Cheukting/mathqa huggingface dataset:
Question (physics): a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 6 hours , b ) 3 hours , c ) 2 hours , d ) 5 hours , e ) 4 hours
Rationale: "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 b ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 b alone will take 3 hours to do the work . answer : b"
Answer: b
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 5 : 2
Rationale: "answer : option b let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 9 = 4 : 3"
Answer: b
Question (gain): at what rate percent on simple interest will rs . 650 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 9.23 %
Rationale: "300 = ( 650 * 5 * r ) / 100 r = 9.23 % answer : e"
Answer: e
Question (other): a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :
Options: a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811
Rationale: "explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681"
Answer: c
Question (general): when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ?
Options: a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750
Rationale: let the value of the item be $ x , then 0.07 ( x − 1000 ) = 87.5 - - > x − 1000 = 1250 x − 1000 = 1250 - - > x = 2250 . answer : c .
Answer: c
Question (gain): the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ?
Options: a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e"
Answer: e
Question (physics): john and steve are speed walkers in a race . john is 12 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 28 seconds
Rationale: let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 12 + 2 - - - > 0.5 t = 14 - - - > t = 28 seconds . e is the correct answer .
Answer: e
Question (general): i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ?
Options: a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100
Rationale: "let x be the number i chose , then x / 6 − 189 = 3 x / 6 = 192 x = 1152 answer is b ."
Answer: b
Question (gain): a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 400 more . what was the sum ?
Options: a ) s . 1200 , b ) s . 800 , c ) s . 1400 , d ) s . 1000 , e ) s . 920
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 400 ( given ) so , at 5 % more rate , the increase in si for 1 year = 400 / 10 = rs . 40 / - i . e . rs . 40 is 5 % of the invested sum so , 1 % of the invested sum = 40 / 5 therefore , the invested sum = 40 × 100 / 5 = rs . 800 answer : b"
Answer: b
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 26000 , e ) 27991
Rationale: "26 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 26 = 1 / 1000 * x = > x = 26000 answer : d"
Answer: d
Question (general): the product of two successive numbers is 462 . which is the smaller of the two numbers ?
Options: a ) 21 , b ) 23 , c ) 26 , d ) 27 , e ) 29
Rationale: a 21 from the given alternatives , 21 × 22 = 462 ∴ smaller number = 21
Answer: a
Question (general): in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total number of cows = 15 answer is b ."
Answer: b
Question (general): two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ?
Options: a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these
Rationale: "explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 ∗ 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c"
Answer: c
Question (general): if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )"
Answer: d
Question (general): the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c"
Answer: c
Question (physics): a and b can do a piece of work in 6 2 / 3 days and 5 days respectively . they work together for 2 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 6 â ½ days , b ) 1 â ½ days , c ) 8 â ½ days , d ) 5 â ½ days , e ) 2 â ½ days
Rationale: "explanation : 3 / 20 * 2 + ( 2 + x ) / 5 = 1 x = 1 â ½ days answer : b"
Answer: b
Question (physics): convert the 13 / 48 m / s into kilometers per hour ?
Options: a ) 1.5 kmph . , b ) 0.91 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 0.98 kmph .
Rationale: "13 / 48 m / s = 13 / 48 * 18 / 5 = 49 / 50 = 0.98 kmph . answer : e"
Answer: e
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 50 cm
Rationale: "let bresdth x cm length = 2 x cm new l = ( 2 x - 5 ) cm new breadth = ( x + 5 ) new area = ( 2 x - 5 ) sq cm = ( 2 x - 5 ) ( x + 5 ) = 2 x 2 + 75 x = 20 cm l = 2 x - 2 = 2 * 20 = 40 cm answer c"
Answer: c
Question (general): there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d ."
Answer: d
Question (general): what is the average of first 21 multiples of 7 ?
Options: a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81
Rationale: "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c"
Answer: c
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 14 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 5 , e ) 9
Rationale: "answer is d . x / x + 36 = 1 / 5 x = 9 14 - 9 = 5"
Answer: d
Question (physics): at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 25 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 55 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 25 / 5 = 5 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 5 = 55 secs . answer : b"
Answer: b
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 2 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 3 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 2 ½ h . d = 5 / 4 * 5 / 2 = 25 / 8 = 3 1 / 8 km answer : c"
Answer: c
Question (physics): if an object travels at 85 feet per second , how many feet does it travel in 30 minutes ?
Options: a ) 3000 , b ) 1500 , c ) 1800 , d ) 9000 , e ) 2500
Rationale: "if an object travels at 85 feet per second it covers 85 x 60 feet in one minute , and 5 x 60 x 30 feet in 30 minutes . answer = 9000 answer : d"
Answer: d
Question (general): if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Question (general): in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 53900 . how many times did he participate in the competition ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is 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 . 15 % 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 ) 31 , 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 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a"
Answer: a
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c"
Answer: c
Question (physics): 34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ?
Options: a ) 36 , b ) 26 , c ) 97 , d ) 26 , e ) 19
Rationale: "explanation : let the required number of days be a . then , less men , more days ( indirect proportion ) 17 : 34 : : 18 : a 17 x a = 34 x 18 a = ( 34 x 18 ) / 17 a = 36 answer : a"
Answer: a
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg ."
