euclaise/mathqa_programs huggingface dataset:
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 96 . what is sum of the numbers ?
Options: a ) 48 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 96 = > 12 x = 96 = > x = 96 / 12 = 8 sum of the numbers = 3 x + 4 x = 7 x = 7 x 8 = 56 answer : option b"
Answer: b
Python program:
a = 3 * 4
b = a * 100
c = 4 * 96
d = b + c
Problem: x ^ y + y ^ x = 2408 find the values of x ?
Options: a ) 2407 , b ) 2408 , c ) 2409 , d ) 2405 , e ) 32
Rationale: 2407 ^ 1 + 1 ^ 2407 = 2408 answer : a
Answer: a
Python program:
a = 2408 - 1
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 10.6 , b ) 5.2 , c ) 10.8 , d ) 5.4 , e ) 5.0
Rationale: "speed downstream = ( 20 + 6 ) = 26 kmph time = 24 minutes = 12 / 60 hour = 1 / 5 hour distance travelled = time × speed = 1 / 5 × 26 = 5.20 km answer is b ."
Answer: b
Python program:
a = 20 + 6 
b = 12 / const_60
c = a * b
Problem: 15 litres of mixture contains 20 % alcohol and the rest water . if 5 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 15 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 5 = 20 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 20 = 15 % answer is c"
Answer: c
Python program:
a = 15 + 5 
b = 100 - 20
c = b / 100
d = c * 15
e = d + 5 
f = a - e
g = 15 + 5 
h = f / g
i = h * 100
Problem: 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 . 1111 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 50 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1111 96 + 225 + 490 + 6 x = 1111 6 x = 300 = > x = 50 . answer : d"
Answer: d
Python program:
a = 16 * 6
b = 1111 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ?
Options: a ) 64 , b ) 32 , c ) 46 , d ) 75 , e ) 47
Rationale: b 32 the total of three numbers must be 48 x 3 = 144 . the total of two numbers must be 56 x 2 = 112 . therefore , 144 - 112 = 32 .
Answer: b
Python program:
a = 3 * 48
b = 2 * 56
c = a - b
Problem: by selling an article for $ 180 , a person gains $ 30 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 180 gain = $ 30 c . p . = 180 - 30 = 150 gain % = 30 / 150 * 100 = 20 % answer is d"
Answer: d
Python program:
a = 30 * 100
b = 180 - 30
c = a / b
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 13 : 1 , b ) 13 : 3 , c ) 13 : 8 , d ) 13 : 5 , e ) 13 : 2
Rationale: quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 4 + 21 / 4 = 13 / 2 = 6.5 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6.5 : 1.5 = 13 : 3 . answer : b
Answer: b
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 2 - g
i = 87 * 5
j = i / 100
k = 6 - j
l = h + k 
m = e / l
Problem: what is 2 / 5 of 5 / 9 of 1 / 2 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b"
Answer: b
Python program:
a = 2 / 5
b = 5 / 9
c = 1 / 2
d = b * c
e = a * d
Problem: john completes a piece of work in 10 days , rose completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 5 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days b )"
Answer: b
Python program:
a = 1 / 10
b = 1 / 40
c = a + b 
d = 1 / c
Problem: at a time a , do 20 % less work than b . if a do any work in 15 / 2 hour , then in how many hour b will finish work ?
Options: a ) 5 hour , b ) 11 / 2 hour , c ) 6 hour , d ) 13 / 2 hour , e ) 8 hour
Rationale: let b will finish a work in x hour . then , in x hour a , 80 / 100 = 4 / 5 work do ratio of work done by a and b = inverse ratio of time taken 4 / 5 : 1 = 2 / 15 : 1 / x 4 / 5 * 1 / x = 1 * 2 / 15 = 4 / 5 x = 2 / 15 ; x = 6 . time = 6 hour answer c
Answer: c
Python program:
a = 15 / 2
b = 20 / 100
c = 1 - b
d = a * c
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 10 so one day work of a and b together = 1 / 8 + 1 / 10 = 9 / 40 so total days required = 40 / 9 answer : b"
Answer: b
Python program:
a = 1 / 8
b = 1 / 10
c = a + b 
d = 1 / c
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units z digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : z . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Python program:
a = 9 * 2
b = a + 2 
c = b ** 2
Problem: 106 ã — 106 + 94 ã — 94 = ?
