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load_in_math_allenai_math

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there is enough provisions for 600 men in an army camp for 25 days . if there were 100 men less , how long will the provision last ?
"exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 100 * d 2 d 2 = 600 * 25 / 100 = 150 days . answer : d"
a ) 10 days , b ) 50 days , c ) 100 days , d ) 150 days , e ) 200 days
d
divide(multiply(600, 25), 100)
multiply(n0,n1)|divide(#0,n2)|
physics
allenai/math_qa
when the number 1 y 92355 is exactly divisible by 11 , then the smallest whole number in place of y is ?
the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 οΏ½ y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e
a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) 0
e
subtract(1, const_1)
subtract(n0,const_1)
general
allenai/math_qa
claire has a total of 92 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
"g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 ( 92 - h ) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b"
a ) 39 , b ) 68 , c ) 54 , d ) 57 , e ) 60
b
add(subtract(92, 25), const_1)
subtract(n0,n1)|add(#0,const_1)|
general
allenai/math_qa
fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
"x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."
a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 %
e
multiply(subtract(divide(22, const_100), divide(subtract(9, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(10, 3), multiply(18, 2)))), const_100)
divide(n6,const_100)|multiply(n1,n5)|multiply(n0,n4)|multiply(#0,#1)|subtract(#2,#1)|subtract(n2,#3)|divide(#5,#4)|subtract(#0,#6)|multiply(#7,const_100)|
gain
allenai/math_qa
a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.2 cm when a man gets on it . the mass of man is
"solution volume of water displaced = ( 3 x 2 x 0.012 ) m 3 = 0.072 m 3 . mass of man = volume of water displaced Γ— density of water = ( 0.072 Γ— 1000 ) kg = 72 kg . answer a"
a ) 72 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
a
multiply(multiply(multiply(3, 2), divide(1.2, const_100)), const_1000)
divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)|
physics
allenai/math_qa
a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 3 th of the other , how many centimeters will the shorter piece be ?
"1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c"
a ) 35 , b ) 20 , c ) 28 , d ) 36 , e ) 30
c
subtract(70, divide(70, add(divide(2, 3), const_1)))
divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)|
physics
allenai/math_qa
when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 134.08 , what is value of j ?
"when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 10 so , 134.08 = 134 + 10 / j so , j = 125 ans a"
a ) 125 , b ) 56 , c ) 78 , d ) 112 , e ) 175
a
divide(10, subtract(134.08, add(const_100, add(multiply(const_4, const_10), const_2))))
multiply(const_10,const_4)|add(#0,const_2)|add(#1,const_100)|subtract(n1,#2)|divide(n0,#3)|
general
allenai/math_qa
a hall 36 m long and 15 m broad is to be paved with stones , each measuring 8 dm by 5 dm . the number of stones required is :
"area of the hall = 3600 * 1500 area of each stone = ( 80 * 50 ) therefore , number of stones = ( 3600 * 1500 / 80 * 50 ) = 1350 answer : e"
a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1350
e
divide(multiply(36, 15), divide(multiply(8, 5), const_100))
multiply(n0,n1)|multiply(n2,n3)|divide(#1,const_100)|divide(#0,#2)|
physics
allenai/math_qa
what is the smallest positive integer x such that 80 - x is the cube of a positive integer
"given 80 - x is a perfect cube so we will take 64 = 4 * 4 * 4 80 - x = 64 x = 80 - 64 = 16 correct option is a"
a ) 16 , b ) 12 , c ) 47 , d ) 9 , e ) 12
a
add(const_3, const_4)
add(const_3,const_4)|
general
allenai/math_qa
how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
"selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - salt avg ) / ( salt avg - salt 1 ) = ( 50 - 40 ) / ( 40 - 35 ) = 2 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 20 lbs . answer ( a )"
a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 25
a
divide(subtract(multiply(48, 40), multiply(divide(add(const_100, 20), const_100), multiply(35, 40))), subtract(multiply(50, divide(add(const_100, 20), const_100)), 48))
add(n3,const_100)|multiply(n1,n4)|multiply(n1,n2)|divide(#0,const_100)|multiply(#3,#2)|multiply(n0,#3)|subtract(#1,#4)|subtract(#5,n4)|divide(#6,#7)|
gain
allenai/math_qa
if a sum of money doubles itself in 8 years at simple interest , the ratepercent per annum is
explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 8 ) = 12.5 option b
a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
b
divide(divide(const_2, divide(8, const_100)), const_2)
divide(n0,const_100)|divide(const_2,#0)|divide(#1,const_2)
gain
allenai/math_qa
if difference between compound interest and simple interest on a sum at 5 % p . a . for 2 years is rs . 60 , then what is the sum ?
"c . i - s . i = 60 si = ( x * 2 * 5 ) / 100 = x / 10 ci = { x * ( 1 + 5 / 100 ) ^ 2 - x } = 41 x / 400 ci - si = 41 x / 400 - x / 10 = 60 x = 24000 answer : e"
a ) rs . 8000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 24000
e
divide(60, multiply(divide(5, const_100), divide(5, const_100)))
divide(n0,const_100)|multiply(#0,#0)|divide(n2,#1)|
gain
allenai/math_qa
without stoppages , a train travels certain distance with an average speed of 250 km / h , and with stoppages , it covers the same distance with an average speed of 125 km / h . how many minutes per hour the train stops ?
"due to stoppages , it covers 125 km less . time taken to cover 125 km = 125 Γ’  β€ž 250 h = 1 Γ’  β€ž 2 h = 1 Γ’  β€ž 2 Γ£ β€” 60 min = 30 min answer b"
a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
b
subtract(const_60, multiply(divide(125, 250), const_60))
divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)|
physics
allenai/math_qa
each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 5 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
"number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 4 and 5 are adjacent - consider 4 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 4 and 5 can be arranged as 45 or 54 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) 72
e
subtract(multiply(multiply(multiply(5, 4), 5), const_2), multiply(multiply(multiply(4, 5), const_2), const_2))
multiply(n1,n4)|multiply(n3,n4)|multiply(n3,#0)|multiply(#1,const_2)|multiply(#2,const_2)|multiply(#3,const_2)|subtract(#4,#5)|
general
allenai/math_qa
each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
"if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 6 . we need to remove 10 of the 20 - pound boxes . the answer is b ."
