euclaise/mathqa_programs huggingface dataset:
Problem: if n = 2 ^ 0.3 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3
Rationale: "30 / 100 = 3 / 10 n = 2 ^ 3 / 10 n ^ b = 2 ^ 4 ( 2 ^ 3 / 10 ) ^ b = 2 ^ 4 b = 40 / 3 answer : e"
Answer: e
Python program:
a = math.log(16)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: the average mark of the students of a class in a particular exam is 90 . if 3 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?
Options: a ) 25 , b ) 35 , c ) 23 , d ) 22 , e ) 33
Rationale: "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 3 ) students = 80 ( x - 3 ) 90 x - ( 3 * 40 ) = 95 ( x - 3 ) 165 = 5 x = > x = 33 answer : e"
Answer: e
Python program:
a = 95 * 3
b = 3 * 40
c = a - b
d = 95 - 90
e = c / d
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 6.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 14 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.065 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 65 f - - > s = 6 f - - > f / s = 1 / 6 - - > f / ( s + f ) = 1 / ( 1 + 6 ) = 1 / 7 = 0.14 . answer : b .
Answer: b
Python program:
a = 3 - 5
b = 6 - 5
c = a / b
d = c * 100
Problem: machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 7 hours . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?
Options: a ) 8 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 420 minutes , so its rate is 1 / 420 of the work per minute . the combined rate is 20 / 420 = 1 / 21 so the work will be completed in 21 minutes . the answer is b .
Answer: b
Python program:
a = 1 / 7
b = 1 / 7
c = 3 * b
d = a + c 
e = 1 / 7
f = 1 / 7
g = 3 * f
h = e + g 
i = d + h 
j = 1 / 7
k = 1 / 7
l = 3 * k
m = j + l 
n = 3 * m
o = i + n 
p = 1 / o
q = p * const_60
Problem: in a company the manager wants to give some gifts to all of the workers . in each block there are about 200 workers are there . the total amount for giving the gifts for all the workers is $ 6000 . the worth of the gift is 2 $ . how many blocks are there in the company ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 20 , e ) 15
Rationale: "each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e"
Answer: e
Python program:
a = 6000 / 2
b = a / 200
Problem: a 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 500 , b ) 289 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 48 = 50 / 3 3 ( x + 300 ) = 2400 è x = 500 m . answer : a"
Answer: a
Python program:
a = 300 / 18
b = a * 48
c = b - 300
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 12 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 12 x = 45 - - > 28 / 25 * x = 45 - - > x = 45 * 25 / 28 = 1125 / 28 = ~ 40 answer : c ."
Answer: c
Python program:
a = 100 + 12 
b = 100 / a
c = b * 45
Problem: what is the average ( arithmetic mean ) of the numbers 100 , 150 , 200 , 200 , 250 , and 300 ?
Options: a ) 100 , b ) 150 , c ) 140 , d ) 200 , e ) 250
Rationale: "{ 100 , 150 , 200 , 200 , 250 , 300 } = { 200 - 100,200 - 50 , 200 , 200,200 + 50,200 + 100 } - - > the average = 200 . answer : d ."
Answer: d
Python program:
a = 100 + 200 
b = 200 - 100
c = b / 100
d = c + 1 
e = a * d
f = e / 2
g = 200 - 100
h = g / 100
i = h + 1 
j = f / i
Problem: andrew purchased 14 kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1376 , c ) 1456 , d ) 1900 , e ) 1566
Rationale: "cost of 14 kg grapes = 54 × 14 = 756 . cost of 10 kg of mangoes = 62 x 10 = 620 . total cost he has to pay = 756 + 620 = 1376 b"
Answer: b
Python program:
a = 14 * 54
b = 10 * 62
c = a + b
Problem: two trains move in the same direction at speeds 50 kmph and 32 kmph respectively . a man in the slower train observes that 15 seconds elapse before the faster train completely passes by him . what is the length of faster train ?
Options: a ) 100 m , b ) 75 m , c ) 120 m , d ) 50 m , e ) 70 m
Rationale: since both trains move in same direction so : average speed = 50 - 32 = 18 kmph = 5 mps speeed = length of train / time length of train = 5 * 15 = 75 m answer : b
Answer: b
Python program:
a = 50 - 32
b = a * const_0_2778
c = b * 15
Problem: what will be the fraction of 30 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 3 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 30 * 1 / 100 = 3 / 10 option c"
Answer: c
Python program:
a = 30 / 2
b = circle_area / (
Problem: jacob is 39 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 63 , b ) 64 , c ) 65 , d ) 76 , e ) 67
Rationale: "j = 39 ; j = 3 b ; b = 39 / 3 = 13 ; twice as old so b = 13 ( now ) + ( 13 ) = 26 ; jacob is 39 + 26 = 65 answer : c"
Answer: c
Python program:
a = 39 * 3
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph ?