Options: a ) 20072 , b ) 20062 , c ) 10072 , d ) 20172 , e ) 10272
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1062 + 942 = ( 100 + 6 ) 2 + ( 100 â ˆ ’ 6 ) 2 = 2 ( 1002 + 62 ) = 2 ( 10000 + 36 ) = 20072 . answer : option a"
Answer: a
Python program:
a = 106 ** 2
b = a - 106
c = 94 ** 2
d = c - 94
e = b + d
Problem: in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 1040 , b ) 2080 , c ) 3120 , d ) 4160 , e ) none of these
Rationale: "number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c"
Answer: c
Python program:
a = 6400 * 65
b = a / 100
c = 100 - 25
d = c / 100
e = b * d
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?
Options: a ) 1 / 7 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a ."
Answer: a
Python program:
a = 100 - 80
b = 100 + 75 
c = a / b
d = 5 / 4
e = c * d
Problem: 9 . the least number which should be added to 28523 so that the sum is exactly divisible by 3 , 5 , 7 and 8 is
Options: a ) 41 , b ) 42 , c ) 32 , d ) 37 , e ) 39
Rationale: lcm of 3 , 5 , 7 and 8 = 840 28523 ÷ 840 = 33 remainder = 803 hence the least number which should be added = 840 - 803 = 37 answer : option d
Answer: d
Python program:
a = math.lcm(3, 5)
b = math.lcm(a, 7)
c = math.lcm(b, 8)
d = math.lcm(3, 5)
e = math.lcm(d, 7)
f = math.lcm(e, 8)
g = c - reminder
Problem: find the value of ( 75983 * 75983 - 45983 * 45983 / 30000 )
Options: a ) 129166 , b ) 121696 , c ) 126196 , d ) 121966 , e ) none of them
Rationale: "given expression = ( 75983 ) 2 - ( 45983 ) 2 / ( 75983 - 45983 ) = ( a - b ) 2 / ( a - b ) = ( a + b ) ( a - b ) / ( a - b ) = ( a + b ) = 75983 + 45983 = 121966 answer is d ."
Answer: d
Python program:
a = 75983 / 45983
b = a + 75983 
c = b * 45983
Problem: what is the value of 10 ^ 6 - 6 ^ 4 ?
Options: a ) 9 , 97,111 , b ) 9 , 97,322 , c ) 9 , 98,704 , d ) 9 , 98,851 , e ) 9 , 98,900
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer c"
Answer: c
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 10
d = c / 100
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ?
Options: a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 1250
i = h / 100
Problem: a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be
Options: a ) 740 % , b ) 540 % , c ) 640 % , d ) 140 % , e ) 240 %
Rationale: "explanation : let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d"
Answer: d
Python program:
a = 20 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: the salary of a worker is first increased by 10 % and afterwards reduced by 10 % . what is the net change in the worker ' s salary ?
Options: a ) 1 % increase , b ) 1 % decrease , c ) 2 % increase , d ) 2 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.9 ( 1.1 x ) = 0.99 x the answer is b ."
Answer: b
Python program:
a = 10 + 100 
b = 10 + 100 
c = b * 10
d = c / 100
e = a - d
f = 100 - e
Problem: 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 . 1051 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 40 , c ) 77 , d ) 99 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b"
Answer: b
Python program:
a = 16 * 6
b = 1051 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be :
Options: a ) rs . 1050 , b ) rs . 1400 , c ) rs . 3150 , d ) rs . 4200 , e ) none
Rationale: explanation : area of 4 walls of the room = [ 2 ( l + b ) × h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) × 3 h ] m 2 = 9 [ 2 ( l + b ) × h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 × 350 ) = rs . 3150 correct option : c
Answer: c
Python program:
a = 3 ** 2
b = 350 * a
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 123 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 18 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 123 6 x + 15 = 123 6 x = 108 x = 18 answer : d"
Answer: d
Python program:
a = 3 * 5
b = 123 - a
c = 3 * 2
d = b / c
Problem: kelsey travelled for 10 hours . he covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph . find the distance travelled by kelsey ?
