question stringlengths 5 806 | choices listlengths 3 5 | answer_index int64 0 4 | answer_text stringlengths 4 156 | source stringclasses 3
values | explanation stringlengths 0 2.74k |
|---|---|---|---|---|---|
two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ? | [
"A. 122",
"B. 121",
"C. 120",
"D. 102"
] | 2 | C. 120 | allenai_math_qa | "( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c" |
find k if 56 / k = 4 . | [
"A. 16",
"B. 17",
"C. 18",
"D. 14"
] | 3 | D. 14 | allenai_math_qa | "since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d" |
a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ? | [
"A. 30 .",
"B. 32 .",
"C. 36 .",
"D. 42 ."
] | 0 | A. 30 . | allenai_math_qa | "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a" |
a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ? | [
"A. 144",
"B. 108",
"C. 278",
"D. 126"
] | 0 | A. 144 | allenai_math_qa | "s = 400 / 10 * 18 / 5 = 144 kmph answer : a" |
a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | [
"A. rs . 2000",
"B. rs . 10",
"C. rs . 15",
"D. rs . 20"
] | 3 | D. rs . 20 | allenai_math_qa | "solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d" |
what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 ) | [
"A. 88888883",
"B. 88888884",
"C. 88888885",
"D. 88888886"
] | 0 | A. 88888883 | allenai_math_qa | "let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a" |
if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ? | [
"A. - 5",
"B. - 3",
"C. 0",
"D. 3"
] | 2 | C. 0 | allenai_math_qa | ( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c . |
the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ? | [
"A. 10 %",
"B. 20 %",
"C. 40 %",
"D. 50 %"
] | 2 | C. 40 % | allenai_math_qa | "explanation : change in the price = rs 420 â € “ rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c" |
39 ! is divided by 41 then what is the remainder ? | [
"A. 1",
"B. 2",
"C. 4",
"D. 6"
] | 0 | A. 1 | allenai_math_qa | "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a" |
if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ? | [
"A. 401",
"B. 411",
"C. 421",
"D. 431"
] | 3 | D. 431 | allenai_math_qa | "x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ." |
the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation : | [
"A. 101",
"B. 107",
"C. 111",
"D. 117"
] | 2 | C. 111 | allenai_math_qa | let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c |
if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ? | [
"A. 6",
"B. 7",
"C. 8",
"D. 9"
] | 3 | D. 9 | allenai_math_qa | "42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d" |
if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? | [
"A. 6",
"B. 16",
"C. 20",
"D. 30"
] | 2 | C. 20 | allenai_math_qa | the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c . |
how many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | [
"A. 287",
"B. 288",
"C. 600",
"D. 277"
] | 2 | C. 600 | allenai_math_qa | "let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c" |
a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ? | [
"A. $ 17",
"B. $ 17",
"C. $ 17",
"D. $ 18"
] | 2 | C. $ 17 | allenai_math_qa | "average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ." |
how many odd numbers between 10 and 1400 are the squares of integers ? | [
"A. 14",
"B. 17",
"C. 20",
"D. 23"
] | 1 | B. 17 | allenai_math_qa | "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ." |
n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 * n is divided by 4 ? | [
"A. 8",
"B. 2",
"C. 6",
"D. 7"
] | 1 | B. 2 | allenai_math_qa | explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2 |
a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ? | [
"A. $ 200",
"B. $ 900",
"C. $ 700",
"D. $ 600"
] | 1 | B. $ 900 | allenai_math_qa | "b ' s share = 2700 * 3 / 9 = $ 900 answer is b" |
the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is : | [
"A. 276",
"B. 414",
"C. 322",
"D. 345"
] | 1 | B. 414 | allenai_math_qa | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b" |
if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) = | [
"A. 2925",
"B. 3456",
"C. 4581",
"D. 3683"
] | 1 | B. 3456 | allenai_math_qa | 6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b |
a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ? | [
"A. 1 / 9",
"B. 1 / 6",
"C. 1 / 2",
"D. 1 / 1"
] | 1 | B. 1 / 6 | allenai_math_qa | given that b alone can complete the same work in days = half the time taken by a = 9 days a ’ s one day work = 1 / 18 b ’ s one day work = 1 / 9 ( a + b ) ’ s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b . |
