euclaise/mathqa_programs huggingface dataset:
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 4,500 meters of fabric ?
Options: a ) $ 8,617 , b ) $ 8,710 , c ) $ 8,810 , d ) $ 8,835 , e ) $ 8,915
Rationale: for first 2000 metres he does not get any discount amount = 2 * 2000 = $ 4000 for next 1500 metres he gets 5 % discount amount = 2 * 1500 - ( 1 / 20 ) * 3000 = $ 2850 for the nest 1000 metres he gets 7 % discount amount = 2 * 1000 - 7 * 20 = $ 1860 total amount = $ 4000 + $ 2850 + $ 1860 = $ 8710 answer : b
Answer: b
Python program:
a = 2 * 3
b = a * 100
Problem: 20 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 17.4 %
Rationale: "alcohol in the 20 litres of mix . = 20 % of 20 litres = ( 20 * 20 / 100 ) = 4 litres water in it = 20 - 3 = 17 litres new quantity of mix . = 20 + 3 = 23 litres quantity of alcohol in it = 4 litres percentage of alcohol in new mix . = 4 * 100 / 23 = 17.4 % answer is e"
Answer: e
Python program:
a = 20 + 3 
b = 100 - 20
c = b / 100
d = c * 20
e = d + 3 
f = a - e
g = 20 + 3 
h = f / g
i = h * 100
Problem: the heights of a wall is 6 times its width and the length of the wall is 7 times its height . if volume of the wall be 16128 cu . m , its width is
Options: a ) 4 m , b ) 4.5 m , c ) 5 m , d ) 6 m , e ) none
Rationale: solution let the width of the wall be x metres . then , height = ( 6 x ) m and length = ( 42 x ) m . 42 x × x × 6 x = 16128 x 3 ‹ = › ( 16128 / 42 × 6 ) = 64 ‹ = › x = 4 . answer a
Answer: a
Python program:
a = 6 * 7
b = a * 6
c = 16128 / b
d = math.sqrt(c)
e = d / 2
Problem: ( 9 ^ 5.6 x 9 ^ 10.3 ) ÷ 9 ^ 2.56256 = 9 ^ ?
Options: a ) 11.34 , b ) 12.34 , c ) 13.34 , d ) 14.34 , e ) 15.34
Rationale: 5.6 + 10.3 = 15.9 i . e . . 15.9 - 2.56 = 13.34 so ur answer is 9 ^ 13.34 answer : c
Answer: c
Python program:
a = 5 + 6 
b = a - 2
Problem: 3850 * 99
Options: a ) 382550 , b ) 384560 , c ) 385690 , d ) 389650 , e ) 381150
Rationale: "explanation : 3850 * ( 100 - 1 ) = 385000 - 3850 = 381150 option e"
Answer: e
Python program:
a = 3850 / 99
b = a * 100
Problem: a milk man has 20 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 22 , b ) 25 , c ) 27 , d ) 29 , e ) 11
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = \ inline \ frac { 5 } { 20 } \ times 100 = 25 % % [ profit % = \ inline \ frac { profit } { cost \ : price } \ times 100 ] answer : b ) 25 %"
Answer: b
Python program:
a = 20 + 5 
b = a + 10 
c = 5 / 2
d = c + 3 
e = b + d 
f = e * 18
g = 20 * 18
h = f - g
i = 20 * 18
j = h / i
k = j * 100
Problem: 10 + 45
Options: a ) 8 , b ) 55 , c ) 87 , d ) 90 , e ) 2
Rationale: b
Answer: b
Python program:
a = 10 / 45
b = a * 100
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 8 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 4
Rationale: "same amount of water made bigger jar 1 / 8 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 8 + 1 / 8 = 1 / 4 full . answer : e ."
Answer: e
Python program:
a = 2 / 8
Problem: a certain bus driver is paid a regular rate of $ 20 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1000 in total compensation , how many total hours did he work that week ?
Options: a ) 46 , b ) 40 , c ) 44 , d ) 48 , e ) 49
Rationale: "for 40 hrs = 40 * 20 = 800 excess = 1000 - 800 = 200 for extra hours = . 75 ( 20 ) = 15 + 20 = 35 number of extra hrs = 200 / 35 = 5.71 = 6 approx . total hrs = 40 + 6 = 46 answer a 46"
Answer: a
Python program:
a = 20 * 40
b = 1000 - a
c = 100 + 75 
d = 20 * c
e = d / 100
f = b / e
g = 40 + f
Problem: a cistern normally takes 6 hours to be filled by a tap but because of a leak , 2 hours more . in how many hours will the leak empty a full cistern ?