Options: a ) 583 km , b ) 400 km , c ) 670 km , d ) 360 km , e ) 234 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 25 + ( x / 2 ) / 40 = 10 = > x / 50 + x / 80 = 10 = > ( 8 x + 5 x ) / 400 = 10 = > x = 400 km answer : b
Answer: b
Python program:
a = 1 / 40
b = 1 / 10
c = a + b 
d = 25 / c
e = d * 2
Problem: a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.8 x = 0.6 ( x + 30 ) 0.2 x = 6 x = 30 the answer is c ."
Answer: c
Python program:
a = 60 / 100
b = 30 * a
c = 40 / 100
d = 30 * c
e = b - d
f = 80 / 100
g = 60 / 100
h = f - g
i = e / h
Problem: lola has $ 240.00 in her checking account . she spent $ 180.00 . what percentage does she have left in her account ?
Options: a ) 75 % , b ) 50 % , c ) 40 % , d ) 55 % , e ) none of these
Rationale: explanation : amount left : 240 - 180 = 60 amount left percentage = ( 60 / 240 x 100 ) % = 25 % answer : e
Answer: e
Python program:
a = 240 - 180
b = a / 240
c = b * 100
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 5 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54
b ) 32
c ) 75
d ) 20
e ) 11
Rationale: a / 8 = 5 * 5 = > a = 5 * 5 * 8 x * 2 x = 5 * 5 * 8 x = 10 = > 2 x = 20 answer : d
Answer: d
Python program:
a = square_area * (
b = a / 8
c = 1/(2)
d = math.sqrt(b)
Problem: if the length of a rectangle is halved and its breadth is tripled , what is the percentage change in its area ?
Options: a ) 30
b ) 40
c ) 50
d ) 60
e ) 70
Rationale: length is halved . i . e . , length is decreased by 50 % breadth is tripled i . e . , breadth is increased by 200 % formula for change in area is : = ( - x + y - xy / 100 ) % = ( − 50 + 200 − 50 × 200 / 100 ) % = 50 % i . e . , area is increased by 50 % answer is c .
Answer: c
Python program:
a = 3 / 2
b = a - 1
c = b * 100
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8587 for a computer table , then what was the cost price of the computer table ?
Options: a ) 6925 , b ) 6887 , c ) 6728 , d ) 6725 , e ) 2871
Rationale: ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8587 ( 100 / 124 ) = rs . 6925 . answer : a"
Answer: a
Python program:
a = 24 / 100
b = 1 + a 
c = 8587 / b
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 25 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 20 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 25 = 75 km / hr time taken = 100 / 75 = 1 hr 20 min answer is b"
Answer: b
Python program:
a = 100 / 1
b = a - 25
c = 100 / b
Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 5 5 5 number of possibilities = 5 * 4 * 4 = 80 . then , just add up the number of 1 digits numbers = 4 , so total is 80 + 4 = 84 . answer : e"
Answer: e
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 90 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 20 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 90 % of republicans ( which is ( 60 * 0.9 ) = 54 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 60 ( 54 + 6 ) voters voted for candidate x and 40 voted for candidate y . thus we can infer that candidate x is expected to win the election by 20 ( 60 - 40 ) votes . therefore candidate x is expected to win the election by ( 20 / 100 ) votes which is equivalent to 20 % . i think the answer is e ."
Answer: e
Python program:
a = 15 / 100
b = a * 2
c = 90 / 100
d = c * 3
e = b + d 
f = 90 / 100
g = f * 3
h = 3 - g
i = 15 / 100
j = i * 2
k = 2 - j
l = h + k 
m = e - l
n = 3 + 2 
o = m / n
p = o * 100
Problem: a man can row downstream at 22 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 16 , 2 , b ) 16 , 4 , c ) 16 , 8 , d ) 16 , 6 , e ) 16 , 7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 22 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 6 . answer : d"
Answer: d
Python program:
a = 22 + 10 
b = a / 2
c = b / 2
Problem: if | 7 x + 2 | = 16 , then find the product of the values of x ?
Options: a ) - 5.14 , b ) 6.19 , c ) - 7.18 , d ) - 8.62 , e ) 5.69
Rationale: "| 7 x + 2 | = 16 7 x + 2 = 16 or 7 x + 2 = - 16 7 x = 14 or 7 x = - 18 x = 2 or x = - 2.57 product = - 2.57 * 2 = - 5.14 answer is a"
Answer: a
Python program:
a = 16 - 2
b = a / 7
Problem: the cost of an article is decreased by 15 % . if the original cost is $ 80 , find the decrease cost .