an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ? | [
"A. 160",
"B. 98",
"C. 100",
"D. 80"
] | 1 | B. 98 | allenai_math_qa | "say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a =... |
the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r... | [
"A. 16",
"B. r = 32",
"C. r = 64",
"D. 128"
] | 1 | B. r = 32 | allenai_math_qa | "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )" |
a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . | [
"A. 8",
"B. 8.5",
"C. 11",
"D. 9.5"
] | 2 | C. 11 | allenai_math_qa | a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve... |
how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ? | [
"A. 6",
"B. 7",
"C. 21",
"D. 9"
] | 2 | C. 21 | allenai_math_qa | "c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21" |
ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | [
"A. 34778",
"B. 26888",
"C. 20350",
"D. 17600"
] | 2 | C. 20350 | allenai_math_qa | "price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no di... |
if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ? | [
"A. 20",
"B. 50",
"C. 108",
"D. 200"
] | 2 | C. 108 | allenai_math_qa | the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c . |
let f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c = | [
"A. 18",
"B. 15",
"C. - 15",
"D. - 11"
] | 3 | D. - 11 | allenai_math_qa | "f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c = f ( 6 ) = 0 = 36 + 6 b + c - - - taking 36 to the other side - > 6 b + c = - 36 f ( - 1 ) = 0 = 1 - b + c - - - taking - b + c to the other side - > b - c = 1 when we add these 2 equations , we get 7 b = - 35 - - - > b = - 5 and while substitut... |
approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 ⁄ 2 mile ? | [
"A. 120",
"B. 180",
"C. 772",
"D. 720"
] | 2 | C. 772 | allenai_math_qa | "diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire... |
if the radius of a circle is increased by 60 % then the area is increased by : | [
"A. 44 %",
"B. 120 %",
"C. 156 %",
"D. 40 %"
] | 2 | C. 156 % | allenai_math_qa | "initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c" |
a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors... | [
"A. 4",
"B. 5",
"C. 6",
"D. 12"
] | 1 | B. 5 | allenai_math_qa | "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b" |
an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 27 metre of cloth ? | [
"A. 211 seconds",
"B. 195 seconds",
"C. 155 seconds",
"D. 115 seconds"
] | 0 | A. 211 seconds | allenai_math_qa | "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a" |
a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight . | [
"A. 19.81 %",
"B. 22.38 %",
"C. 37.5 %",
"D. 25 %"
] | 1 | B. 22.38 % | allenai_math_qa | "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while ... |
the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ? | [
"A. 21.23",
"B. 52.85",
"C. 23.26",
"D. 41.67"
] | 3 | D. 41.67 | allenai_math_qa | "distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d" |
1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 … … … … … … … … + 2012 * 2 ^ 2012 | [
"A. 8100312",
"B. 8100313",
"C. 8100412",
"D. 8200312"
] | 0 | A. 8100312 | allenai_math_qa | take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a |
stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock ... | [
"A. 4",
"B. 6",
"C. 9",
"D. 14"
] | 3 | D. 14 | allenai_math_qa | based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewra... |
if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ? | [
"A. 25 % loss",
"B. 20 % loss",
"C. 25 % profit",
"D. 20 % profit"
] | 1 | B. 20 % loss | allenai_math_qa | "let the cost price of 1 article be rs . 1 . therefore , cost price of 20 articles = 20 * 1 = rs . 20 the selling price of 25 articles = cost price of 20 articles = rs . 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = rs . 25 . therefore , profit made on sale of 25 articles = selli... |
the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is | [
"A. 35.2",
"B. 32.5",
"C. 36.5",
"D. 39.1"
] | 1 | B. 32.5 | allenai_math_qa | "sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b" |
0.009 / x = 0.05 . find the value of x | [
"A. 0.00018",
"B. 0.09",
"C. 0.018",
"D. 0.18"
] | 3 | D. 0.18 | allenai_math_qa | "x = 0.009 / 0.18 = 0.05 answer : d" |
a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ? | [
"A. 50 hours",
"B. 62 hours",
"C. 90 hours",
