euclaise/mathqa_programs huggingface dataset:
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 864
Rationale: "distance = ( 240 x 6 ) = 1440 km . speed = distance / time speed = 1440 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1440 x 3 / 5 ) km / hr = 864 km / hr answer e ) 864 km / hr"
Answer: e
Python program:
a = 240 * 6
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursday , bow much coal will be required for 8 engines , each running 13 hours a day , it being given that 3 engines of former type consume as much as 4 engines of latter type ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct prportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) [ 9 x 8 x ( 1 / 3 ) x x ) = ( 8 x 13 x ( 1 / 4 ) x 24 ) = 24 x = 624 = x = 26 . hence , the required consumption of coal = 26 metric tonnes . answer is c .
Answer: c
Python program:
a = 3 * 24
b = 9 * 8
c = a / b
d = c * 2
e = 13 * d
Problem: the value of log 2 ( log 5625 ) is
Options: a ) 2 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: solution let log 5625 = x . then , 5 x = 625 = 54 ‹ = › x = 4 . let log 2 ( log 5625 ) = y . then , log 24 = y ‹ = › 2 y = 4 y ; 2 . answer a
Answer: a
Python program:
a = 4 + 1 
b = a * 1000
c = 5625 - b
d = math.log(c)
e = 4 + 1 
f = math.log(e)
g = d / f
h = math.log(g)
Problem: if 16 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 64
Rationale: "let x be the number of students in the school . 0.16 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 % . the answer is e"
Answer: e
Python program:
a = 100 - 75
b = a / 100
c = 16 / b
Problem: a man sitting in a train which is traveling at 55 kmph observes that a goods train , traveling in opposite direction , takes 10 seconds to pass him . if the goods train is 320 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 60 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 320 / 10 m / sec = ( ( 320 / 10 ) × ( 18 / 5 ) ) kmph = 115 kmph . speed of goods train = ( 115 - 55 ) kmph = 60 kmph answer : option c"
Answer: c
Python program:
a = 320 / 10
b = a * const_3_6
c = b - 55
Problem: a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 10 % stock at 90 , investment = rs . ( 90 / 10 ) = rs . 9 . for an income of rs . 1 in 5 % stock at 90 , investment = rs . ( 90 / 5 ) = rs . 18 . ∴ ratio of investments = 9 : 18 = 1 : 2 answer a"
Answer: a
Python program:
a = 90 * 2
b = 90 * 3
c = a / b
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 98 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"
Answer: d
Python program:
a = 32 + 6 
b = 10 + 1 
c = a * b
d = 10 * 32
e = c - d
Problem: solve below question 2 x + 1 = - 23
Options: a ) - 8 , b ) - 9 , c ) - 12 , d ) - 4 , e ) 12
Rationale: 1 . subtract 1 from both sides : 2 x + 1 - 1 = - 23 - 1 2 . simplify both sides : 2 x = - 24 3 . divide both sides by 2 : 4 . simplify both sides : x = - 12 c
Answer: c
Python program:
a = 23 + 1 
b = negate / (
Problem: calculate 85184 ÷ ? = 352
Options: a ) 241 , b ) 242 , c ) 244 , d ) 247 , e ) 240
Rationale: "answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b"
Answer: b
Python program:
a = 85184 * 352
Problem: 7.51 8.22 7.86 8.36 8.09 7.83 8.30 8.01 7.73 8.25 7.96 8.53 a vending machine is designed to dispense 8 ounces of coffee into a cup . after a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine , the 12 listed amounts , in ounces , were selected from the data above . if the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces , how many of the 12 listed amounts are within 1.5 standard deviation of the mean ?
Options: a ) four , b ) six , c ) nine , d ) ten , e ) twelve
Rationale: mean = 8.1 standard deviation = 0.4 within 1.5 standard deviation of the mean i . e . 1.5 standard deviation above the mean = 8.1 + 1.5 * 0.4 = 8.7 and 1.5 standard deviation below the mean = 8.1 - 1.5 * 0.4 = 7.5 all values are within the range hence , 12 values fall within 1.5 sd from mean answer : option e
Answer: e
Python program:
a = 1 * 5
b = 8 - 1
c = 8 + 1