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
b
divide(subtract(add(multiply(10, divide(subtract(multiply(20, 20), multiply(20, 18)), subtract(20, 10))), multiply(20, subtract(20, divide(subtract(multiply(20, 20), multiply(20, 18)), subtract(20, 10))))), multiply(20, 16)), subtract(20, 16))
multiply(n0,n2)|multiply(n0,n3)|multiply(n0,n4)|subtract(n2,n1)|subtract(n2,n4)|subtract(#0,#1)|divide(#5,#3)|multiply(n1,#6)|subtract(n0,#6)|multiply(n2,#8)|add(#7,#9)|subtract(#10,#2)|divide(#11,#4)|
general
allenai/math_qa
speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
"sol . speed upstream = 3 kmph ; speed downstream = 9 kmph . ∴ total time taken = [ 210 / 3 + 210 / 9 ] hours = 84 hours . answer c"
a ) 92 hours , b ) 24 hours , c ) 84 hours , d ) 48 hours , e ) none
c
add(divide(210, add(9, 6)), divide(210, subtract(9, 6)))
add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)|
physics
allenai/math_qa
how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length ?
"d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c"
a ) 16.5 , b ) 16.0 , c ) 15 , d ) 16.8 , e ) 16.1
c
divide(add(110, 140), multiply(60, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
physics
allenai/math_qa
tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 39 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 06 , at what time will they be reading the same page ?
"since tom reads an average of 1 page every 2 minutes , tom will read 18 pages in the first 36 minutes . jan can catch tom at a rate of 9 pages per hour , so it will take 2 hours to catch tom . the answer is c ."
a ) 6 : 06 , b ) 6 : 36 , c ) 7 : 06 , d ) 7 : 36 , e ) 8 : 06
c
divide(add(5, divide(multiply(add(subtract(5, 4), divide(subtract(06, 30), const_60)), 30), subtract(39, 30))), 06)
subtract(n5,n3)|subtract(n4,n2)|subtract(n1,n0)|divide(#0,const_60)|add(#3,#1)|multiply(n0,#4)|divide(#5,#2)|add(n4,#6)|divide(#7,n5)|
general
allenai/math_qa
tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ?
there are 6 ways to roll a seven : 1 and 6 , 6 and 1 , 2 and 5 , 5 and 2 , 3 and 4 , 4 and 3 . there are 6 * 6 = 36 ways to roll two six - sided dice . thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6 / 36 = 1 / 6 c
a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
c
divide(6, multiply(6, 6))
multiply(n0,n0)|divide(n0,#0)
probability
allenai/math_qa
3 numbers are randomly selected , with replacement , from the set of integers { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . if the first number selected is w , the second number selected is x , and the third number is y , what is the probability that w < x < y ?
solution : total possible ways = 10 * 10 * 10 = 1000 case 1 : w = 0 . if x = 1 , then y can have 8 ways . if x = 2 , then y can have 7 ways and so on . so , no . of ways = 8 + 7 + . . + 1 case 2 : w = 1 . if x = 2 , then y can have 7 ways . if x = 3 , then y can have 6 ways and so on . so , no . of ways = 7 + 6 + . . + 1 there will be 8 cases in this way and they will follow a pattern which looks like this : no . of ways for case 1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 no . of ways for case 2 : 1 + 2 + 3 + 4 + 5 + 6 + 7 no . of ways for case 3 : 1 + 2 + 3 + 4 + 5 + 6 no . of ways for case 4 : 1 + 2 + 3 + 4 + 5 no . of ways for case 5 : 1 + 2 + 3 + 4 no . of ways for case 6 : 1 + 2 + 3 no . of ways for case 7 : 1 + 2 no . of ways for case 8 : 1 ____________________________________________________________ total number of ways : 8 ( 1 ) + 7 ( 2 ) + 6 ( 3 ) + 5 ( 4 ) + 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) = 2 ( 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) ) = 2 ( 60 ) = 120 therefore , ans is 120 / 1000 = 3 / 25 . option c .
a ) 3 / 40 , b ) 28 / 243 , c ) 3 / 25 , d ) 33 / 100 , e ) 64 / 125
c
divide(1, 8)
divide(n2,n9)
physics
allenai/math_qa
a cricketer scored 132 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
"explanation : number of runs made by running = 132 - ( 12 x 4 + 2 x 6 ) = 132 - ( 60 ) = 72 now , we need to calculate 72 is what percent of 132 . = > 72 / 132 * 100 = 54.54 % answer : b"
a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
b
multiply(divide(subtract(132, add(multiply(12, const_4), multiply(2, multiply(2, const_3)))), 132), const_100)
multiply(n1,const_4)|multiply(n2,const_3)|multiply(n2,#1)|add(#0,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)|
general
allenai/math_qa
how many even number in the range between 6 to 100 inclusive are not divisible by 3
"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 6 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 48 . for 6 , 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 16 . hence , only divisible by 2 but not 3 = 48 - 16 = 32 . hence , answer c"
a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
c
subtract(divide(subtract(subtract(100, 6), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(100, const_2), multiply(3, const_4)), 3), 3), 3), const_2))
multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)|
general
allenai/math_qa
12,21 , 48,87 , __
"21 = 12 * 2 - 3 48 = 21 * 2 + 6 87 = 48 * 2 - 9 so next number is 87 * 2 + 12 = 186 answer : b"
a ) 176 , b ) 186 , c ) 184 , d ) 174 , e ) 164
b
multiply(divide(12,21, 48,87), const_100)
divide(n0,n1)|multiply(#0,const_100)|
general
allenai/math_qa
in plutarch enterprises , 60 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
"for sake of ease , let ' s say there are 10 employees : 6 marketers , 2 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 160,000 = $ 340,000 . the correct answer is e ."