"D. 75 hours"
] | 2 | C. 90 hours | allenai_math_qa | "let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c" |
the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | [
"A. 35",
"B. 30",
"C. 25",
"D. data inadequate"
] | 0 | A. 35 | allenai_math_qa | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a" |
mrs . evans gave a test to her freshmen economics class , which has 50 students enrolled and 25 of them answered question 1 correctly . if 20 answered question 2 correctly and 20 did not take the test then how many answered both questions correctly ? | [
"A. 23",
"B. 22",
"C. 21",
"D. 20"
] | 3 | D. 20 | allenai_math_qa | "total number of enrolled students = 50 number of students who did not take test = 20 hence , number of students who took test = 50 - 20 = 30 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also ans... |
carl can wash all the windows of his house in 8 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ? | [
"A. 2",
"B. 2 1 / 4",
"C. 3 2 / 2",
"D. 4 1 / 2"
] | 2 | C. 3 2 / 2 | allenai_math_qa | "work hrs = ab / ( a + b ) = 32 / 12 = 3 2 / 2 answer is c" |
in a certain parking lot , 3 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what % of cars in the parking lot are parked illegally . ' | [
"A. 11",
"B. 13",
"C. 15",
"D. 60"
] | 2 | C. 15 | allenai_math_qa | "so total no . of cars parked illegally : 300 total no . of cars : 2000 300 / 2000 * 100 , so 15 % answer : c" |
if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ? | [
"A. 20 %",
"B. 25 %",
"C. 18 %",
"D. 30 %"
] | 0 | A. 20 % | allenai_math_qa | "here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a" |
starting from his house one day , a student walk at a speed of 2 kmph and reaches his school 10 minutes late . next he increased his speed by 1 kmph and reaches the school 10 minutes early . how far is the school from his house ? | [
"A. 1 km",
"B. 2 km",
"C. 3 km",
"D. 4 km"
] | 1 | B. 2 km | allenai_math_qa | let the distance be x km difference in timings = 20 min = 20 / 60 = 1 / 3 hr x / 2 - x / 3 = 1 / 3 x = 2 km answer is b |
if 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? | [
"A. 176",
"B. 253",
"C. 342",
"D. 458"
] | 1 | B. 253 | allenai_math_qa | "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . s... |
what is the compound interest on rs . 6500 at 5.5 % p . a . compounded half - yearly for 1 year . | [
"A. 369.42",
"B. 762.42",
"C. 162.42",
"D. 362.42"
] | 3 | D. 362.42 | allenai_math_qa | "compound interest : a = p ( 1 + r / n ) nt a = 6 , 862.42 c . i . > > 6 , 862.42 - 6500 > > rs . 362.42 answer : d" |
the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 6 units ? | [
"A. 140",
"B. 84",
"C. 88",
"D. 72"
] | 1 | B. 84 | allenai_math_qa | "given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 6 units area of the rectangle = lb = 14 * 6 = 84 sq . units answer : b" |
the sum of the non - prime numbers between 20 and 30 , non - inclusive , is | [
"A. 173",
"B. 185",
"C. 197",
"D. 209"
] | 0 | A. 173 | allenai_math_qa | "sum of consecutive integers from 21 to 29 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 21 + 29 ) / 2 * 9 = 25 * 9 = 225 sum of non - prime numbers b / w 20 and 30 , non inclusive = = = > 225 - 52 ( i . e . , 23 + 29 , being the prime # s in the range ) = 173 answer : a" |
there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 22 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ? | [
"A. 20",
"B. 31",
"C. 41",
"D. 53"
] | 2 | C. 41 | allenai_math_qa | "x + ( x - 22 ) = 60 - - > x = 41 . answer : c ." |
a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ? | [
"A. 51",
"B. 53",
"C. 55",
"D. 56"
] | 0 | A. 51 | allenai_math_qa | total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 365 â ‰ ˆ 51 answer : a |
how much water should be added to 15 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ? | [
"A. 25 liters",
"B. 27 liters",
"C. 30 liters",
"D. 32 liters"
] | 0 | A. 25 liters | allenai_math_qa | "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 15 + x ) ) ) 2 = 5 % * ( 15 + x ) - - - - - - - - > x = 25 ans a" |
in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 27 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? | [
"A. 12",
"B. 18",
"C. 24",
"D. 30"
] | 2 | C. 24 | allenai_math_qa | "200 are sophomores . the number of freshmen is 600 - 160 - 0.27 ( 800 ) = 224 the answer is c ." |
tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and th... | [
"A. 1 / 3",
"B. 1 / 2",