Options: a ) 21.4 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 42 * 5 / 18 = 11.7 mps t = 250 / 11.7 = 21.4 sec answer : a"
Answer: a
Python program:
a = 150 + 100 
b = 42 * const_0_2778
c = a / b
Problem: two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 30 sec , c ) 40 sec , d ) 20 s , e ) 50 sec
Rationale: d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 s .
Answer: d
Python program:
a = 280 + 120 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: a student is ranked 6 th from right and 5 th from left . how many students are there in totality ?
Options: a ) 10 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 6 , from left 5 total = 6 + 5 - 1 = 10 answer : a"
Answer: a
Python program:
a = 6 + 5 
b = a - 1
Problem: if 6 men can reap 60 acres of land in 10 days , how many acres of land can 12 men reap in 20 days ?
Options: a ) 120 , b ) 360 , c ) 240 , d ) 182 , e ) 1000
Rationale: "6 men 60 acres 10 days 12 men ? 20 days 60 * 12 / 6 * 20 / 10 60 * 2 * 2 60 * 4 = 240 answer : c"
Answer: c
Python program:
a = 12 / 6
b = 20 / 10
c = a * b
d = 60 * c
Problem: solve for x and check : 15 x = 165
Options: a ) 98 , b ) 165 , c ) 180 , d ) 253 , e ) none of these
Rationale: solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b
Answer: b
Python program:
a = 165 / 15
b = 15 * a
Problem: if ram and gohul can do a job in 10 days and 15 days independently . how many days would they take to complete the same job working simultaneously ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 7 , e ) 6
Rationale: "if total work is x . ram rate of working = x / 10 per day . gohul rate of working = x / 15 per day . rate of work = ( x / 10 ) + ( x / 15 ) = 30 x / 5 x = 6 days answer is option e"
Answer: e
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1/(c)
Problem: what will be the difference between simple and compound interest at 8 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 64.19 , b ) 64.12 , c ) 40.5 , d ) 64.1 , e ) 64.11
Rationale: "s . i . = ( 1000 * 8 * 4 ) / 100 = rs . 320 c . i . = [ 1000 * ( 1 + 8 / 100 ) 4 - 1000 ] = rs . 360.5 difference = ( 360.5 - 320 ) = rs . 40.5 answer : c"
Answer: c
Python program:
a = 8 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 8 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 40 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 67.5
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 40 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 40 = 180 / 4 t t = 67.5 b - c = 67.5 mph answer e"
Answer: e
Python program:
a = 120 / 2
b = a + 120 
c = b / 40
d = c / 4
e = 120 / 2
f = d * e
Problem: company x sells a selection of products at various price points . listed below are unit sales made for one particular day . how many unit sales on that day were greater than the mean sale price but less than the median sale price ? $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: taking the prices of products in ascending order ( already arranged ) $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239 we see that median value is the 6 th value as there in total 11 values given arithmetic mean = total / number of entries = 1428 / 11 = 129.8181 we are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $ 120 and $ 129.81 , answer is 1 unit correct answer - b
Answer: b
Python program:
a = 50 + 50 
b = a + 97 
c = b + 97 
d = c + 97 
e = d + 120 
f = e + 125 
g = f + 155 
h = g + 199 
i = h + 199 
j = i + 239 
k = 10 + 1 
l = j / k
m = 50 + 50 
n = m + 97 
o = n + 97 
p = o + 97 
q = p + 120 
r = q + 125 
s = r + 155 
t = s + 199 
u = t + 199 
v = u + 239 
w = 10 + 1 
x = v / w
y = l / x
Problem: the average age of an adult class is 40 years . 15 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 15 x 32 = ( y + 15 ) x 36 â ‡ ’ 40 y + 480 = 36 y + 540 â ‡ ’ 4 y = 60 â ˆ ´ y = 15 c"
Answer: c
Python program:
a = 40 - 4
b = 15 * a
c = 15 * 32
d = b - c
e = d / 4
Problem: if log 10 2 = 0.3010 , then log 2 10 is equal to :
Options: a ) 100 / 6 , b ) 289 / 4 , c ) 128 / 7 , d ) 456 / 6 , e ) 1000 / 301
Rationale: explanation : log 2 10 = 1 / log 102 = 1 / 0.3010 = 10000 / 3010 = 1000 / 301 answer e
Answer: e
Python program:
a = 1 / 0
Problem: find two integers , neither of which ends in a zero , and whose product is exactly 00000
Options: a ) 64 and 15,625 , b ) 32 and 3,125 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625
Rationale: 1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b
Answer: b
Python program:
a = 100 * 1000
b = math.log(a)
c = math.log(10)
d = b / c
e = 100 * 1000
f = math.log(e)
g = math.log(10)
h = f / g
i = h - 1
j = d ** i
k = j + 0
Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: a = { 4,5 , 6,7 , 8,9 , 10,11 , 12,13 , 14,15 } b = { 6 , 7,8 , 9,10 , 11,12 . . . 20 } thus we see that there are 10 distinct integers that are common to both . e is the correct answer .