a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 340,000
e
divide(subtract(subtract(multiply(multiply(add(60, 20), const_1000), const_100), multiply(20, multiply(add(60, 20), const_1000))), multiply(multiply(multiply(divide(20, const_2), 20), const_1000), 60)), 20)
add(n0,n1)|divide(n1,const_2)|multiply(#0,const_1000)|multiply(#1,n1)|multiply(#2,const_100)|multiply(#2,n1)|multiply(#3,const_1000)|multiply(n0,#6)|subtract(#4,#5)|subtract(#8,#7)|divide(#9,n1)|
general
allenai/math_qa
with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity e of the pool ?
d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters .
a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
d
multiply(50, multiply(const_60, multiply(divide(48, const_60), add(const_4, const_1))))
add(const_1,const_4)|divide(n0,const_60)|multiply(#0,#1)|multiply(#2,const_60)|multiply(n2,#3)
physics
allenai/math_qa
of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 16 boys and 44 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 16 boys . so 16 - 6 - 6 = 4 boys must be neither happy nor sad . answer ( b )
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
b
subtract(subtract(16, subtract(10, 4)), 6)
subtract(n2,n7)|subtract(n4,#0)|subtract(#1,n6)
other
allenai/math_qa
a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
"number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e"
a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters
e
divide(subtract(multiply(divide(25, const_100), 200), multiply(divide(20, const_100), 200)), subtract(const_1, divide(25, const_100)))
divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(const_1,#0)|subtract(#2,#3)|divide(#5,#4)|
general
allenai/math_qa
in a family 11 people eat only vegetarian , 6 people eat only non veg . , 9 people eat both veg and non veg . . how many people eat veg in the family ?
"total people eat veg = only veg + both veg and non veg total = 11 + 9 = 20 answer = a"
a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21
a
add(11, 9)
add(n0,n2)|
other
allenai/math_qa
two trains 110 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 110 + 160 = 270 m . required time = 270 * 9 / 250 = 243 / 25 = 9.72 sec . ' answer : e"
a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.8 , e ) 9.72
e
divide(add(110, 160), multiply(add(60, 40), const_0_2778))
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
physics
allenai/math_qa
you enter a weight loss challenge game and manage to lose 10 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
"( 100 % - 10 % ) * ( 100 % + 2 % ) = 0.90 * 1.02 = 8.2 % the weigh in records your weight loss at 8.2 % ! the answer is b"
a ) 13 % , b ) 8.2 % , c ) 9 % , d ) 14 % , e ) 12 %
b
multiply(subtract(const_1, multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(2, const_100)))), const_100)
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100)|
gain
allenai/math_qa
a chemical supply company has 60 liters of a 40 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
"60 liters of a 40 % hno 3 solution means hno 3 = 24 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 24 + x = 50 % of ( 60 + x ) or x = 12 . hence , a"
a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
a
multiply(subtract(divide(60, const_2), divide(multiply(60, 40), const_100)), const_2)
divide(n0,const_2)|multiply(n0,n1)|divide(#1,const_100)|subtract(#0,#2)|multiply(#3,const_2)|
gain
allenai/math_qa
in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.6 times as old as robert ?
"in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 1950 ro = 10 , ri = 40 1990 ro = 50 , ri = 80 = 1.6 times thus ans : e"
a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1990
e
add(1950, add(1.6, add(4, 3)))
add(n3,n1)|add(n4,#0)|add(n0,#1)|
general
allenai/math_qa
how many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards ? ( 1 mile = 1,160 yards )
speed = 9 miles / hr = 4.4 yard / s = 29.33 yards / min distance = 106 yards time = distance / speed = 106 / 29.33 = 3.61 minutes ans - d
a ) 2 , b ) 5 , c ) 4 , d ) 3.61 , e ) 4.3
d
multiply(divide(106, add(add(multiply(add(const_3, const_4), const_100), multiply(multiply(const_2, const_3), const_10)), const_1000)), const_60)
add(const_3,const_4)|multiply(const_2,const_3)|multiply(#0,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,const_1000)|divide(n1,#5)|multiply(#6,const_60)
physics
allenai/math_qa
4 , 5 , 7 , 11 , 19 , ( . . . )
"4 4 Γ— 2 - 3 = 5 5 Γ— 2 - 3 = 7 7 Γ— 2 - 3 = 11 11 Γ— 2 - 3 = 19 19 Γ— 2 - 3 = 35 answer is c"
a ) 32 , b ) 22 , c ) 35 , d ) 27 , e ) 28
c
subtract(negate(11), multiply(subtract(5, 7), divide(subtract(5, 7), subtract(4, 5))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
allenai/math_qa
what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 12 ?
"denote | x - 4 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 3 - - > x = 7 or x = 0 . the sum = 7 . answer : e ."
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
e
add(add(const_4, 4), subtract(4, const_4))
add(n0,const_4)|subtract(n0,const_4)|add(#0,#1)|
general
allenai/math_qa
a 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
"relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 270 / 9 = 500 / 9 x = 230 ans is 230 m answer : c"
a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
c
subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 270)
add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)|
physics
allenai/math_qa
it takes avery 2 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
"avery ' s efficiency is 100 / 2 = 50 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 70 % of the job remaining = 30 % tom will complete 20 % in 60 minutes , and 10 % in 60 * 10 / 20 minutes = 30 minutes time taken by tom to finish the remaining on his own = 60 + 30 = 90 minutes answer : d"
a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 1 hour and 30 minutes , e ) 1 hour and 20 minutes
d
multiply(divide(subtract(const_1, add(divide(const_1, 2), divide(const_1, 5))), divide(const_1, 5)), const_60)
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|subtract(const_1,#2)|divide(#3,#1)|multiply(#4,const_60)|
physics
allenai/math_qa
if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 8 m of the same rod ?
explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 8 : : 42.75 : x = > 11.25 x x = 8 x 42.75 = > x = ( 8 x 42.75 ) / 11.25 = > x = 30.4 answer : d
a ) 22.8 kg , b ) 25.6 kg , c ) 28 kg , d ) 30.4 kg , e ) none of these
d
divide(multiply(8, 42.75), 11.25)
multiply(n1,n2)|divide(#0,n0)
physics
allenai/math_qa
a sum fetched total simple interest of 4016.25 at the rate of 13 p . c . p . a . in 5 years . what is the sum ?
