question
stringlengths 1
1.87k
| choices
dict | answerKey
listlengths 1
5
| rationale
stringlengths 1
3.56k
| dataset
stringclasses 5
values |
|---|---|---|---|---|
a zeebra chases a tiger 5 hours after the tiger runs . zeebra takes 6 hours to reach the tiger . if the average speed of the zeebra is 55 kmph , what s the average speed of the tiger ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"35 kmph",
"32 kmph",
"30 kmph",
"31 kmph",
"20 kmph"
]
}
|
[
"C"
] |
tiger take 11 hours and zeebra take 6 hours . . . then distance chased by them is 55 * 6 . so speed of tiger is ( 55 * 6 ) / 11 = 30 kmph . answer is c
|
MathQA
|
if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 4 flips but not on the last flip ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"1 / 2",
"1 / 4",
"1 / 8",
"1 / 16",
"1 / 32"
]
}
|
[
"E"
] |
p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e .
|
MathQA
|
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 :
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"2 : 5",
"2 : 3",
"2 : 4",
"1 : 1",
"2 : 9"
]
}
|
[
"D"
] |
"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"
|
MathQA
|
a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"8",
"10",
"12",
"14",
"15"
]
}
|
[
"A"
] |
"explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a"
|
MathQA
|
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
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"40 %",
"50 %",
"65 %",
"71.4 %",
"75 %"
]
}
|
[
"D"
] |
"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"
|
MathQA
|
( 112 x 5 ^ 4 ) = ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"70000",
"80000",
"90000",
"90090",
"100000"
]
}
|
[
"A"
] |
"( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )"
|
MathQA
|
x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 )
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"2",
"3.25",
"4.25",
"5.25",
"6.25"
]
}
|
[
"A"
] |
"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"
|
MathQA
|
what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"344545629",
"723437481",
"354595321",
"964564944",
"458449909"
]
}
|
[
"B"
] |
"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b"
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"1 / 6",
"2 / 9",
"6 / 11",
"9 / 16",
"3 / 4"
]
}
|
[
"C"
] |
"# 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"
|
MathQA
|
if a sum of money doubles itself in 15 years at simple interest , the ratepercent per annum is
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"12",
"12.5",
"6.67",
"13.5",
"14"
]
}
|
[
"C"
] |
"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c"
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"25",
"76",
"29",
"12",
"20"
]
}
|
[
"D"
] |
"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"
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"50 km",
"58 km",
"60 km",
"70 km",
"40 km"
]
}
|
[
"E"
] |
"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"
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"2 / 3",
"5 / 6",
"7 / 12",
"11 / 12",
"17 / 24"
]
}
|
[
"C"
] |
"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ."
|
MathQA
|
find the area of trapezium whose parallel sides are 26 cm and 18 cm long , and the distance between them is 15 cm .
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"227",
"299",
"330",
"161",
"212"
]
}
|
[
"C"
] |
"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 answer : c"
|
MathQA
|
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
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"54 kmph",
"60 kmph",
"66 kmph",
"72 kmph",
"90 kmph"
]
}
|
[
"E"
] |
"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"
|
MathQA
|
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 :
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"520",
"620",
"820",
"740",
"864"
]
}
|
[
"E"
] |
"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"
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22",
"24",
"26",
"28"
]
}
|
[
"C"
] |
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 .
|
MathQA
|
the value of log 2 ( log 5625 ) is
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"2",
"5",
"10",
"15",
"20"
]
}
|
[
"A"
] |
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
|
MathQA
|
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 ?
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"95",
"90",
"85",
"80",
"64"
]
}
|
[
"E"
] |
"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"
|
MathQA
|
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
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"52 kmph",
"56 kmph",
"60 kmph",
"62 kmph",
"72 kmph"
]
}
|
[
"C"
] |
"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"
|
MathQA
|
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 :
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 2",
"3 : 5",
"4 : 5",
"16 : 15"
]
}
|
[
"A"
] |
"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"
|
MathQA
|
average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .
|
{
"label": [
"A",
"A",
"B",
"B",
"C",
"C",
"D",
"D",
"E",
"E"
],
"text": [
"",
"70",
"",
"76",
"",
"78",
"",
"98",
"",
"88"
]
}
|
[
"D"
] |
"explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"
|
MathQA
|
solve below question 2 x + 1 = - 23
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"- 8",
"- 9",
"- 12",
"- 4",
"12"
]
}
|
[
"C"
] |
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
|
MathQA
|
calculate 85184 ÷ ? = 352
|
{
"label": [
"A",
"B",
"C",
"D",
"E"
],
"text": [
"241",
"242",
"244",
"247",
"240"
]
}
|
[
"B"
] |
"answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b"
|
MathQA
|
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