euclaise/mathqa_programs huggingface dataset:
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 2.5 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 ?
Options: a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 55 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 2.5 = 40 % they worked together for 1 hour and finished 73 % of the job remaining = 27 % tom will complete 40 % in 60 minutes , 20 % in 30 minutes and , 7 % in 60 * 7 / 40 minutes = 10.5 minutes time taken by tom to finish the remaining on his own = 30 + 10.5 = 40.5 minutes ( adjusting for the 0.333 ) ~ 40 minutes answer : c"
Answer: c
Python program:
a = 1 / 3
b = 1 / 2
c = a + b 
d = 1 - c
e = 1 / 2
f = d / e
g = f * const_60
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 200 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Python program:
a = 350 - 340
b = 5 / 100
c = a / b
Problem: the current of a stream runs at the rate of 3 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7.24 , b ) b ) 2 , c ) c ) 8.5 , d ) d ) 6.67 , e ) e ) 3
Rationale: "s = 3 m = x ds = x + 3 us = x - 3 6 / ( x + 3 ) + 6 / ( x - 3 ) = 2 x = 7.24 answer : a"
Answer: a
Python program:
a = 3 ** 2
b = a / 2
Problem: an article with cost price of 180 is sold at 15 % profit . what is the selling price ?
Options: a ) 198 , b ) 200 , c ) 204 , d ) 207 , e ) 210
Rationale: "sp = 1.15 * 180 = 207 answer : d"
Answer: d
Python program:
a = 15 / 100
b = 180 * a
c = 180 + b
Problem: the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c"
Answer: c
Python program:
a = 1800 + 150 
b = 15 + 1 
c = a * b
d = 1800 * 15
e = c - d
Problem: 8 machines , each working at the same constant rate , together can complete a certain job in 24 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 24 to 16 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 8 = 12 so we need 12 - 8 = 4 more machines . answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 8 * a
c = b / 24
d = 4 + 1 
e = c - d
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 52 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 62.5 % of the boy scouts arrived with signed permission slips , then what percentage of the children were girl scouts who arrived with signed permission slips ?
Options: a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31
Rationale: "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip ( since we only are concerned with percents in the answer ) 40 % were boy scouts so 40 % of 100 = 40 were boy scouts 62.5 % of the boy scouts brought their permission slips signed , so . 625 * 40 = 25 boy scouts had signed slips 15 boy scouts did not 52 % of all the scouts had signed slips , so . 52 * 100 = 52 in total had signed slips thus 52 - 25 = 27 girl scouts had signed slips thus the percentage of scouts who were girl scouts arriving with signed permission slips is 27 / 100 = . 27 = 27 % a"
Answer: a
Python program:
a = 40 * 62
b = a / 100
c = 52 - b
d = 100 - 40
e = c / d
f = e * 100
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
Options: a ) 10 % , b ) 33 1 / 3 % , c ) 40 % , d ) 50 % , e ) 66 2 / 3 %
Rationale: "assuming the weight of the mixture to be 100 g * * , then the weight of ryegrass in the mixture would be 30 g . also , assume the weight mixture x used in the mixture is xg , then the weight of mixture y used in the mixture would be ( 100 - x ) g . so we can now equate the parts of the ryegrass in the mixture as : 0.4 x + 0.25 ( 100 - x ) = 30 0.4 x + 25 - 0.25 x = 30 0.15 x = 5 x = 5 / 0.15 = 500 / 15 = 100 / 3 so the weight of mixture x as a percentage of the weight of the mixture = ( weight of x / weight of mixture ) * 100 % = ( 100 / 3 ) / 100 * 100 % = 33 % answer : b"
Answer: b
Python program:
a = 30 - 25
b = 40 / 100
c = 25 / 100
d = b - c
e = a / d
Problem: a , b and c invests rs . 4000 , rs . 3000 and rs . 2000 in a business . after one year b removed his money ; a and c continued the business for one more year . if the net profit after 2 years be rs . 2400 , then b ' s share in the profit is ?
Options: a ) 276 , b ) 289 , c ) 480 , d ) 400 , e ) 278
Rationale: "4 * 24 : 3 * 12 : 2 * 24 8 : 3 : 4 3 / 15 * 2400 = 480 answer : c"
Answer: c
Python program:
a = 3000 * 2
b = 2000 * 2
c = a + b 
d = 4000 + c 
e = 4000 / d
f = e * 4000
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water in ?
