 x = 780 - 10 x - - > 40 x = 160 and x = 4 . thus , it happens in 1994 . c ."
Answer: c
Question (general): at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 35 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 35 . in any case , there is no necessity to know each item ' s price , just the sum . answer : b"
Answer: b
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 the same number of hours as on the first day at 1 mile faster than 2 nd day for same hours . how many miles in total did she walk ?
Options: a ) 63 , 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 5 hours - 25 miles total 18 + 20 + 25 = 63 answer : option a ."
Answer: a
Question (general): simplify : ( 4 + 3 ) + ( 8 - 3 - 1 )
Options: a ) - 11 , b ) – 12 , c ) 11 , d ) 12 , e ) 10
Rationale: solution : ( 4 + 3 ) + ( 8 - 3 - 1 ) = 7 + ( 8 - 3 - 1 ) = 7 + 8 - 3 - 1 = 15 - 1 = 11 answer : ( c )
Answer: c
Question (physics): a train running at the speed of 56 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 140 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec length of train ( distance ) = speed * time ( 140 / 9 ) * 9 = 140 meter answer : a"
Answer: a
Question (general): how many 9 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 123454321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 90000
Rationale: take the task of building palindromes and break it intostages . stage 1 : select the 9 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 8 th , 7 th , 6 th , 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 9 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 90000 ways ) answer : e
Answer: e
Question (geometry): the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?
Options: a ) 37.2 %
b ) 37.5 %
c ) 30.2 %
d ) 37.7 %
e ) 33.2 %
Rationale: explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b
Answer: b
Question (gain): when sold at a 60 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 66.67 % , d ) 80 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 40 or x = 33.33 . . . marked price was 100 so . . . so answer is 66.67 % . . c"
Answer: c
Question (gain): jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 56,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 28,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 56,000 i . e . rs . 28,000 answer : a"
Answer: a
Question (geometry): if the sides of a square are multiplied by sqrt ( 5 ) , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 5 %
b ) 20 %
c ) 50 %
d ) 100 %
e ) 120 %
Rationale: let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt ( 5 ) * x , so the area is 5 x ^ 2 . the area of the original square is 1 / 5 = 20 % times the area of the new square . the answer is b .
Answer: b
Question (physics): a start walking from a place at a uniform speed of 3 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 3.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 3 + 5 / 9 = 3.55 answer b"
Answer: b
Question (gain): find the 25 % of rs . 600 .
Options: a ) s . 150 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 600 = > 25 / 100 * 600 = rs . 150 answer : a"
Answer: a
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 60900 . what is his profit percent ?
Options: a ) 10.7 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 60900 profit ( % ) = ( 60900 - 55000 ) / 55000 * 100 = 10.7 % answer : a"
Answer: a
Question (general): 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 10 - meter platform and caught it after it had traveled 29.65 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 10 + 10 + 5 + 2.5 + 1.25 + 0.6 + 0.3 ans b"
Answer: b
Question (geometry): if the length of the sides of two cubes are in the ratio 2 : 1 , what is the ratio of their total surface area ?
Options: a ) 2 : 1 , b ) 3 : 1 , c ) 4 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 2 x ) ^ 2 = 24 x ^ 2 . the ratio of surface areas is 4 : 1 . the answer is c ."
Answer: c
Question (probability): a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55
Rationale: "there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a"
Answer: a