Cheukting/mathqa huggingface dataset:
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.2 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 1 : 1 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.2 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.2 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.4 = 1 / 1 required ratio = 1 / 1 : 1 = 1 : 1 . answer : d"
Answer: d
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a"
Answer: a
Question (general): a batsman scored 210 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 71.4 % , e ) 75 %
Rationale: "number of runs made by running = 210 - ( 3 x 4 + 8 x 6 ) = 210 - ( 60 ) = 150 now , we need to calculate 60 is what percent of 120 . = > 150 / 210 * 100 = 71.4 % d"
Answer: d
Question (general): ( 112 x 5 ^ 4 ) = ?
Options: a ) 70000 , b ) 80000 , c ) 90000 , d ) 90090 , e ) 100000
Rationale: "( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )"
Answer: a
Question (general): x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 2 ^ 2 x ^ 2 + 1 / x ^ 2 = 4 - 2 x ^ 2 + 1 / x ^ 2 = 2 answer : a"
Answer: a
Question (general): what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ?
Options: a ) 344545629 , b ) 723437481 , c ) 354595321 , d ) 964564944 , e ) 458449909
Rationale: "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b"
Answer: b
Question (general): in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "# defective pens = 3 # good pens = 9 probability of the 1 st pen being good = # of favorable outcomes / # of total outcomes = 9 / 12 probability of the 2 nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11 total probability = 9 / 12 * 8 / 11 = 6 / 11 answer will be c"
Answer: c
Question (gain): if a sum of money doubles itself in 15 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 6.67 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c"
Answer: c
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 883 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 883 96 + 225 + 490 + 6 x = 883 6 x = 72 = > x = 12 . answer : d"
Answer: d
Question (general): if a person walks at 16 km / hr instead of 8 km / hr , he would have walked 20 km more . the distance traveled by him if he walked at 16 km / hr ?
Options: a ) 50 km , b ) 58 km , c ) 60 km , d ) 70 km , e ) 40 km
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 16 2 x - x = 20 = > x = 20 km . the required distance is = ( 20 + 20 ) km = 40 km answer : e"
Answer: e
Question (general): drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 3 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 12 , d ) 11 / 12 , e ) 17 / 24
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ."
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 26 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 330 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 answer : c"
Answer: c
Question (physics): a train 160 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 90 kmph
Rationale: "speed of train relative to man : 160 / 6 * 18 / 5 km / hr = 96 km / hr let speed of train = x therefore x + 6 = 96 x = 96 - 6 x = 90 km / hr answer : e"
Answer: e
Question (physics): an aeroplane covers a certain distance at a speed of 240 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 864
Rationale: "distance = ( 240 x 6 ) = 1440 km . speed = distance / time speed = 1440 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1440 x 3 / 5 ) km / hr = 864 km / hr answer e ) 864 km / hr"
Answer: e
Question (physics): if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursday , bow much coal will be required for 8 engines , each running 13 hours a day , it being given that 3 engines of former type consume as much as 4 engines of latter type ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct prportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) [ 9 x 8 x ( 1 / 3 ) x x ) = ( 8 x 13 x ( 1 / 4 ) x 24 ) = 24 x = 624 = x = 26 . hence , the required consumption of coal = 26 metric tonnes . answer is c .
Answer: c
Question (other): the value of log 2 ( log 5625 ) is
Options: a ) 2 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: solution let log 5625 = x . then , 5 x = 625 = 54 ‹ = › x = 4 . let log 2 ( log 5625 ) = y . then , log 24 = y ‹ = › 2 y = 4 y ; 2 . answer a
Answer: a
Question (general): if 16 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 64
Rationale: "let x be the number of students in the school . 0.16 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 % . the answer is e"
Answer: e
Question (physics): a man sitting in a train which is traveling at 55 kmph observes that a goods train , traveling in opposite direction , takes 10 seconds to pass him . if the goods train is 320 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 60 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 320 / 10 m / sec = ( ( 320 / 10 ) × ( 18 / 5 ) ) kmph = 115 kmph . speed of goods train = ( 115 - 55 ) kmph = 60 kmph answer : option c"
Answer: c
Question (other): a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 10 % stock at 90 , investment = rs . ( 90 / 10 ) = rs . 9 . for an income of rs . 1 in 5 % stock at 90 , investment = rs . ( 90 / 5 ) = rs . 18 . ∴ ratio of investments = 9 : 18 = 1 : 2 answer a"
Answer: a
Question (general): average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 98 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"
Answer: d
Question (general): solve below question 2 x + 1 = - 23
Options: a ) - 8 , b ) - 9 , c ) - 12 , d ) - 4 , e ) 12
Rationale: 1 . subtract 1 from both sides : 2 x + 1 - 1 = - 23 - 1 2 . simplify both sides : 2 x = - 24 3 . divide both sides by 2 : 4 . simplify both sides : x = - 12 c
Answer: c
Question (general): calculate 85184 ÷ ? = 352
Options: a ) 241 , b ) 242 , c ) 244 , d ) 247 , e ) 240
Rationale: "answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b"
Answer: b
Question (general): 7.51 8.22 7.86 8.36 8.09 7.83 8.30 8.01 7.73 8.25 7.96 8.53 a vending machine is designed to dispense 8 ounces of coffee into a cup . after a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine , the 12 listed amounts , in ounces , were selected from the data above . if the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces , how many of the 12 listed amounts are within 1.5 standard deviation of the mean ?
Options: a ) four , b ) six , c ) nine , d ) ten , e ) twelve
Rationale: mean = 8.1 standard deviation = 0.4 within 1.5 standard deviation of the mean i . e . 1.5 standard deviation above the mean = 8.1 + 1.5 * 0.4 = 8.7 and 1.5 standard deviation below the mean = 8.1 - 1.5 * 0.4 = 7.5 all values are within the range hence , 12 values fall within 1.5 sd from mean answer : option e
Answer: e