Options: a ) 10 hr , b ) 14 hr , c ) 12 hr , d ) 9 hr , e ) 15 hr
Rationale: "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b"
Answer: b
Python program:
a = 1 / 2
b = 2 * 3
c = b + 1 
d = c / 3
e = 1/(d)
f = a - e
g = 1/(f)
Problem: the cost of 16 pens and 8 pencils is rs . 352 and the cost of 4 pens and 4 pencils is rs . 96 . find the cost of each pen ?
Options: a ) rs . 32 , b ) rs . 28 , c ) rs . 36 , d ) rs . 25 , e ) none of these
Rationale: "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 16 p + 8 q = 352 - - - ( 1 ) 4 p + 4 q = 96 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 20 answer : e"
Answer: e
Python program:
a = 16 * 4
b = 16 + 4 
c = 352 / b
d = a * c
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 55 minutes ?
Options: a ) 80 , b ) 100 , c ) 150 , d ) 180 , e ) 220
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 55 minutes the population increases by 55 x 4 = 220 people . answer . e ."
Answer: e
Python program:
a = const_60 / 15
b = a * 55
Problem: five 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: in the junior basketball league there are 21 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 11 .
Rationale: "total teams = 21 bad teams = ( 1 / 3 ) * 21 = 7 rich teams = 10 so maximum value that the both rich and bad can take will be 10 . so e = 11 can not be that value . ans e ."
Answer: e
Python program:
a = 1 / 1
b = 21 * a
c = b + 1
Problem: a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a .
Options: a ) 500 , b ) 600 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is b"
Answer: b
Python program:
a = 4 + 3 
b = a + 1 
c = 1 / b
d = c * 1200
Problem: a can do a half of certain work in 60 days and b one third of the same in 35 days . they together will do the whole work in .
Options: a ) 56 days , b ) 420 days , c ) 46 days , d ) 560 days , e ) 96 days
Rationale: "a = 120 days b = 105 days 1 / 120 + 1 / 105 = 45 / 2520 = 1 / 56 = > 56 days answer : a"
Answer: a
Python program:
a = 60 * 2
b = 1/(a)
c = 35 * 3
d = 1/(c)
e = b + d
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 .
Options: a ) 6 , b ) 4 , c ) 0 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ."
Answer: b
Python program:
a = 1 + 4 
b = a ** 2
c = 15 + b 
d = 12 * 3
e = c - d
Problem: a merchant marks his goods up by 40 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 14 % , c ) 26 % , d ) 15 % , e ) 17 %
Rationale: "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 10 % on 126 . profit = 126 - 100 26 % answer c"
Answer: c
Python program:
a = 40 + 100 
b = 40 + 100 
c = b * 10
d = c / 100
e = a - d
f = e - 100
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a = 4.5 and b is a bit more than 2 , then a ^ 3 + b ^ 3 can equal 100 . if a > 5 , then a ^ 3 + b ^ 3 > 100 . the answer is c ."
Answer: c
Python program:
a = 1/(3)
b = 100 ** a
c = math.floor(b)
d = c * 10
e = 1/(3)
f = 100 ** e
g = math.floor(f)
h = g + 1 
i = d + h
Problem: the average age of 18 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 9 , b ) 31 , c ) 56 , d ) 72 , e ) 90
Rationale: age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c
Answer: c
Python program:
a = 18 * 15
b = 5 * 14
c = a - b
d = 9 * 16
e = c - d
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1800 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 16,200 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a"
Answer: a
Python program:
a = 112 / 8
b = 28 / a
c = 3 ** b
d = 1800 * c
Problem: a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 240 , b ) s . 140 , c ) s . 340 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 3
c = a + b 
d = 700 / c
e = d / 2
f = 1 / 2
g = 1 / 3
h = f + g 
i = 700 / h
j = i / 3
k = e - j
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 × ( 100 + 23.5 ) / ( 100 − 5 ) = 100 × 247 / 190 = 130 hence , required % profit = 130 – 100 = 30 % answer c"
Answer: c
Python program:
a = 100 + 23 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d"
Answer: d
Python program:
a = 10000 / 15000
Problem: 0.99999 + 0.11112 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111
Rationale: "0.99999 + 0.11112 = 0.99999 + 0.11111 + 0.00001 = ( 0.99999 + 0.00001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e"
Answer: e
Python program:
a = 0 / 99999
b = a * 100