"let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a"
a ) 6178.85 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
a
divide(multiply(const_100, 4016.25), multiply(13, 5))
multiply(n0,const_100)|multiply(n1,n2)|divide(#0,#1)|
gain
allenai/math_qa
which is the least number that must be subtracted from 1100 so that the remainder when divided by 7 , 12 , 16 is 4 ?
"first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1100 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 88 d"
a ) 58 , b ) 68 , c ) 78 , d ) 88 , e ) 90
d
subtract(1100, add(4, multiply(gcd(1100, lcm(lcm(7, 12), 16)), lcm(lcm(7, 12), 16))))
lcm(n1,n2)|lcm(n3,#0)|gcd(n0,#1)|multiply(#2,#1)|add(n4,#3)|subtract(n0,#4)|
general
allenai/math_qa
let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ?
"the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ."
a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42
c
subtract(45, multiply(const_2, divide(divide(45, const_2), add(const_1, const_4))))
add(const_1,const_4)|divide(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)|subtract(n0,#3)|
general
allenai/math_qa
in a 200 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
"b runs 56 m in 7 sec . = > b runs 200 m in 7 / 56 * 200 = 25 seconds since a beats b by 7 seconds , a runs 200 m in ( 25 - 7 ) = 18 seconds hence , a ' s time over the course = 18 seconds answer : d"
a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
d
subtract(multiply(divide(7, 56), 200), 7)
divide(n2,n1)|multiply(n0,#0)|subtract(#1,n2)|
physics
allenai/math_qa
the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ?
"$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ."
a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
b
sqrt(36)
sqrt(n2)|
gain
allenai/math_qa
a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ?
difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a )
a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km
a
multiply(divide(divide(multiply(35, 15), subtract(40, 35)), const_60), 40)
multiply(n1,n2)|subtract(n0,n1)|divide(#0,#1)|divide(#2,const_60)|multiply(n0,#3)
physics
allenai/math_qa
the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?
increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
a
multiply(subtract(divide(192000, 120000), const_1), const_100)
divide(n3,n0)|subtract(#0,const_1)|multiply(#1,const_100)
general
allenai/math_qa
the least number which when divided by 3 , 4 , 5 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
"explanation : l . c . m of 3 , 4 , 5 , 8 = 120 therefore required number is of the form 120 k + 3 . least value of k for which ( 120 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 120 x 2 + 3 ) = 243 answer : b"
a ) 167 , b ) 243 , c ) 252 , d ) 336 , e ) none of these
b
multiply(lcm(lcm(lcm(3, 4), 5), 8), const_2)
lcm(n0,n1)|lcm(n2,#0)|lcm(n3,#1)|multiply(#2,const_2)|
general
allenai/math_qa
a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
"let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 Γ— 6500 = > 34009 + x = 39000 = > x = 39000 βˆ’ 34009 = 4991 answer : d"
a ) 4857 , b ) 4184 , c ) 4012 , d ) 4991 , e ) 5291
d
subtract(multiply(6500, add(5, const_1)), add(add(add(6855, add(6435, 6927)), 7230), 6562))
add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)|
general
allenai/math_qa
a certain galaxy is known to comprise approximately 4 x 10 ^ 12 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
"total no . of stars on galaxy = 4 * 10 ^ 12 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 12 / 50 * 10 ^ 6 = 40 * 10 ^ 4 / 5 = 80000 therefore answer is c"
a ) 800 , b ) 1,250 , c ) 80,000 , d ) 12,000 , e ) 80,000
c
multiply(divide(multiply(divide(multiply(4, 10), 50), power(10, const_4)), const_1000), 4)
multiply(n0,n1)|power(n1,const_4)|divide(#0,n3)|multiply(#2,#1)|divide(#3,const_1000)|multiply(n0,#4)|
general
allenai/math_qa
evaluate : 40 - 12 Γ· 6 Γ— 2 =
"according to order of operations , 12 Γ· 6 Γ— 2 ( division and multiplication ) is done first from left to right 12 Γ· 6 Γ— 2 = 2 Γ— 2 = 4 hence 40 - 12 Γ· 6 Γ— 2 = 40 - 4 = 36 correct answer is b ) 36"
a ) a ) 24 , b ) b ) 36 , c ) c ) 48 , d ) d ) 60 , e ) e ) 72
b
subtract(40, multiply(multiply(12, 6), 2))
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
general
allenai/math_qa
a sum fetched a total simple interest of 4025.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
"principal = ( 100 x 4025.25 ) / ( 9 x 5 ) = 402525 / 45 = 8945 . answer d"
a ) 5768 , b ) 8925 , c ) 2345 , d ) 8945 , e ) 8723
d
divide(divide(multiply(4025.25, const_100), 9), 5)
multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)|
gain
allenai/math_qa
in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 21 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 21 ) = 36 / 30 = 6 / 5 . answer : c ."
a ) 2 / 1 , b ) 4 / 1 , c ) 6 / 5 , d ) 3 / 4 , e ) 3 / 2
c
divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 21))
add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)|
general
allenai/math_qa
find the area of a parallelogram with base 30 cm and height 12 cm ?
"area of a parallelogram = base * height = 30 * 12 = 360 cm 2 answer : b"
a ) 290 cm 2 , b ) 360 cm 2 , c ) 270 cm 2 , d ) 280 cm 2 , e ) 260 cm 2
b
multiply(30, 12)
multiply(n0,n1)|
geometry
allenai/math_qa
if the height of a cone is increased by 160 % then its volume is increased by ?
"160 % answer : e"
a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 160
e
rectangle_area(160, const_1)
rectangle_area(n0,const_1)|
geometry
allenai/math_qa
a hostel had provisions for 250 men for 40 days . if 50 men left the hostel , how long will the food last at the same rate ?