Options: a ) 20 hours , b ) 24 hours , c ) 26 hours , d ) 18 hours , e ) none of these
Rationale: ∵ cistern fill in 6 hours . ∴ in 1 hour , filled part = 1 ⁄ 6 th now , due to leakage , filled part in 1 hour = 1 ⁄ 8 th part of the cistern emptied , due to leakage in 1 hour = 1 ⁄ 6 - 1 ⁄ 8 = 1 ⁄ 24 th ∴ the leakage will empty the full cistern in 24 hrs . answer b
Answer: b
Python program:
a = 1/(6)
b = 2 + 6 
c = 1/(b)
d = a - c
e = 1/(d)
Problem: what is the greatest integer m for which the number 20 ! / 10 ^ m is an integer ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 20 ! the multiples of 5 are : 5 , 10 , 15 , 20 . thus 5 ^ 4 will divide 20 ! but 5 ^ 5 will not . clearly 2 ^ 4 will divide 20 ! so m = 4 is the largest possible integer . the answer is b ."
Answer: b
Python program:
a = 10 / 2
b = 20 / a
c = math.floor(b)
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 4 ?
Options: a ) 5 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 4 + 1 ) / ( 4 - 1 ) = 5 / 3 = 5 / 3 answer : a"
Answer: a
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: doughnuts , cookies and muffins in a pastry shop are in the ratio of 5 : 3 : 1 . if there are 50 doughnuts , the number of muffins in the shop is : .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let doughnuts = 5 x , cookies = 3 x & muffins = 1 x . now , 5 x = 50 hence x = 10 . number of muffins = 1 x which is 10 . answer : c
Answer: c
Python program:
a = 50 / 5
Problem: what least number must be subtracted from 9679 so that the remaining number is divisible by 15 ?
Options: a ) 3 , b ) 1 , c ) 16 , d ) 4 , e ) 15
Rationale: "on dividing 9679 by 15 , we get remainder = 4 . required number be subtracted = 4 answer : d"
Answer: d
Python program:
a = 9679 / 15
b = math.floor(a)
c = b * 15
d = 9679 - c
Problem: the ages of two person differ by 20 years . if 8 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 33 , 13 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: let their ages be x and ( x + 20 ) years . then , 5 ( x - 8 ) = ( x + 20 - 8 ) = > 4 x = 52 = > x = 13 their present ages are 33 years and 13 year . answer : a
Answer: a
Python program:
a = 5 * 8
b = 20 - 8
c = a + b 
d = 5 - 1
e = c / d
f = e + 20
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Python program:
a = 9 / 12
b = a * 100
c = 100 - b
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 17 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 6800 , e ) none of these
Rationale: sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 17 , the sum = 400 × 17 = 6800 answer d
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 5 / 100
e = 2 * d
f = 1 + e 
g = c - f
h = 17 / g
Problem: a train speeds past a pole in 20 seconds and a platform 100 m long in 25 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 150 m , e ) 400 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 20 = > y = x / 20 x + 100 / 25 = x / 20 x = 400 m . answer : e"
Answer: e
Python program:
a = 2 - 1
b = 100 * a
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 850 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 750 , c ) s . 650 , d ) s . 730 , e ) s . 735
Rationale: "s . i . for 1 year = ( 850 - 825 ) = rs . 25 s . i . for 3 years = 25 * 3 = rs . 75 principal = ( 825 - 75 ) = rs . 750 . answer : b"
Answer: b
Python program:
a = 850 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: the difference between a number and its three - fourth is 100 . what is 25 % of that number ?
Options: a ) 120 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: "explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 100 * a
c = 1 + 2 
d = b / c
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 11 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer b"
Answer: b
Python program:
a = 3 * 16
b = 11 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 50 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 240 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: the total distance d traveled by john is given by d = 45 * 2 + 3 * 50 = 240 miles . answer c
Answer: c
Python program:
a = 45 * 2
b = 3 * 50
c = a + b
Problem: what least number must be subtracted from 3830 so that the remaining number is divisible by 15 ?
Options: a ) 3 , b ) 1 , c ) 5 , d ) 11 , e ) 15
Rationale: "on dividing 3830 by 15 , we get remainder = 5 . required number be subtracted = 5 answer : c"
Answer: c
Python program:
a = 3830 / 15
b = math.floor(a)
c = b * 15
d = 3830 - c
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what isthe probability that theextracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initially in the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 8
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Python program:
a = 1 / 2
b = 1 + 3 
c = 1 / b
d = 1 + 3 
e = 3 / d
f = c + e 
g = a + f 
h = 1 + g 
i = 1 + 3 
j = h / i
Problem: find a sum for 1 st 8 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 77 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d"
Answer: d
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b 
d = 2 + 3 
e = d + 2 
f = c + e 
g = 8 + 2 
h = f + g 
i = 8 + 2 
j = i + 2 
k = h + j 
l = 8 + 2 
m = l + 2 
n = m + 4 
o = k + n 
p = 8 + 2 
q = p + 2 
r = q + 4 
s = r + 2 
t = o + s 
u = 8 + 2 
v = u + 2 
w = v + 4 
x = w + 2 
y = x + 4 
z = t + y
Problem: if 1,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 100 , b ) 10 , c ) 1,000 , d ) 10,000 , e ) 100,000
Rationale: "given that 1,000 microns = 1 decimeter = 1 , 000,000 angstroms so , 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 1 / a
c = 100 * 100
d = b * c
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 50 meters , what is the height of the building ( in meters ) ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 50 x = 20 the answer is b ."