Answer: e
Python program:
a = 6 + 4
Problem: what is the probability that the sum of two dice will yield a 9 , and then when both are thrown again , their sum will again yield a 9 ? assume that each die has 8 sides with faces numbered 1 to 8 .
Options: a ) 1 / 64 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Rationale: "solution - rolling dices is an independent event . the combinations to get 9 are ( 1,8 ) , ( 8,1 ) , ( 2,7 ) , ( 7,2 ) , ( 3,6 ) , ( 6,3 ) , ( 4,5 ) , ( 5,4 ) , and total combinations of both dices is 64 . the probability of getting 9 in first attempt is 8 / 64 = 1 / 8 . probability of getting 9 again in second attempt = ( 1 / 8 ) * ( 1 / 8 ) = 1 / 64 . ans a"
Answer: a
Python program:
a = 8 ** 2
b = 8 / a
c = 8 ** 2
d = 8 / c
e = b * d
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 20 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 20 = 80 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 80 / 100 ) * 100 = ( 0.8 ) * 100 = 80 % . e"
Answer: e
Python program:
a = 100 - 20
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent q of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is q = 40 % of 80 hence , d is the answer"
Answer: d
Python program:
a = 80 / 2
Problem: how many two - digit numbers yield a remainder of 1 when divided by both 4 and 17 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: easier to start with numbers that are of the form 17 p + 1 - - - > 18 , 35,52 , 69,86 . out of these , there is only one ( 69 ) is also of the form 4 q + 1 . thus 1 is the answer . b is the correct answer .
Answer: b
Python program:
a = 17 * 4
b = 1 + a 
c = 17 * 4
d = b - c
Problem: the cost of an article is decreased by 20 % . if the original cost is $ 120 , find the decrease cost .
Options: a ) 33 , b ) 11 , c ) 96 , d ) 36 , e ) 91
Rationale: "original cost = $ 120 decrease in it = 20 % of $ 120 = 20 / 100 ã — 120 = 2400 / 100 = $ 24 therefore , decrease cost = $ 120 - $ 24 = $ 96 answer : c"
Answer: c
Python program:
a = 120 * 20
b = a / 100
Problem: 3 log 3 ( - 5 ) = ?
Options: a ) 1 , b ) undentified , c ) 3 , d ) 7 , e ) 5
Rationale: "since - 5 is not in the domain of function log 3 ( x ) , 3 log 3 ( - 5 ) is undefined correct answer b"
Answer: b
Python program:
a = 3 * 3
b = math.log(a)
c = math.log(10)
d = b / c
Problem: a cylinder with 6 meter radius and 12 meter height is filled to capacity with water . if the content of the cylinder is used to fill several smaller cylinders of 4 meter diameter and 8 meter height , how many smaller cylinders will be filled to capacity ?
Options: a ) 13
b ) 12
c ) 4
d ) 16
e ) 18
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 1357.17 smaller cylinder volume = 100.53 therefore the number of cylinders b that can be filled to capacity = 1357.17 / 100.53 = 13.5 answer is a only 13 smaller cylinders can be filled to capacity .
Answer: a
Python program:
a = volume_cylinder / (
Problem: sonika deposited rs . 12000 which amounted to rs . 19500 after 4 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 20940 , b ) 21009 , c ) 23000 , d ) 23450 , e ) 30000
Rationale: "( 12000 * 4 * 3 ) / 100 = 1440 19500 - - - - - - - - 20940 answer : a"
Answer: a
Python program:
a = 3 / 100
b = 19500 - 12000
c = b / 4
d = c / 12000
e = a + d 
f = e * 12000
g = f * 4
h = g + 12000
Problem: 8 k 8 + k 88 - - - - - - - - 16 y 6 if k and y represent non - zero digits within the integers above , what is y ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17
Rationale: 8 k 8 k 88 - - - - - - - - 16 y 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and y = 6 . answer : a .