"a hostel had provisions for 250 men for 40 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 40 250 Γ— 40 = 200 x 5 Γ— 40 = 4 x x = 5 Γ— 10 = 50 answer c"
a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
c
divide(multiply(250, 40), subtract(250, 50))
multiply(n0,n1)|subtract(n0,n2)|divide(#0,#1)|
gain
allenai/math_qa
if sum of two no . is 12 and subtraction to that is 4 . so how much min . should added to smaller no . to make it even ?
let smaller no . be x . bigger no . = 12 - x . 12 - x - x = 4 . 12 - 2 x = 4 2 x = 8 , x = 4 . so 4 is itself even no . so , zero should be added . answer e
a ) 1 , b ) 2 , c ) 0.5 , d ) 1.5 , e ) 0
e
multiply(divide(subtract(12, 4), const_2), const_1)
subtract(n0,n1)|divide(#0,const_2)|multiply(#1,const_1)
general
allenai/math_qa
the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is re . 1 . the sum ( in rs . ) is ?
"let the sum be rs . x . then , [ x ( 1 + 4 / 100 ) 2 - x ] = ( 676 / 625 x - x ) = 51 / 625 x s . i . = ( x * 4 * 2 ) / 100 = 2 x / 25 51 x / 625 - 2 x / 25 = 1 or x = 625 . answer : a"
a ) 625 , b ) 827 , c ) 657 , d ) 726 , e ) 634
a
inverse(multiply(power(divide(4, const_100), 2), 1))
divide(n1,const_100)|power(#0,n0)|multiply(n2,#1)|inverse(#2)|
gain
allenai/math_qa
how many integer values are there for x such that 1 < 3 x + 5 < 17 ?
the inequality given is 1 < 3 x + 5 < 17 it can further reduced to - 4 < 3 x < 12 finally - 4 / 3 < x < 4 so can only take 5 integer values i . e . - 1 , 0,1 , 2,3 correct answer - d
a ) two , b ) three , c ) four , d ) five , e ) six
d
floor(subtract(divide(subtract(17, 5), 3), divide(subtract(1, 5), 3)))
subtract(n3,n2)|subtract(n0,n2)|divide(#0,n1)|divide(#1,n1)|subtract(#2,#3)|floor(#4)
general
allenai/math_qa
3 machines operating independently , simultaneously , and at the same constant rate can fill a certain production order in 44 hours . if one additional machine were used under the same operating conditions , in how manyfewerhours of simultaneous operation could the production order be fulfilled ?
if 3 machines can do the work in 44 hr then 4 machines can do the work in 3 / 4 * 44 = 33 hrs . hence time saved will be 11 hr option d is the correct answer
a ) 6 , b ) 9 , c ) 12 , d ) 11 , e ) 48
d
subtract(44, divide(multiply(3, 44), add(3, const_1)))
add(n0,const_1)|multiply(n0,n1)|divide(#1,#0)|subtract(n1,#2)
general
allenai/math_qa
how many bricks , each measuring 80 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
"number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 80 x 11.25 x 6 ) = 2000 answer : b"
a ) 6400 , b ) 2000 , c ) 5500 , d ) 7400 , e ) 3000
b
divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(80, 11.25), 6))
multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)|
physics
allenai/math_qa
on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 390 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 390 ) = 2 + 2 ( extra ) = > 2 x - 780 = x = > x = 780 . answer : b"
a ) 237 , b ) 780 , c ) 197 , d ) 287 , e ) 720
b
multiply(390, const_2)
multiply(n0,const_2)|
general
allenai/math_qa
what is the local value of 7 in the difference of 100889 and local value of 3 in 28943712 ?
"100889 - ( local value of 3 ) = 100889 - 3000 = 97889 local value of 7 in 97889 = 7000 a"
a ) 7000 , b ) 700 , c ) 70000 , d ) 70 , e ) 7
a
reminder(multiply(reminder(subtract(28943712, reminder(28943712, const_1000)), multiply(const_10, const_1000)), 100889), multiply(const_10, const_1000))
multiply(const_10,const_1000)|reminder(n3,const_1000)|subtract(n3,#1)|reminder(#2,#0)|multiply(n1,#3)|reminder(#4,#0)|
general
allenai/math_qa
find the sum of first 32 natural numbers
"explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 32 ( 32 + 1 ) / 2 = 32 ( 33 ) / 2 = 528 answer : option e"
a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 528
e
add(divide(divide(32, divide(divide(divide(divide(divide(32, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(32, divide(divide(divide(divide(divide(32, const_2), const_2), const_2), const_2), const_2)), const_2))))
divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(n0,#4)|divide(#5,const_2)|sqrt(#6)|add(#7,const_1)|add(#8,#6)|
general
allenai/math_qa
a train 880 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
"speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 880 + x ) / 60 = 65 / 3 x = 420 m . answer : option d"
a ) 510 , b ) 540 , c ) 500 , d ) 420 , e ) 589
d
divide(880, multiply(subtract(78, 1), const_0_2778))
subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)|
physics
allenai/math_qa
in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 800 m ?
"when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 800 m , the number of meters by which a beats c = ( 800 * 212.5 ) / 1000 = 170 m . answer : b"
a ) 122.9 m , b ) 170 m . , c ) 122.2 m , d ) 222.9 m , e ) 12289 m
b
subtract(1000, divide(multiply(subtract(1000, 100), subtract(800, 100)), 800))
subtract(n0,n1)|subtract(n2,n1)|multiply(#0,#1)|divide(#2,n2)|subtract(n0,#3)|
physics
allenai/math_qa
the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ?
x - x - x - x - x - - > there are 3 even digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 3 - x - x - x - 2 . other x ' s can take following values : 3 - 5 - 4 - 3 - 2 - - > 3 * 5 * 4 * 3 * 2 = 360 . answer : c .
a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440
c
multiply(factorial(const_3), divide(factorial(5), const_2))
factorial(n0)|factorial(const_3)|divide(#0,const_2)|multiply(#2,#1)
general
allenai/math_qa
if 20 men can build a wall 66 metres long in 15 days , what length of a similar can be built by 86 men in 8 days ?
