Cheukting/mathqa huggingface dataset:
Question (general): a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 300 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 300 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 500 = 375 300 - - - - - - - - - - - - - 75 1 / 4 - - - - - - - - 75 1 - - - - - - - - - ? = > rs . 300 answer : d"
Answer: d
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 800 sq . ft , how many feet of fencing will be required ?
Options: a ) 100 feet , b ) 120 feet , c ) 150 feet , d ) 180 feet , e ) 186 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 800 = > breadth = 40 feet area to be fenced = 2 b + l = 2 * 40 + 20 = 100 feet answer : option a"
Answer: a
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) rs . 1090 , b ) rs . 1160 , c ) rs . 1190 , d ) rs . 1202 , e ) none
Rationale: "solution s . p = 90 % of rs . 1400 = rs . ( 90 / 100 × 1400 ) rs . 1260 . answer ce"
Answer: e
Question (physics): every day daniel drives 60 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 60 miles at 4 miles / hour . d = ( r ) ( t ) 60 = ( 4 ) ( t ) 60 / 4 = 15 = t it takes 15 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 28 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 28 = ( 2 ) ( t ) 28 / 2 = 14 = t it takes 14 hours for the second part total time to drive home on monday = 4 + 14 = 18 hours we ' re asked by what percent 18 hours is greater than 15 hours . 18 / 15 = 1.2 , so it is 20 % greater . b"
Answer: b
Question (geometry): the length of a rectangle is halved , while its breadth is tripled . watis the % change in area ?
Options: a ) 43 % , b ) 47 % , c ) 50 % , d ) 65 % , e ) 68 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Question (other): the number of sailors on a ship is 85 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 37 : 20 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.85 * officer sailor / officer = 1.85 / 1 = 185 / 100 = 37 / 20 answer will be a"
Answer: a
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 270 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 250 , e ) 109
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 270 ) / 26 = 20 x = 250 m . answer : d"
Answer: d
Question (physics): the volume of water inside a swimming pool doubles every hour . if the pool is filled to its full capacity within 8 hours , in how many hours was it filled to one quarter of its capacity ?
Options: a ) 2
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: d
Answer: d
Question (general): if pintu is coded as 79523 in a certain code language , how would you code mintu in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 49523 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . mintu is 49523 . . . answer : c"
Answer: c
Question (geometry): there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure y in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = y = 10 ans e ."
Answer: e
Question (general): evaluate : 2.5 + 0.0005
Options: a ) 2000 , b ) 3000 , c ) 1000 , d ) 5000 , e ) 4000
Rationale: "25 / 0.0005 = ( 25 * 10000 ) / ( 0.0005 * 10000 ) = 25000 / 5 = 5000 answer is d ."
Answer: d
Question (physics): it costs $ 2 for the first 1 / 5 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 15 minutes , how much will it cost him ?
Options: a ) $ 25 . , b ) $ 26 . , c ) $ 29 . , d ) $ 30 . , e ) $ 31 .
Rationale: "2 hrs 15 min = 135 min first 12 min - - - - - - > $ 2 time left is 135 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 135 min costs $ 12 / 60 * 135 = > $ 27 so , total cost will be $ 27 + $ 2 = > $ 29 hence answer will be c"
Answer: c
Question (physics): a train 200 m long can cross an electric pole in 5 sec and then find the speed of the train ?
Options: a ) 114 , b ) 124 , c ) 134 , d ) 144 , e ) 154
Rationale: "length = speed * time speed = l / t s = 200 / 5 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"
Answer: d
Question (physics): water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 9 meters . what is value of the radius in meters ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 9 ) which is about 9 r = 3 the answer is b ."
Answer: b
Question (physics): a person crosses a 800 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 1.23 , b ) 2.86 , c ) 4.36 , d ) 9.25 , e ) 9.61
Rationale: "distance = 800 meter time = 5 minutes = 5 x 60 seconds = 300 seconds speed = distance / time = 800 / 300 = 2.67 m / s = 2.67 ã — 18 / 5 km / hr = 9.61 km / hr answer : e"
Answer: e
Question (geometry): the ratio , by volume , of soap to alcohol to water in a certain solution is 20 : 50 : 80 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 520 , b ) 640 , c ) 700 , d ) 750 , e ) 800
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 20 : 50 : 80 initial soap : alcohol = 20 / 50 = 20 : 50 after doubled soap : alcohol = 2 * 20 / 50 = 40 : 50 initial soap : water = 20 / 80 = 20 : 80 after halved soap : water : 1 / 2 * 20 / 80 = 10 / 80 = 10 : 80 after soap : alcohol : water - - > 40 : 50 : 320 - - > 4 : 5 : 32 given alcohol 100 cubic centimeter . ratio is 80 : 100 : 640 ( 4 : 5 : 32 ) for 100 cubic centimeter of alcohol - - - 640 cubic cm water is required . answer - b"
Answer: b
Question (physics): in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 15 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 17 seconds
Rationale: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 15 m ahead . that means jhon was 15 m away from finishing line when they started together . so he will cover 15 m in 5 seconds . so his speed = 15 / 5 = 3 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 17 seconds . correct answer = e"
Answer: e
Question (physics): a 150 meter long train crosses a man standing on the platform in 3 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 180 kmph
Rationale: "s = 150 / 3 * 18 / 5 = 180 kmph answer : e"
Answer: e
Question (general): in an examination , 300 students appeared . out of these students ; 29 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 51 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 29 % of 300 = 29 / 100 × 300 = 8700 / 100 = 87 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 87 + 162 ) = 51 answer : a"
Answer: a
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 104 m , find the area of the rectangle ?