"C. 1 / 4",
"D. 1 / 5"
] | 1 | B. 1 / 2 | allenai_math_qa | "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( ... |
a train 440 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | [
"A. 80",
"B. 26",
"C. 24",
"D. 54"
] | 2 | C. 24 | allenai_math_qa | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 440 * 3 / 55 = 24 sec . answer : c" |
a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ? | [
"A. 09 2 / 3",
"B. 10 2 / 3",
"C. 11 2 / 3",
"D. 12 2 / 3"
] | 1 | B. 10 2 / 3 | allenai_math_qa | "b 10 2 / 3 2 / 10 + 4 / 15 + x / 20 = 1 x = 32 / 3 = 10 2 / 3" |
find two integers , neither of which ends in a zero , and whose product is exactly 1 , 00,000 | [
"A. 64 and 15",
"B. 32 and 3",
"C. 64 and 15",
"D. 64 and 15"
] | 1 | B. 32 and 3 | allenai_math_qa | 1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b |
a man starts walking at 3 pm . ha walks at a speed of 4 km / hr on level ground and at a speed of 3 km / hr on uphill , 6 km / hr downhill and then 4 km / hr on level ground to reach home at 9 pm . what is the distance covered on one way | [
"A. 10 km",
"B. 12 km",
"C. 14 km",
"D. 16 km"
] | 1 | B. 12 km | allenai_math_qa | avg speed = 2 * 3 * 6 / ( 3 + 6 ) = 4 so speed of man = 4 km / hr distance = 4 * 6 = 24 km since we want one way distance it will be 24 / 2 = 12 km answer : b |
a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ? | [
"A. 271",
"B. 266",
"C. 225",
"D. 277"
] | 2 | C. 225 | allenai_math_qa | "length of the platform = 36 * 5 / 18 * 40 = 400 – 175 = 225 answer : c" |
the population of a town increases 22 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1220 . then what is the population of the town 2 years ago ? | [
"A. a ) 600",
"B. b ) 700",
"C. c ) 800",
"D. d ) 900"
] | 2 | C. c ) 800 | allenai_math_qa | "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 answer : option c" |
in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ? | [
"A. 720",
"B. 864",
"C. 900",
"D. 936"
] | 3 | D. 936 | allenai_math_qa | total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d |
the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is | [
"A. 70",
"B. 72",
"C. 75",
"D. 78"
] | 3 | D. 78 | allenai_math_qa | "income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d" |
in the xy - coordinate system , what is the slope of the line that goes through the point ( 4 , 4 ) and is equidistant from the two points p = ( 0 , 2 ) and q = ( 12 , 8 ) ? | [
"A. 0.1",
"B. 0.3",
"C. 0.5",
"D. 0.7"
] | 2 | C. 0.5 | allenai_math_qa | "first , get the middle coordinate between ( 0,2 ) and ( 12,8 ) . . . x = 0 + ( 12 - 0 ) / 2 = 6 y = 2 + ( 8 - 2 ) / 2 = 5 second , get the slope of ( 6,5 ) and ( 4,4 ) . m = 5 - 4 / 6 - 4 = 1 / 2 = 0.5 answer : c" |
a sum of money is sufficient to pay b ' s wages for 12 days and c ' s wages for 24 days . the same money is sufficient to pay the wages of both for ? | [
"A. 6",
"B. 7",
"C. 8",
"D. 9"
] | 2 | C. 8 | allenai_math_qa | let the total money be $ x b ' s 1 day work = $ x / 12 c ' s 1 day work = $ x / 24 a + b 1 day work = $ x / 8 money is sufficient to pay the wages of both for 8 days answer is c |
jonathan , matthew and zac are picking strawberries from their yard . together they have picked a total of 550 strawberries . jonathan and matthew have picked 350 strawberries together . matthew and zac have picked 250 strawberries together . how many strawberries has zac picked by himself ? | [
"A. 100",
"B. 200",
"C. 350",
"D. 50"
] | 1 | B. 200 | allenai_math_qa | jonathan = matthew + zac = 550 strawberries j + m = 350 m + z = 250 use j + m = 350 to plug into the original formula ( j + m ) + z = 550 350 + z = 550 subtract 350 from each side z = 200 answer : b |
in a certain parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle ? | [
"A. 55",
"B. 80",
"C. 85",
"D. 90"
] | 0 | A. 55 | allenai_math_qa | in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 70 ) = 180 - - > x = 55 . answer : a . |
a candidate got 35 % of the votes and lost to the rival by 1350 votes . how many votes were cast ? | [
"A. 4000",
"B. 4500",
"C. 5000",
"D. 5500"
] | 1 | B. 4500 | allenai_math_qa | "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1350 10 % = 450 100 % of the votes = 4500 answer : b" |
the product of two numbers is 2028 and their h . c . f . is 13 . the number of such pairs is : | [
"A. 1",
"B. 2",
"C. 3",
"D. 4"
] | 1 | B. 2 | allenai_math_qa | "explanation : let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer is b" |