Answer: a
Python program:
a = 16 * 100
b = a + 6 
c = 8 * 100
d = c + 8 
e = d + 88 
f = b - e
g = f / 10
h = 10 + 1 
i = g / h
j = math.floor(i)
Problem: a rectangular garden is to be twice as long as it is wide . if 900 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 200 , e ) 300
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 900 so , 2 ( l + b ) = 900 or , l + b = 450 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 200 l = 200 ; b = 100 l + b = 300 ( e ) 300 l = 300 ; b = 150 l + b = 450 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )"
Answer: e
Python program:
a = 2 + 1 
b = a * 2
c = 900 / b
d = c * 2
Problem: if x is an integer and 2.134 × 10 ^ x is less than 2 , 100,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 6 2.134 × 10 ^ 6 = 2 , 134,000 > 2 , 100,000 so , x = 5 answer : c"
Answer: c
Python program:
a = 2 / 2
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: a man can do a piece of work in 8 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 4 4 / 5 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 8 = 5 / 24 son alone can do the work in 24 / 5 days = 4 4 / 5 days answer is c"
Answer: c
Python program:
a = 4 * 0
b = 8 - 3
c = a / b
Problem: caleb and kyle built completed the construction of a shed in 10 and half days . if they were to work separately , how long will it take each for each of them to build the shed , if it will take caleb 2 day earlier than kyle ?
Options: a ) 10 and 12 , b ) 9 and 11 , c ) 20 and 22 , d ) 8 and 10 , e ) 19 and 21
Rationale: work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two workers would complete a job in 12 days . this means that ( individually ) each of them would take more than 10 days to do the job . answers e , a and c are illogical , since the individual times must both be greater than 10 days . so we can test the values for answers b and d . using the values for answers b and d . . . answer b : ( 20 ) ( 22 ) / ( 20 + 22 ) = 440 / 42 = 10.5 this is a match final answer : c
Answer: c
Python program:
a = 10 * 2
b = a + 2 
c = 10 * 10
d = 10 * 2
e = c * d
f = b + e
Problem: in a manufacturing plant , it takes 36 machines 8 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 8 * 36 / 72 * 12 / 8 = 6 ans b"
Answer: b
Python program:
a = 36 * 12
b = a * 8
c = b / 72
d = c / 8
Problem: what is the smallest positive integer x such that 864 x is the cube of a positive integer
Options: a ) 6 , b ) 12 , c ) 9 , d ) 5 , e ) 2
Rationale: "given 864 x is a perfect cube so we will take 1728 = 12 * 12 * 12 864 x = 1728 x = 1728 / 864 = 2 correct option is e"
Answer: e
Python program:
a = 3 + 4
Problem: at the beginning of the year , the ratio of boys to girls in high school x was 3 to 4 . during the year , 10 boys and twice as many girls transferred to another high school , while no new students joined high school x . if , at the end of the year , the ratio of boys to girls was 4 to 5 , how many boys were there in high school x at the beginning of the year ?
Options: a ) 70 , b ) 120 , c ) 100 , d ) 90 , e ) 110
Rationale: let the total number of boys and girls at the beginning of the year be 3 x and 4 x respectively . now 10 boys and 20 girls are transferred to another school . thus no . of boys and girls students left in the school x are 3 x - 10 and 4 x - 20 respectively . the ratio of these boys and girls students = 4 / 5 thus we have ( 3 x - 10 ) / ( 4 x - 20 ) = 4 / 5 15 x - 50 = 16 x - 80 x = 30 thus total no . of boys at the beginning of the year = 4 ( 30 ) = 120 answer is option b
Answer: b
Python program:
a = 10 * 4
b = a * 3
Problem: the total number of digits used in numbering the pages of a book having 360 pages is
Options: a ) 972 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 261 ) = ( 9 + 180 + 783 ) = 972 . answer : a"
Answer: a
Python program:
a = 360 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
Problem: 222 , 224 , 228 , 234 , 242 , ( . . . . )
Options: a ) 260 , b ) 258 , c ) 252 , d ) 250 , e ) 244
Rationale: "explanation : the pattern is 2 , 4 , 6 , 8 , 10 , etc . hence 10 = 252 answer : c"
Answer: c
Python program:
a = negate - (
Problem: a 2000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 48
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 1,000 by that net inflow to get the minutes ) - 12 min . answer b ."
Answer: b
Python program:
a = 6 + 4 
b = a + 2 
c = 2000 / 2
d = b * c
e = d / 1000