Answer: b
Python program:
a = 18 / 45
b = 50 * a
Problem: if 7 ^ ( x - y ) = 343 and 7 ^ ( x + y ) = 16807 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 7
Rationale: 7 ^ ( x - y ) = 343 = 7 ^ 3 = > x - y = 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 1 ) 7 ^ ( x + y ) = 16807 = 7 ^ 5 = > x + y = 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 2 ) ( equation 1 ) + ( equation 2 ) = > 2 x = 3 + 5 = 8 = > x = 8 / 2 = 4 answer is b
Answer: b
Python program:
a = 7 - 4
b = 7 - 2
c = a + b 
d = c / 2
Problem: 242 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 200 , e ) 220
Rationale: "let b be the number of boys in the school . 242 = xb / 100 b = 0.5 x 24200 = 0.5 x ^ 2 x ^ 2 = 48400 x = 220 the answer is e ."
Answer: e
Python program:
a = 242 * 100
b = 50 / 100
c = a / b
d = math.sqrt(c)
Problem: a certain number of workers can do a work in 75 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 65 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 75 - 10 ) / 10 = 65 answer is a"
Answer: a
Python program:
a = 75 - 10
b = a * 10
c = 75 - 10
d = 75 - c
e = b / d
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find his expenditure on food and conveyance .
Options: a ) $ 8600 , b ) $ 2400 , c ) $ 1000 , d ) $ 3000 , e ) $ 3400
Rationale: remaining part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1 - ( 33 / 40 ) = 7 / 40 let the monthly salary be $ x then , 7 / 40 of x = $ 1400 x = ( 1400 * 40 / 7 ) = $ 8600 expenditure on food = $ ( 3 / 10 * 800 ) = $ 2400 expenditure on conveyance = $ ( 1 / 8 * 8000 ) = $ 1000 $ 2400 + $ 1000 = $ 3400 so the answer is option e ) $ 3400
Answer: e
Python program:
a = 2 / 5
b = 3 / 10
c = a + b 
d = 1 / 8
e = c + d 
f = 1 - e
g = 1400 / f
h = 3 / 10
i = g * h
j = 2 / 5
k = 3 / 10
l = j + k 
m = 1 / 8
n = l + m 
o = 1 - n
p = 1400 / o
q = 1 / 8
r = p * q
s = i + r
Problem: some of 15 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 2 , e ) 3 / 5
Rationale: "let total paint = 1 let amount replaced = x 15 ( 1 - x ) + 25 x = 30 x = 3 / 2 answer : d"
Answer: d
Python program:
a = 30 / 100
b = 15 / 100
c = a - b
d = 25 / 100
e = 15 / 100
f = d - e
g = c / f
Problem: find the compound interest on $ 1200 for 2 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 548 , d ) $ 250 , e ) $ 300
Rationale: a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 2 = $ 1728 ci = $ 548 answer is c
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 2
d = 1200 * c
e = d - 1200
Problem: it takes avery 2 hours to build a brick wall while tom can do it in 4 hour . 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 ?
Options: a ) 70 , b ) 20 , c ) 50 , d ) 60 , e ) 30
Rationale: avery takes 2 hours tom takes 4 hours efficiency of avery is 1 / 2 units / hr efficiency of tom is 1 / 4 units / hr combined efficiency of tom and avery is 1 / 2 + 1 / 4 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 4 hours = > 1 * 60 = 60 minutes . . . answer will be ( d )
Answer: d
Python program:
a = 1 / 2
b = 1 / 4
c = a + b 
d = 1 - c
e = 1 / 4
f = d / e
g = f * const_60
Problem: how many of the integers between 25 and 45 are even ?
Options: a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9
Rationale: number start between 25 to 45 is 20 numbers half of them is even . . which is 10 answer : d
Answer: d
Python program:
a = 45 - 25
b = a / 2
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 28 more . what was his original selling price ?
