Datasets:

math_qa

like 67

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 ?

"explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 answer : option c"

a ) a ) 600 , b ) b ) 700 , c ) c ) 800 , d ) d ) 900 , e ) e ) 1000

c

divide(1220, multiply(add(const_1, divide(22, const_100)), add(const_1, divide(25, const_100))))

divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#2,#3)|divide(n2,#4)|

gain

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 ?

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

a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 1296

d

subtract(power(add(4, const_2), 4), multiply(divide(factorial(add(4, const_2)), multiply(factorial(const_2), factorial(4))), factorial(4)))

add(n0,const_2)|factorial(const_2)|factorial(n0)|factorial(#0)|multiply(#1,#2)|power(#0,n0)|divide(#3,#4)|multiply(#6,#2)|subtract(#5,#7)

general

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

"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"

a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) none of the above

d

divide(add(add(multiply(85, 6), multiply(60, 4)), 30), add(6, 4))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(n4,#3)|divide(#4,#0)|

general

what is the greatest positive integer x such that 7 ^ x is a factor of 343 ^ 10 ?

"343 ^ 10 = ( 7 ^ 3 ) ^ 10 = 7 ^ 30 answer : e"

a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30

e

multiply(subtract(343, 10), 10)

subtract(n1,n2)|multiply(n2,#0)|

general

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 ) ?

"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 ) 0.1 , b ) 0.3 , c ) 0.5 , d ) 0.7 , e ) 0.9

c

divide(divide(add(0, 2), 2), divide(add(const_4.0, 4), 2))

add(n2,n3)|add(n0,n2)|divide(#0,n3)|divide(#1,n3)|divide(#2,#3)|

general

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 ?

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

a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10

c

inverse(add(divide(const_1, 24), divide(const_1, 12)))

divide(const_1,n1)|divide(const_1,n0)|add(#0,#1)|inverse(#2)

general

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 ?

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

a ) 100 , b ) 200 , c ) 350 , d ) 50 , e ) 250

b

multiply(const_4, negate(subtract(550, add(350, 250))))

add(n1,n2)|subtract(n0,#0)|negate(#1)|multiply(#2,const_4)

general

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 ?

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 ) 55 , b ) 80 , c ) 85 , d ) 90 , e ) 95

a

divide(subtract(divide(const_3600, const_10), multiply(70, const_2)), const_4)

divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)

geometry

a candidate got 35 % of the votes and lost to the rival by 1350 votes . how many votes were cast ?

"35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1350 10 % = 450 100 % of the votes = 4500 answer : b"

a ) 4000 , b ) 4500 , c ) 5000 , d ) 5500 , e ) 6000

b

divide(1350, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100)))

divide(n0,const_100)|subtract(const_1,#0)|subtract(#1,#0)|divide(n1,#2)|

gain

the product of two numbers is 2028 and their h . c . f . is 13 . the number of such pairs is :

"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 ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5

b

sqrt(add(power(sqrt(subtract(13, multiply(const_2, 2028))), const_2), multiply(const_4, 2028)))

multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)|

general

a train 140 m long crosses a platform 160 m long in 16 sec ; find the speed of the train ?

"d = 140 + 160 = 300 t = 16 s = 300 / 16 * 18 / 5 = 67.5 kmph answer : c"

a ) 87 kmph , b ) 65 kmph , c ) 68 kmph , d ) 16 kmph , e ) 18 kmph

c

subtract(multiply(16, multiply(160, const_0_2778)), 140)

multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|

physics

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 ?

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 ) 35 kmph , b ) 32 kmph , c ) 30 kmph , d ) 31 kmph , e ) 20 kmph

c

divide(multiply(55, 6), add(5, 6))

add(n0,n1)|multiply(n1,n2)|divide(#1,#0)

physics

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 ?

p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e .

a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32

e

power(divide(1, 2), 5)

divide(n0,n1)|power(#0,n2)

probability

a fruit seller had some apples . he sells 40 % and still has 420 apples . originally , he had ?

"answer ∵ 60 % of n = 420 ∴ n = ( 420 x 100 ) / 60 = 700 correct option : d"

a ) 588 apples , b ) 600 apples , c ) 672 apples , d ) 700 apples , e ) none

d

original_price_before_loss(40, 420)

original_price_before_loss(n0,n1)|

gain

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 :

"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 ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 1 : 1 , e ) 2 : 9

d

divide(subtract(15.8, 15.4), subtract(16.2, 15.8))

subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1)|

general

a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number

"explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a"

a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15

a

divide(subtract(75, multiply(const_3, 9)), multiply(const_3, const_2))

multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)|

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

"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"

a ) 40 % , b ) 50 % , c ) 65 % , d ) 71.4 % , e ) 75 %

d

multiply(divide(subtract(210, add(multiply(3, 8), multiply(8, 3))), 210), const_100)

multiply(n1,n2)|multiply(n1,n2)|add(#0,#1)|subtract(n0,#2)|divide(#3,n0)|multiply(#4,const_100)|

general

( 112 x 5 ^ 4 ) = ?

"( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )"

a ) 70000 , b ) 80000 , c ) 90000 , d ) 90090 , e ) 100000

a

multiply(112, power(add(const_4, const_1), const_4))

add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)|

general

x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 )

"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"

a ) 2 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25

a

subtract(power(2, 2), 2)

power(n1,n2)|subtract(#0,n2)|

general

what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ?

"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b"

a ) 344545629 , b ) 723437481 , c ) 354595321 , d ) 964564944 , e ) 458449909

b

subtract(427398, multiply(floor(divide(427398, 15)), 15))

divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)|

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 ?

"# 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"

a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4

c

multiply(divide(subtract(12, 3), 12), divide(subtract(subtract(12, 3), const_1), subtract(12, const_1)))

subtract(n0,n1)|subtract(n0,const_1)|divide(#0,n0)|subtract(#0,const_1)|divide(#3,#1)|multiply(#2,#4)|

general

if a sum of money doubles itself in 15 years at simple interest , the ratepercent per annum is

"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c"

a ) 12 , b ) 12.5 , c ) 6.67 , d ) 13.5 , e ) 14

c

divide(divide(const_2, divide(15, const_100)), const_2)

divide(n0,const_100)|divide(const_2,#0)|divide(#1,const_2)|

gain

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 ?

"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"

a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20

d

divide(subtract(subtract(subtract(883, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)|

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 ?

"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"

a ) 50 km , b ) 58 km , c ) 60 km , d ) 70 km , e ) 40 km

e

multiply(8, divide(20, subtract(16, 8)))

subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)|

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 ?

"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ."

a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 12 , d ) 11 / 12 , e ) 17 / 24

c

divide(add(multiply(divide(1, 3), const_12), multiply(divide(const_12, 2), divide(1, 2))), const_12)

divide(n0,n3)|divide(const_12,n1)|divide(n0,n1)|multiply(#0,const_12)|multiply(#1,#2)|add(#3,#4)|divide(#5,const_12)|

general

find the area of trapezium whose parallel sides are 26 cm and 18 cm long , and the distance between them is 15 cm .

"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 answer : c"

a ) 227 , b ) 299 , c ) 330 , d ) 161 , e ) 212

c

quadrilateral_area(15, 18, 26)

quadrilateral_area(n2,n1,n0)|

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

"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"

a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 90 kmph

e

divide(divide(subtract(160, multiply(multiply(6, const_0_2778), 6)), 6), const_0_2778)

multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)|

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 :

"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"

a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 864

e

divide(divide(multiply(240, 6), add(const_1, divide(const_2, const_3))), const_2)

divide(const_2,const_3)|multiply(n0,n1)|add(#0,const_1)|divide(#1,#2)|divide(#3,const_2)|

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 ?

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 .

a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them

c

multiply(13, multiply(divide(multiply(3, 24), multiply(9, 8)), const_2))

multiply(n1,n5)|multiply(n0,n2)|divide(#0,#1)|multiply(#2,const_2)|multiply(n4,#3)

physics

the value of log 2 ( log 5625 ) is

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 ) 2 , b ) 5 , c ) 10 , d ) 15 , e ) 20

a

log(divide(log(subtract(5625, multiply(add(const_4, const_1), const_1000))), log(add(const_4, const_1))))

add(const_1,const_4)|log(#0)|multiply(#0,const_1000)|subtract(n1,#2)|log(#3)|divide(#4,#1)|log(#5)

other

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 ?

"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"

a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 64

e

divide(16, divide(subtract(100, 75), 100))

subtract(n1,n2)|divide(#0,n1)|divide(n0,#1)|

general

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

"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 ) 52 kmph , b ) 56 kmph , c ) 60 kmph , d ) 62 kmph , e ) 72 kmph

c

subtract(multiply(divide(320, 10), const_3_6), 55)

divide(n2,n1)|multiply(#0,const_3_6)|subtract(#1,n0)|

physics

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 :

"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"

a ) 1 : 2 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none

a

divide(multiply(90, const_2), multiply(90, const_3))

multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)|

other

average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .

"explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"

a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 98 , e ) e ) 88

d

subtract(multiply(add(32, 6), add(10, const_1)), multiply(10, 32))

add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|

general

solve below question 2 x + 1 = - 23

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

a ) - 8 , b ) - 9 , c ) - 12 , d ) - 4 , e ) 12

c

divide(negate(add(23, 1)), 2)

add(n1,n2)|negate(#0)|divide(#1,n0)

general

calculate 85184 ÷ ? = 352

"answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b"

a ) 241 , b ) 242 , c ) 244 , d ) 247 , e ) 240

b

multiply(85184, 352)

multiply(n0,n1)|

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 ?

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

a ) four , b ) six , c ) nine , d ) ten , e ) twelve

e

add(8.1, subtract(8.1, multiply(1.5, 0.4)))

multiply(n17,n19)|subtract(n16,#0)|add(n16,#1)

general