"if 20 men can build a wall 66 metres long in 15 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 15 * 20 ) = 151.36 mtrs answer : a"
a ) 151.36 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
a
multiply(66, divide(multiply(86, 8), multiply(20, 15)))
multiply(n3,n4)|multiply(n0,n2)|divide(#0,#1)|multiply(n1,#2)|
physics
allenai/math_qa
ashis ' s height is 25 % more than babji , by how much percent babji ' s height is less than ashis .
explanation : solution : babji is less than ashis by ( 25 / ( 100 + 25 ) * 100 ) % = 20 % answer : d
a ) 30 % , b ) 25 % , c ) 75 % , d ) 20 % , e ) none of these
d
multiply(divide(25, add(const_100, 25)), const_100)
add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)
general
allenai/math_qa
two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 81 hours respectively . the ratio of their speeds is ?
"let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 81 : √ 16 = 9 : 4 answer : b"
a ) 4 : 9 , b ) 9 : 4 , c ) 4 : 5 , d ) 4 : 1 , e ) 4 : 2
b
divide(sqrt(81), sqrt(16))
sqrt(n1)|sqrt(n0)|divide(#0,#1)|
physics
allenai/math_qa
the l . c . m of two numbers is 48 . the numbers are in the ratio 4 : 3 . the sum of numbers is :
"let the numbers be 4 x and 3 x . then , their l . c . m = 12 x . so , 12 x = 48 or x = 4 . the numbers are 16 and 12 . hence , required sum = ( 16 + 12 ) = 28 . answer : a"
a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
a
divide(multiply(4, 48), 3)
multiply(n0,n1)|divide(#0,n2)|
other
allenai/math_qa
a sum of rs . 1000 at simple interest amounts to rs . 1192 in 4 years . the s . i . for 1 year is :
s . i . for 4 years = rs . ( 1192 - 1000 ) = rs . 192 . s . i . for 1 year = rs . 192 / 4 = rs . 48 . answer : option e
a ) rs . 45 , b ) rs . 70 , c ) rs . 39 , d ) rs . 72 , e ) rs . 48
e
multiply(divide(subtract(divide(1192, const_10), const_100), 4), const_10)
divide(n1,const_10)|subtract(#0,const_100)|divide(#1,n2)|multiply(#2,const_10)
gain
allenai/math_qa
the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 4 years hence ?
"a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 4 years , their ages will be 44 and 24 . sum of their ages = 44 + 24 = 68 . answer : d"
a ) 22 , b ) 77 , c ) 70 , d ) 68 , e ) 71
d
add(add(multiply(divide(60, 4), const_2), 4), add(divide(60, 4), 4))
divide(n0,n1)|add(#0,n1)|multiply(#0,const_2)|add(#2,n1)|add(#3,#1)|
general
allenai/math_qa
a train 300 m long takes 9 sec to cross a man walking at 3 kmph in a direction opposite to that of the train . find the speed of the train ?
"let the speed of the train be x kmph speed of the train relative to man = x + 3 = ( x + 3 ) * 5 / 18 m / sec 300 / [ ( x + 3 ) * 5 / 18 ] = 9 9 ( x + 3 ) = 1080 x = 117 kmph answer is d"
a ) 100 kmph , b ) 90 kmph , c ) 120 kmph , d ) 117 kmph , e ) 125 kmph
d
subtract(divide(divide(300, 9), const_0_2778), 3)
divide(n0,n1)|divide(#0,const_0_2778)|subtract(#1,n2)|
physics
allenai/math_qa
a = { 0 , 1 , - 3 , 6 , - 8 , - 10 } b = { - 1 , 2 , - 4 , 7 , 6 , - 9 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab < 0 ?
for the product of 2 numbers to be negative either of them must be positive or negative : p ( positive , negative ) = 2 / 6 * 3 / 6 = 6 / 36 ; p ( negative , positive ) = 3 / 6 * 3 / 6 = 9 / 36 p = 6 / 36 + 9 / 36 p = 15 / 36 p = 5 / 12 answer : d
a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 2
d
add(multiply(divide(3, 6), divide(3, 6)), multiply(divide(2, 6), divide(const_3, 6)))
divide(n2,n3)|divide(n7,n3)|divide(const_3,n3)|multiply(#0,#0)|multiply(#1,#2)|add(#3,#4)
general
allenai/math_qa
how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ?
"speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d"
a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec
d
divide(multiply(20, const_4), multiply(12, divide(const_1000, const_3600)))
divide(const_1000,const_3600)|multiply(n0,const_4)|multiply(n1,#0)|divide(#1,#2)|
gain
allenai/math_qa
what least number must be subtracted from 427398 so that remaining no . is divisible by 11
"explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"
a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
b
subtract(427398, multiply(floor(divide(427398, 11)), 11))
divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)|
general
allenai/math_qa
there are 193 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 25 are members of both sets a and b . how many of the members of set u are members of set a ?
you had the answer almost right . the x = 85 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 85 + 25 = 110 c
a ) 72 , b ) 85 , c ) 110 , d ) 98 , e ) 108
c
subtract(add(subtract(193, 59), 25), 49)
subtract(n0,n2)|add(n3,#0)|subtract(#1,n1)
other
allenai/math_qa
of all the homes on gotham street , 1 / 3 are termite - ridden , and 5 / 8 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
"the fraction of homes which are termite - infested but not collapsing is 3 / 8 * 1 / 3 = 1 / 8 the answer is e ."
a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8
e
divide(add(1, const_2.0), multiply(3, 8))
add(n0,const_2.0)|multiply(n1,n3)|divide(#0,#1)|
general
allenai/math_qa
if an object travels 90 feet in 3 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
"90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ."