Options: a ) 507 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 525 sq m
Rationale: "2 ( 3 x + x ) = 104 l = 39 b = 13 lb = 39 * 13 = 507 answer : a"
Answer: a
Question (general): if x + y = 20 , x - y = 36 , for integers of x and y , x = ?
Options: a ) 20 , b ) 25 , c ) 28 , d ) 20 , e ) 42
Rationale: "x + y = 20 x - y = 36 2 x = 56 x = 28 answer is c"
Answer: c
Question (general): if x , y is 20 % , 25 % greater than z then how much percentage is x smaller than y ?
Options: a ) 3 1 / 13 % , b ) 3 % , c ) 3 11 / 13 % , d ) 4 % , e ) none of these
Rationale: explanation : x = 125 % y = 130 % z = 100 % x - y / y * 100 = 5 / 130 * 100 = 500 / 130 % = 3 11 / 13 % smaller than y answer : option c
Answer: c
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 14 % , then the cost price of the article is :
Options: a ) 500 , b ) 540 , c ) 555 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 114 = rs . 540 answer : option b"
Answer: b
Question (physics): the speed of a boat in still water is 14 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 8 minutes is
Options: a ) 1.6 km , b ) 2.5 km , c ) 3.6 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 14 + 5 ) kmph = 19 kmph . distance travelled = ( 19 x 8 / 60 ) km = 2.5 km option b"
Answer: b
Question (general): what is the tens digit of 6 ^ 19 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e .
Answer: e
Question (physics): aa is two digit number then m times its cube of aa has 1 in its tens place then what is m .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when aa = 11 7 * ( 11 ) ^ 3 = 7 * 1331 = 9317 m = 7 answer : e
Answer: e
Question (probability): a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability w = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Question (physics): the curved surface of a sphere is 64 π cm 2 . find its radius ?
Options: a ) 8
b ) 3
c ) 4
d ) 9
e ) 7
Rationale: explanation : 4 π r 2 = 64 = > r = 4 answer : option c
Answer: c
Question (gain): dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 62 % , e ) 52.5 %
Rationale: "say dhoni ' s earning last month was $ 100 . dhoni spent 30 percent of his earning last month on rent - - > $ 25 on rent ; 10 percent less than what he spent on rent to purchase a new dishwasher - - > $ 25 * 0.9 = $ 22.5 on the dishwasher . left over amount 100 - ( 25 + 22.5 ) = $ 52.5 answer : e"
Answer: e
Question (gain): a present value of a machine is $ 800 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 648
Rationale: "p = $ 800 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 800 * 9 / 10 * 9 / 10 = $ 648 answer is e"
Answer: e
Question (gain): the effective annual rate of interest corresponding to a nominal rate of 16 % per annum payable half - yearly is ?
Options: a ) 16.64 % , b ) 16.07 % , c ) 16.08 % , d ) 16.09 % , e ) 16.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 8 / 100 ) 2 ] = rs . 116.64 effective rate = ( 116.64 - 100 ) = 116.64 % answer : a"
Answer: a
Question (general): cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?
Options: a ) 50 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: 2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b
Answer: b
Question (general): m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 2 , - 1 , 1 , 2 , 3 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5
Answer: e
Question (general): what will be the vulgar fraction of 0.5
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.5 = 50 / 100 = 1 / 2 option b"
Answer: b
Question (general): what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 8.38 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85
Rationale: "answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38"
Answer: a
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 50 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 27 , c ) 45 , d ) 99 , e ) 12
Rationale: "relative speed = 50 + 30 = 80 km / hr . 80 * 5 / 18 = 200 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 200 = 45 sec . answer : c"
Answer: c
Question (general): set x consists of all two - digit primes and set y consists of all positive even multiples of 5 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 10 , 20 , 30 , . . . . . . . . . . . . . . . , 70 , 80 , 90 } combining two sets , say set z set z = { 10,11 , 13 , 17 , 20,30 , . . . . . . . . . . . . . . . . . . . , 70 , 80 , 83 , 89 , 90 , 97 } range = max value - min value range ( z ) = 97 - 10 = 87 oa a is the answer ."