Options: a ) $ 200 , b ) $ 260 , c ) $ 320 , d ) $ 380 , e ) $ 440
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 28 0.07 = 28 p = 400 the original selling price was 400 * 1.1 = 440 . the correct answer is e ."
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = 30 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 + f 
h = e - g
i = 28 / h
j = 10 / 100
k = 1 + j 
l = i * k
Problem: if 0.4 of a number is equal to 0.07 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 7 : 40 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.4 a = 0.08 b â ‡ ” a / b = 0.07 / 0.40 = 7 / 40 . â ˆ ´ a : b = 7 : 40 . answer b"
Answer: b
Python program:
a = 0 * 7
b = 0 * 4
c = a / b
Problem: sixty 5 percent of a number is 21 less than 4 fifth of that number . what is the number
Options: a ) 140 , b ) 165 , c ) 150 , d ) 142 , e ) 174
Rationale: let the number be x . then , 4 * x / 5 – ( 65 % of x ) = 21 4 x / 5 – 65 x / 100 = 21 5 x = 2100 x = 140 . answer a 140
Answer: a
Python program:
a = 21 * 100
b = 3 * 5
c = a / b
Problem: a wooden cube whose edge length is 7 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 59.8 % , b ) 63.6 % , c ) 67.2 % , d ) 70.5 % , e ) 73.6 %
Rationale: "there are a total of 7 * 7 * 7 = 343 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 5 * 5 * 5 = 125 cubes . the number of cubes with at least one side painted red is 343 - 125 = 218 cubes the probability that a cube has at least one side painted red is 218 / 343 which is about 63.6 % the answer is b ."
Answer: b
Python program:
a = 1 * 4
b = volume_cube / (
c = 1 - b
d = 100 * c
Problem: two numbers a and b are such that the sum of 7 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 9 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 7 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 7 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 7 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 21 a + 12 b = 12 a + 16 b ⇒ 9 a = 4 b ⇒ ab = 4 / 9 ⇒ a : b = 4 : 9 answer : option c"
Answer: c
Python program:
a = 8 / 100
b = a * 4
c = b / 3
d = 4 / 100
e = c - d
f = 7 / 100
g = 6 / 100
h = g * 4
i = h / 3
j = f - i
k = e / j
Problem: the average weight of a class is x pounds . when a new student weighing 50 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 85 pounds . answer : a ."
Answer: a
Python program:
a = 50 + 4 
b = 4 + 1 
c = a + b
Problem: the speed of a car is 140 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 75 kmph , c ) 30 kmph , d ) 90 kmph , e ) 82 kmph
Rationale: "s = ( 140 + 40 ) / 2 = 90 kmph answer : d"
Answer: d
Python program:
a = 140 + 40 
b = a / 2
Problem: a train of 50 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 4.5 , e ) 2
Rationale: "d = 50 * 60 + 1500 = 3000 m t = 4500 / 60 * 18 / 5 = 270 sec = 4.5 mins answer : d"
Answer: d
Python program:
a = 50 + 1 
b = a * 60
c = b / 1000
d = c + 1
Problem: how much space , in cubic units , is left vacant when maximum number of 5 x 5 x 5 cubes are fitted in a rectangular box measuring 10 x 15 x 18 ?
Options: a ) 50 , b ) 150 , c ) 250 , d ) 350 , e ) 450
Rationale: "no of cubes that can be accommodated in box = ( 10 * 15 * 18 ) / ( 5 * 5 * 5 ) 15 * 10 in numerator can be perfectly divided by 5 * 5 in denominator . side with length 18 ca n ' t be perfectly divided by 5 and hence is the limiting factor . closet multiple of 5 less that 18 is 15 . so vacant area in cube = = 15 * 10 * ( 18 - 15 ) = 15 * 10 * 3 = 450 ans - e"
Answer: e
Python program:
a = 4 * 0
b = 10 - a
c = 15 * 18
d = b * c
Problem: 12 buckets of water fill a tank when the capacity of each bucket is 49 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 7 litres ?
Options: a ) 39 , b ) 84 , c ) 80 , d ) 82 , e ) 86
Rationale: capacity of the tank = ( 12 ã — 49 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 49 / 7 = 12 ã — 7 = 84 answer is b
Answer: b
Python program:
a = 49 * 12
b = a / 7
Problem: if n is an integer and 101 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 101 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b"
Answer: b
Python program:
a = 8100 / 101
b = math.sqrt(a)
c = math.floor(b)
Problem: if the perimeter of a rectangular garden is 950 m , its length when its breadth is 100 m is ?
Options: a ) 338 m , b ) 778 m , c ) 375 m , d ) 276 m , e ) 971 m
Rationale: "2 ( l + 100 ) = 950 = > l = 375 m answer : c"
Answer: c
Python program:
a = 950 / 2
b = a - 100