Answer: b
Question (geometry): the perimeter of one square is 48 cm and that of another is 24 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 13.4 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 24 a = 12 a = 6 a 2 = 144 a 2 = 36 combined area = a 2 = 180 = > a = 13.4 d = 13.4 √ 2 answer : c"
Answer: c
Question (general): if a certain number when divided by the numbers 5 , 32 one after other successively , leaves a remainder 0 , 21 then what will be the remainders if it is divided by the numbers 2 , 35
Options: a ) 1 , 20 , b ) 1 , 21 , c ) 1 , 22 , d ) 1 , 23 , e ) 1 , 24
Rationale: the number is 35 , when divided by 5 , 32 leaves remainder 0 , 21 respectively . so if 35 is divided by 2 , 35 leaves remainder 1 , 20 respectively . answer : a
Answer: a
Question (gain): p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 30000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 45000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 30000 : q = 2 : 3 ⇒ 30000 × 3 = 2 q ⇒ q = ( 30000 × 3 ) / 2 = 45000 answer is c ."
Answer: c
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: ( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b
Answer: b
Question (general): a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 30 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 28 answer : b"
Answer: b
Question (general): what is the value of ( 4 ) ^ - 6 ?
Options: a ) 1 / 1008 , b ) 1 / 6400 , c ) 1 / 6550 , d ) 1 / 6660 , e ) 1 / 4096
Rationale: "4 ^ - 6 = 1 / ( 4 ) ^ 6 = 1 / 4096 answer : e"
Answer: e
Question (general): machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3
Rationale: machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 60 so , x = 60 . hence 6 x = 6 * 60 = 360 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 360 = 3 hence option ( e ) .
Answer: e
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b"
Answer: b
Question (physics): a train running at the speed of 52 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 130 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec length of train ( distance ) = speed * time ( 130 / 9 ) * 9 = 130 meter answer : a"
Answer: a
Question (general): what is the remainder when 1234 * 6789 * 1111 is divided by 19
Options: a ) 15 , b ) 23 , c ) 7 , d ) 10 , e ) 43
Rationale: "12345 / 19 = = > remainder = 14 678910 / 19 = = > remainder = 2 111111 / 19 = = > remainder = 18 = 14 * 2 * 18 = 504 / 19 = = > remainder = 10 answer : d"
Answer: d
Question (general): how many 1 / 4 s are there in 37 1 / 2 ?
Options: a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a"
Answer: a
Question (general): if x : y = 2 : 9 , find the value of ( 2 x + 2 y ) : ( 5 x – y )
Options: a ) 22 : 1 , b ) 22 : 3 , c ) 7 : 1 , d ) 5 : 3 , e ) 8 : 1
Rationale: "explanation : given : x / y = 2 / 9 ( 2 x + 2 y ) : ( 5 x – y ) = ( 2 * 2 + 2 * 9 ) : ( 5 * 2 – 9 ) = 22 : 1 answer : a"
Answer: a
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 8 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 8 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 8 = 7 / 8 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 7 / 8 = 4 / 9 - - - > p ( of burning out in a six mnth period ) = 1 - 4 / 9 = 4 / 7 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 7 / 8 * 4 / 7 = 1 / 2 ans c"
Answer: c
Question (physics): a train 360 m long is running at a speed of 90 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 20 sec , e ) 34 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 25 = 20 sec answer : d"
Answer: d
Question (gain): the sale price sarees listed for rs . 200 after successive discount is 20 % and 5 % is ?
Options: a ) 187 , b ) 169 , c ) 152 , d ) 178 , e ) 175
Rationale: "200 * ( 80 / 100 ) * ( 95 / 100 ) = 152 answer : c"
Answer: c
Question (geometry): the radius of the base of cone is 3 cm and height is 4 cm . find the volume of the cone ?
Options: a ) 12
b ) 75
c ) 97
d ) 15
e ) 91
Rationale: 1 / 3 * π * 3 * 3 * 4 = 12 π answer : a
Answer: a
Question (physics): bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ?
Options: a ) 40 , b ) 80 , c ) 120 , d ) 160 , e ) 180
Rationale: bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ? average speed = total distance / total time we know the total distance is 5 + 5 ( going from a to b then from b to a ) time = distance / speed time = 5 / 15 time = 1 / 3 hour average speed = ( 10 ) / ( 1 hr + 1 / 3 hr ) average speed ( bexi ) = 10 / 1.33 therefore , if ben ' s average speed is 1 / 2 of bexi ' s then his speed = 10 / 2.66 . this means it took him 2.66 hours to cover the same 10 miles bexi did . 2.66 hours = roughly 160 minutes . answer : d ) . 160
Answer: d
Question (general): the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 260
Rationale: "x - y = 1365 divide larger number by the smaller , we get 6 as quotient and the 15 as remainder x / y = 6 quotient and 15 reminder convert this as x = 6 y + 15 apply this x in above eqn therefore , 6 y + 15 - y = 1365 5 y + 15 = 1365 y + 3 = 273 y = 270 answer : b"
Answer: b
Question (gain): running at the same constant rate , 4 identical machines can produce a total of 16 bottles per minute . at this rate , how many bottles could 8 such machines produce in 3 minutes ?
Options: a ) 11 , b ) 92 , c ) 96 , d ) 174 , e ) 115
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 16 / 4 = 4 . 8 machines = 32 per minute . 3 minutes worth = 96 bottles . looking at the answers it is clear . . . we can only choose ( c ) the correct answer is c ."
Answer: c
Question (general): 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 12 , the how old is b ?
Options: a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 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 = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )"
Answer: b
Question (general): how many digits are required to number a book containing 300 pages ?
Options: a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a ."
Answer: a
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 4 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.25 , e ) 3.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 4 km / hour x / 3 = 4 x = 12 km the average speed while climbing = distance / time = 12 / 4 = 3 km / h the answer is c ."
Answer: c