Options: a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 91
Rationale: "original cost = $ 80 decrease in it = 15 % of $ 80 = 15 / 100 × 80 = 1200 / 100 = $ 12 therefore , decrease cost = $ 80 - $ 12 = $ 68 answer : c"
Answer: c
Python program:
a = 80 * 15
b = a / 100
Problem: sandy bought 65 books for $ 1280 from one shop and 55 books for $ 880 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 12 , b ) $ 14 , c ) $ 16 , d ) $ 18 , e ) $ 20
Rationale: "average price per book = ( 1280 + 880 ) / ( 65 + 55 ) = 2160 / 120 = $ 18 the answer is d ."
Answer: d
Python program:
a = 1280 + 880 
b = 65 + 55 
c = a / b
Problem: each of the integers from 0 to 8 , inclusive , is written on a separate slip of blank paper and the 10 slips are dropped into hat . if the slips are then drawn one at a time without replacement , how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: you should consider the worst case scenario : if you pick numbers 0 , 1 , 2 , 3 , 4 and 5 then no two numbers out of these 6 add up to 10 . now , the next , 7 th number whatever it ' ll be ( 6,7 , or 8 ) will guarantee that two number will add up to 10 . so , 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 answer : c
Answer: c
Python program:
a = 8 - 2
b = 1 + a
Problem: at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 7 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 25 c"
Answer: c
Python program:
a = 44 / 3
b = math.floor(a)
c = b * 3
d = c + 20 
e = 44 / 7
f = math.floor(e)
g = f * 7
h = d - g
i = h + 3
Problem: an ore contains 25 % of an alloy that has 90 % iron . other than this , in the remaining 75 % of the ore , there is no iron . how many kilograms of the ore are needed to obtain 60 kg of pure iron ?
Options: a ) 250 kg , b ) 275 kg , c ) 300 kg , d ) 266.66 kg , e ) none
Rationale: solution : let there is 100 kg of ore . 25 % ore contains 90 % off iron that means 25 kg contains ; 25 * 90 / 100 = 22.5 kg iron . 22.5 kg iron contains 100 kg of ore . then , 1 kg of iron contains = 25 / 100 kg ore ; hence , 60 kg iron contains = 100 * 60 / 22.5 = 266.66 kg ore . answer : option d
Answer: d
Python program:
a = 100 * 60
b = 25 * 90
c = b / 100
d = a / c
Problem: how many integers are between 5 and 74 / 5 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . the different integers between 5 and 74 / 5 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 . total number of integers = 10 option e"
Answer: e
Python program:
a = 74 / 5
b = a - 5
c = b + 1
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 8 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1557.9 , c ) 1378 , d ) 1635 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 8 x + 15 7 x = 1350 x = 192.9 large number = 192.9 + 1365 = 1557.9 b"
Answer: b
Python program:
a = 1365 - 15
b = 8 - 1
c = a / b
d = c * 8
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 6 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 16 , e ) 24
Rationale: if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 24 , which also equals b . b is the second positive multiple of n , thus n = 24 / 2 = 12 . the answer is c .
Answer: c
Python program:
a = 6 * 4
b = a / 2
Problem: cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 3 : 7 , c ) 2 : 5 , d ) 1 : 8 , e ) 1 : 5
Rationale: "2 % is 1 % - points below 3 % and 11 % is 8 % - points above 3 % . the ratio of a : b should be 1 : 8 . the answer is d ."
Answer: d
Python program:
a = 3 - 2
b = 11 - 3
c = a / b
Problem: in a class of 20 students , 2 students did not borrow any books from the library , 10 students each borrowed 1 book , 5 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 10 * 1 + 5 * 2 = 20 books . the 3 students who borrowed at least three books borrowed 40 - 20 = 20 books . if 2 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 20 - 6 = 14 books . the answer is c ."
Answer: c
Python program:
a = 20 * 2
b = 10 * 1
c = b + 5 
d = c + 2 
e = 20 - d
f = e - 1
g = f * 3
h = 10 * 1
i = 5 * 2
j = h + i 
k = g + j 
l = a - k