a ) 17.36 , b ) 20.45 , c ) 23.87 , d ) 26.92 , e ) 29.56
b
divide(divide(90, 5280), multiply(3, divide(1, const_3600)))
divide(n0,n3)|divide(n2,const_3600)|multiply(n1,#1)|divide(#0,#2)|
physics
allenai/math_qa
if a certain number when divided by the numbers 5 , 32 one after other successively , leaves a remainder 0 , 21 then what will be the remainders if it is divided by the numbers 2 , 35
the number is 35 , when divided by 5 , 32 leaves remainder 0 , 21 respectively . so if 35 is divided by 2 , 35 leaves remainder 1 , 20 respectively . answer : a
a ) 1 , 20 , b ) 1 , 21 , c ) 1 , 22 , d ) 1 , 23 , e ) 1 , 24
a
reminder(multiply(5, 21), 2)
multiply(n0,n3)|reminder(#0,n4)
general
allenai/math_qa
each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 105 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
let x be the monthly salary 15 % of 1 / 5 * x = 105 x = 3500 answer c
a ) $ 2400 , b ) $ 3200 , c ) $ 3500 , d ) $ 6400 , e ) $ 9600
c
multiply(multiply(const_100, add(const_3, const_2)), divide(105, subtract(const_100, add(add(30, 20), 35))))
add(n0,n1)|add(const_2,const_3)|add(n2,#0)|multiply(#1,const_100)|subtract(const_100,#2)|divide(n3,#4)|multiply(#5,#3)
gain
allenai/math_qa
the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is :
let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e
a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
e
add(divide(subtract(102, add(add(const_1, const_2), 3)), 4), 3)
add(const_1,const_2)|add(n2,#0)|subtract(n1,#1)|divide(#2,n0)|add(n2,#3)
physics
allenai/math_qa
of the 150 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
"full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 10 answer : option a"
a ) 10 , b ) 30 , c ) 50 , d ) 80 , e ) 100
a
subtract(subtract(150, 80), 10)
subtract(n0,n1)|subtract(#0,n3)|
general
allenai/math_qa
an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ?
break down the question in to steps : step # 1 : incentives received by 5 salesmen - - > abcde step # 2 : mean and median of the incentives is $ 7000 : via number properties - - > total incentives = 7000 * 5 = 35000 ab 7000 de step # 3 : only mode among the observations is $ 12000 : mode is the value that appears most often in a set of data . therefore 12000 must occur more then once and since 12000 is larger than the mean ( 7000 ) the most it can occur is twice in our list . if we place the numbers in ascending order we haveab 70001200012000 step # 4 : what is the difference z between the highest and the lowest incentive : - the total paid has to equal mean * # of numbers = 7000 * 5 = 35 000 . - the three values we have so far ( 12000 12000 and 7000 ) equal 31000 . - therefore the first two numbers ( ab ) must equal 4000 - there is only one mode which is 12000 , therefore 4000 must be equal to a set of two numbers that are not the and a < b if a = 1000 b = 3000 - - > difference between the highest and the lowest incentive = 12000 - 1000 = 11000 no other options for a or b to fit the criteria final list : 1000300070001200012000 answer d
a ) $ 4000 , b ) $ 5000 , c ) $ 9000 , d ) $ 11000 , e ) $ 13000
d
subtract(12000, const_1000)
subtract(n2,const_1000)
general
allenai/math_qa
car z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
"the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 51 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40.8 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40.8 miles / gallon * 10 gallons = 408 miles . answer d ."
a ) 320 , b ) 375.2 , c ) 400 , d ) 408 , e ) 440
d
multiply(multiply(subtract(const_1, divide(20, const_100)), 51), 10)
divide(n2,const_100)|subtract(const_1,#0)|multiply(n0,#1)|multiply(n4,#2)|
gain
allenai/math_qa
what is the angle between the minute hand and the hour hand when the time is 1540 hours ?
solution : the total angle made by the minute hand during an hour is 360 o . if it takes 360 o for an hour , it will take ( 40 / 60 ) * 360 = 240 o . the angle between the hour hand the minute hand will therefore , be somewhere between 240 - 90 = 150 o , as the hour hand is between 3 and 4 . the angle made by the hour hand when it moves from say 3 to 4 will be 30 o . that is the hour hand makes 30 o during the course of an hour . the hour hand will therefore , move ( 40 / 60 ) * 30 = 20 o . therefore , the net angle between the hour hand and the minute hand will be 150 - 20 = 130 o . answer d
a ) 150 , b ) 160 , c ) 140 , d ) 130 , e ) none
d
divide(divide(1540, const_4), const_3)
divide(n0,const_4)|divide(#0,const_3)
physics
allenai/math_qa
a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is ?
"s . i . for 1 year = ( 854 - 825 ) = rs . 29 s . i . for 3 years = 29 * 3 = rs . 87 principal = ( 825 - 87 ) = rs . 738 . answer : a"
a ) rs . 738 , b ) rs . 638 , c ) rs . 650 , d ) rs . 730 , e ) rs . 735
a
subtract(825, divide(multiply(subtract(854, 825), 3), 4))
subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)|
gain
allenai/math_qa
what is the rate percent when the simple interest on rs . 9100 amount to rs . 455 in 3 years ?
"455 = ( 4100 * 3 * r ) / 100 r = 3.7 % answer : a"
a ) 3.7 % , b ) 5.7 % , c ) 6.7 % , d ) 8.7 % , e ) 9.7 %
a
divide(multiply(const_100, 455), multiply(9100, 3))
multiply(n1,const_100)|multiply(n0,n2)|divide(#0,#1)|
gain
allenai/math_qa
ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ?
"total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b"
a ) 16 % , b ) 17.5 % , c ) 18.2 % , d ) 58.5 % , e ) 13 %
b
multiply(divide(subtract(72900, add(48000, 14000)), add(48000, 14000)), const_100)
add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)|
gain
allenai/math_qa
if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i βˆ— 3 ^ k βˆ— 5 ^ m βˆ— 7 ^ p , then i + k + m + p =
"here the idea is to go expressing each factor from one to eight , decomposed into its primes : 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 * ( 2 * 2 ) * 5 + ( 2 * 3 ) * 7 * ( 2 * 2 * 2 ) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 then i = 7 k = 2 m = 1 p = 1 i + k + m + p = 11 correct answer d"
a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
d
add(add(add(7, 2), divide(5, 5)), divide(3, 3))
add(n2,n5)|divide(n4,n4)|divide(n3,n3)|add(#0,#1)|add(#3,#2)|
general
allenai/math_qa
in what time will a railway train 65 m long moving at the rate of 32 kmph pass a telegraph post on its way ?