Answer: a
Question (physics): a woman complete a journey in 5 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 112 km . , d ) 224 km . , e ) 544 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 5 - - > x / 21 + x / 24 = 10 - - > x = 112 km . c"
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 74 ft , b ) 88 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft"
Answer: a
Question (physics): how many shots of 1 cm radius can be prepared from a sphere of 6 cm radius ?
Options: a ) 33 , b ) 88 , c ) 216 , d ) 288 , e ) 299
Rationale: "4 / 3 ï € * 6 * 6 * 6 = 4 / 3 ï € * 1 * 1 * 1 * x x = 216 answer : c"
Answer: c
Question (physics): a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 4 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 20
Rationale: "son ' s 1 day work = 1 / 4 - 1 / 5 = 1 / 20 son alone can do the work in 20 days = 20 days answer is e"
Answer: e
Question (general): for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the standard deviation for the exam ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 0 , e ) 2
Rationale: "mean - 2 sd = 58 mean + 3 sd = 98 by solving above equation we get , sd ( absolute value ) = 8 ans . c"
Answer: c
Question (probability): a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 7 , d ) 3 / 11 , e ) 4 / 5
Rationale: let a = event that the husband is selected and b = event that the wife is selected . then , p ( a ) = 1 / 7 and p ( b ) = 1 / 5 ∴ p ( a ¯ ) = ( 1 - 17 / 5 ) = 6 / 7 and = ( 1 - 1 / 5 ) = 4 / 5 required probability = p [ ( a and not b ) or ( b and not a ) ] = p [ ( a and b ¯ ) or ( b and a ¯ ) ] = p ( a and b ¯ ) + p ( b and a ¯ ) = p ( a ) . p ( b ¯ ) + p ( b ) . p ( a ¯ ) = ( 1 / 7 * 4 / 5 ) + ( 1 / 5 * 6 / 7 ) = 10 / 35 = 2 / 7 c
Answer: c
Question (physics): find the length of the wire required to go 11 times round a square field containing 27889 m 2 .
Options: a ) 7348 , b ) 3388 , c ) 2667 , d ) 8766 , e ) 66711
Rationale: "a 2 = 27889 = > a = 167 4 a = 668 668 * 11 = 7348 answer : a"
Answer: a
Question (general): a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 4 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 234
Rationale: "if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 11 / 4 solving it 28 x = 26 x + 52 x = 11 which means m ( d ) = 182 and b ( d ) = 52 so total initially is m ( d ) + b ( d ) = 234 e"
Answer: e
Question (probability): there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "9 = 5 blue balls + 20 / 5 answer : b"
Answer: b
Question (geometry): a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 301.6
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 24 ) m 3 ‹ = › 301.6 m 3 . answer e"
Answer: e
Question (general): priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are
Options: a ) 11 , 42 , b ) 12 , 24 , c ) 15 , 42 , d ) 16 , 19 , e ) 33 , 44
Rationale: a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 – 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years
Answer: a
Question (physics): if 7 spiders make 7 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 14 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 7 : 1 ( webs ) 1 : 7 } : : x : 7 ⇒ 7 × 1 × 7 = 1 × 7 × x ⇒ x = 7 answer : option b"
Answer: b
Question (general): the price of lunch for 13 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.85 , d ) 14 , e ) 15.87
Rationale: "clearly c is the answer i used poe here lets consider option ( c ) 13 * 13.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo c"
Answer: c
Question (gain): a shopkeeper sold an article at $ 1800 with 20 % profit . then find its cost price ?
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1850 , d ) $ 1600 , e ) $ 2000
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 1800 * 100 / 120 = $ 1500 answer is b"
Answer: b
Question (gain): find the principle on a certain sum of money at 5 % per annum for 2 years if the amount being rs . 1120 ?
Options: a ) 1018 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 2 ) / 100 ] p = 1018 answer : a"
Answer: a
Question (physics): a man swims downstream 24 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 8 , b ) 5 , c ) 24 , d ) 12 , e ) 36
Rationale: "24 - - - 4 ds = 6 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"
Answer: b
Question (general): when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c"
Answer: c
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 6000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 750 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 6000 ) = rs . 750 answer = d"
Answer: d