a train 140 m long crosses a platform 160 m long in 16 sec ; find the speed of the train ? | [
"A. 87 kmph",
"B. 65 kmph",
"C. 68 kmph",
"D. 16 kmph"
] | 2 | C. 68 kmph | allenai_math_qa | "d = 140 + 160 = 300 t = 16 s = 300 / 16 * 18 / 5 = 67.5 kmph answer : c" |
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 ? | [
"A. 35 kmph",
"B. 32 kmph",
"C. 30 kmph",
"D. 31 kmph"
] | 2 | C. 30 kmph | allenai_math_qa | 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 |
a fruit seller had some apples . he sells 40 % and still has 420 apples . originally , he had ? | [
"A. 588 apples",
"B. 600 apples",
"C. 672 apples",
"D. 700 apples"
] | 3 | D. 700 apples | allenai_math_qa | "answer ∵ 60 % of n = 420 ∴ n = ( 420 x 100 ) / 60 = 700 correct option : d" |
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 : | [
"A. 2 : 5",
"B. 2 : 3",
"C. 2 : 4",
"D. 1 : 1"
] | 3 | D. 1 : 1 | allenai_math_qa | "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" |
a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number | [
"A. 8",
"B. 10",
"C. 12",
"D. 14"
] | 0 | A. 8 | allenai_math_qa | "explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a" |
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 | [
"A. 40 %",
"B. 50 %",
"C. 65 %",
"D. 71.4 %"
] | 3 | D. 71.4 % | allenai_math_qa | "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" |
( 112 x 5 ^ 4 ) = ? | [
"A. 70000",
"B. 80000",
"C. 90000",
"D. 90090"
] | 0 | A. 70000 | allenai_math_qa | "( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )" |
x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 ) | [
"A. 2",
"B. 3.25",
"C. 4.25",
"D. 5.25"
] | 0 | A. 2 | allenai_math_qa | "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" |
what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ? | [
"A. 344545629",
"B. 723437481",
"C. 354595321",
"D. 964564944"
] | 1 | B. 723437481 | allenai_math_qa | "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b" |
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 ? | [
"A. 1 / 6",
"B. 2 / 9",
"C. 6 / 11",
"D. 9 / 16"
] | 2 | C. 6 / 11 | allenai_math_qa | "# 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" |
if a sum of money doubles itself in 15 years at simple interest , the ratepercent per annum is | [
"A. 12",
"B. 12.5",
"C. 6.67",
"D. 13.5"
] | 2 | C. 6.67 | allenai_math_qa | "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c" |
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 ? | [
"A. 25",
"B. 76",
"C. 29",
"D. 12"
] | 3 | D. 12 | allenai_math_qa | "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" |
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 ? | [
"A. 2 / 3",
"B. 5 / 6",
"C. 7 / 12",
"D. 11 / 12"
] | 2 | C. 7 / 12 | allenai_math_qa | "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ." |
find the area of trapezium whose parallel sides are 26 cm and 18 cm long , and the distance between them is 15 cm . | [
"A. 227",
"B. 299",
"C. 330",
"D. 161"
] | 2 | C. 330 | allenai_math_qa | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 answer : c" |
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 ? | [
"A. 22",
"B. 24",
"C. 26",
"D. 28"
] | 2 | C. 26 | allenai_math_qa | 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 ... |
the value of log 2 ( log 5625 ) is | [
"A. 2",
"B. 5",
"C. 10",
"D. 15"
] | 0 | A. 2 | allenai_math_qa | 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 |
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 | [
"A. 52 kmph",
"B. 56 kmph",
"C. 60 kmph",
"D. 62 kmph"
] | 2 | C. 60 kmph | allenai_math_qa | "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" |
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 : | [
"A. 1 : 2",
"B. 3 : 5",
"C. 4 : 5",
"D. 16 : 15"
] | 0 | A. 1 : 2 | allenai_math_qa | "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" |
average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs . | [
"A. a ) 70",
"B. b ) 76",
"C. c ) 78",
"D. d ) 98"
] | 3 | D. d ) 98 | allenai_math_qa | "explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d" |
solve below question 2 x + 1 = - 23 | [
"A. - 8",
"B. - 9",
"C. - 12",
"D. - 4"
] | 2 | C. - 12 | allenai_math_qa | 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 |
calculate 85184 ÷ ? = 352 | [
"A. 241",
"B. 242",
"C. 244",
"D. 247"
] | 1 | B. 242 | allenai_math_qa | "answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b" |
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