"t = 65 / 32 * 18 / 5 = 7 sec answer : e"
a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
e
divide(65, multiply(32, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
allenai/math_qa
x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
"the exponents of x ^ 2 * y ^ 2 * z ^ 2 are 2 , 2 , and 2 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 27 the answer is c ."
a ) 9 , b ) 18 , c ) 27 , d ) 36 , e ) 45
c
subtract(power(2, const_4), const_4)
power(n0,const_4)|subtract(#0,const_4)|
general
allenai/math_qa
find the average of all the numbers between 6 and 36 which are divisible by 5 .
"solution average = ( 10 + 15 + 20 + 25 + 30 + 35 ) / 6 ) = 135 / 6 = 22.5 answer e"
a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 22.5
e
divide(add(add(6, const_4), subtract(36, const_4)), const_2)
add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)|
general
allenai/math_qa
in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 400 m ?
"when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 400 m , the number of meters by which a beats c = ( 400 * 212.5 ) / 1000 = 85 m . answer : d"
a ) 122.9 m , b ) 127.5 m . , c ) 122.2 m , d ) 85 m , e ) 12289 m
d
subtract(400, divide(multiply(subtract(400, 100), subtract(800, const_100.0)), 800))
subtract(n4,n1)|subtract(n2,n1)|multiply(#0,#1)|divide(#2,n2)|subtract(n4,#3)|
physics
allenai/math_qa
a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 9 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 9 the total number of traditionalists is 6 p / 9 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e .
a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5
e
subtract(1, divide(divide(6, 9), add(divide(6, 9), 1)))
divide(n0,n2)|add(n1,#0)|divide(#0,#1)|subtract(n1,#2)
general
allenai/math_qa
the radii of two cones are in ratio 2 : 1 , their volumes are equal . find the ratio of their heights .
explanation : let their radii be 2 x , x and their heights be h and h resp . then , volume of cone = 1 / 3 Ο€ r 2 h 1 / 3 βˆ— Ο€ βˆ— ( 2 x ) 2 βˆ— h / 1 / 3 βˆ— Ο€ βˆ— x 2 βˆ— h = > hh = 14 = > h : h = 1 : 4 option a
['a ) 1 : 4', 'b ) 1 : 3', 'c ) 1 : 2', 'd ) 1 : 5', 'e ) none of these']
a
divide(1, power(2, 2))
power(n0,n0)|divide(n1,#0)
geometry
allenai/math_qa
how many numbers from 10 to 100000 are exactly divisible by 9 ?
"10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b"
a ) 900 , b ) 11110 , c ) 1100 , d ) 1200 , e ) 1400
b
add(divide(subtract(multiply(floor(divide(100000, 9)), 9), multiply(add(floor(divide(10, 9)), const_1), 9)), 9), const_1)
divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)|
general
allenai/math_qa
a person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes . if field has a length that is twice its width , find the area of the field in square meters .
let us first find the distance d jogged distance = rate * time = ( 12 km / hr ) * 30 minutes = ( 12 km / hr ) * 0.5 hr = 6 km the distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to 6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters let l and w be the length and width of the field . the length is twice the width . hence l = 2 w the perimeter is 600 meters and is given by 2 ( l + w ) = 600 substitute l by 2 w 2 ( 2 w + w ) = 600 simplify and solve for w 4 w + 2 w = 600 6 w = 600 w = 100 find l l = 2 w = 200 find the area a of the rectangle a = l * w = 200 * 100 = 20,000 square meters correct answer a
['a ) 20,000 square meters', 'b ) 10,000 square meters', 'c ) 30,000 square meters', 'd ) 40,000 square meters', 'e ) 50,000 square meters']
a
rectangle_area(multiply(divide(divide(multiply(divide(divide(12, const_2), 10), const_1000), const_2), const_3), const_2), divide(divide(multiply(divide(divide(12, const_2), 10), const_1000), const_2), const_3))
divide(n1,const_2)|divide(#0,n0)|multiply(#1,const_1000)|divide(#2,const_2)|divide(#3,const_3)|multiply(#4,const_2)|rectangle_area(#4,#5)
geometry
allenai/math_qa
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
"sol . let the total number of workers be x . then , 8000 x = ( 20000 Γ— 7 ) + 6000 ( x – 7 ) β€Ή = β€Ί 2000 x = 98000 β€Ή = β€Ί x = 49 . answer b"
a ) 20 , b ) 49 , c ) 22 , d ) 23 , e ) none
b
add(7, divide(multiply(7, subtract(20000, 8000)), subtract(8000, 6000)))
subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)|
general
allenai/math_qa
a rectangular swimming pool is 8 feet by 20 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 540 square feet . what is the width of the deck ?
"let the width = w total area of the pool and deck = ( 2 w + 8 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 12 * 24 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 13 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 14 * 26 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 16 * 28 has unit digit 8 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 18 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : e w = 5"
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
e
divide(subtract(sqrt(add(power(subtract(20, const_1), const_2), subtract(540, rectangle_area(8, 20)))), subtract(20, const_1)), const_2)
rectangle_area(n0,n1)|subtract(n1,const_1)|power(#1,const_2)|subtract(n2,#0)|add(#2,#3)|sqrt(#4)|subtract(#5,#1)|divide(#6,const_2)|
geometry
allenai/math_qa
salesperson a ' s compensation for any week is $ 350 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
"sometime , setting up an equation is an easy way to go with : 350 + 0.06 ( x - 1000 ) = 0.08 x x = 14,500 ans : d"
a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 14,500 , e ) $ 4,000
d
divide(add(divide(subtract(350, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100))), divide(subtract(350, multiply(divide(6, const_100), 1,000)), subtract(divide(8, const_100), divide(6, const_100)))), 1,000)
divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|add(#5,#5)|divide(#6,n2)|
general
allenai/math_qa