Problem: the perimeter of one square is 40 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 11.2 √ 2 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 40 4 a = 20 a = 10 a = 5 a 2 = 100 a 2 = 25 combined area = a 2 = 125 = > a = 11.2 d = 11.2 √ 2 answer : a"
Answer: a
Python program:
a = 40 / 4
b = a ** 2
c = 20 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 860 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 680 , d ) s . 700 , e ) s . 720
Rationale: "s . i . for 1 year = rs . ( 860 - 815 ) = rs . 45 . s . i . for 3 years = rs . ( 45 x 3 ) = rs . 135 . principal = rs . ( 815 - 135 ) = rs . 680 . answer : option c"
Answer: c
Python program:
a = 860 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 874 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 638 , c ) s . 698 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 874 - 815 ) = rs . 59 . s . i . for 3 years = rs . ( 59 x 3 ) = rs . 177 . principal = rs . ( 815 - 177 ) = rs . 638 . answer : option b"
Answer: b
Python program:
a = 874 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 3 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 3 / 42
Rationale: 2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e
Answer: e
Python program:
a = 2 * 7
b = 1/(a)
Problem: find the quantities of two types of rice to be mixed , first variety is of rs . 12 per kg and second variety is of rs . 20 per kg . to get 12 kg of rice mixture worth rs . 15 per kg ? ( in kg )
Options: a ) 3.5 , 8.5 , b ) 7 , 5 , c ) 7.5 , 4.5 , d ) 8 , 4 , e ) 8 , 5
Rationale: from allegation & mixture ratio = c - m / m - d = 20 - 15 / 15 - 12 = 5 / 3 . from the option c r = 7.5 / 4.5 = 5 / 3 answer : c
Answer: c
Python program:
a = 12 * 15
b = 12 * 12
c = a - b
d = 20 - 12
e = c / d
f = 12 - e
g = math.floor(f)
Problem: there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 3 and for second = 2 so total methods = 3 * 2 = 6 answer : d"
Answer: d
Python program:
a = math.comb(3, 2)
b = math.comb(3, 2)
c = a + b
Problem: a boy is traveling from his house to school at 10 km / hr and reached school 2 hours late . next day he traveled 20 km / hr and reached 1 hour early . then find the distance between house and school ?
Options: a ) 50 km , b ) 45 km , c ) 33 km , d ) 60 km , e ) 54 km
Rationale: let distance be x s 1 = 10 km / hr s 2 = 20 km / hr t 1 = x / 10 hr t 2 = x / 20 hr difference in time = 2 + 1 = 3 hr ( x / 10 ) - ( x / 20 ) = 3 x = 60 km answer is d
Answer: d
Python program:
a = 2 * 10
b = a + 20 
c = 20 - 10
d = b / c
e = d + 2 
f = e * 10
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 285 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 415 , e ) none of these
Rationale: "average would be : 350 = ( 285 + x ) / 2 on solving , x = 415 . answer : d"
Answer: d
Python program:
a = 30 * 350
b = 15 * 285
c = a - b
d = c / 15
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.20 , what total number of apples and bananas did the customer purchase ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.20 until we get a multiple of $ 0.50 . $ 7.20 , $ 6.40 , $ 5.60 , $ 4.80 , $ 4.00 = 8 * $ 0.50 the customer purchased 8 bananas and 4 apples . the answer is c ."
Answer: c
Python program:
a = 0 * 80
b = 7 - 20
c = b / 0
d = c + 2
Problem: in the first 7 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 8.42 , c ) 8.3 , d ) 8.1 , e ) 6.21
Rationale: "required run rate = [ 282 - ( 4.2 * 7 ) ] / 30 = 252.60 / 40 = 8.42 answer : b"
Answer: b
Python program:
a = 7 * 4
b = 282 - a
c = b / 30
Problem: an empty tank be filled with an inlet pipe ‘ a ’ in 42 minutes . after 12 minutes an outlet pipe ‘ b ’ is opened which can empty the tank in 30 minutes . after 6 minutes another inlet pipe ‘ c ’ opened into the same tank , which can fill the tank in 35 minutes and the tank is filled . find the time taken to fill the tank ?
Options: a ) 51.6 , b ) 51.5 , c ) 51.7 , d ) 51.1 , e ) 51.0
Rationale: assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x × 5 + 6 × ( − 2 ) + 4 x = 210 x × 5 + 6 × ( − 2 ) + 4 x = 210 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 total time taken to fill the tank = 40.5 + 12 + 6 = 51.5 answer : b
Answer: b
Python program:
a = 30 + 35 
b = a + 42 
c = b - 2
d = c / 2
Problem: in a group of 50 people , 25 have visited iceland and 23 have visited norway . if 21 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Python program:
a = 25 + 23 
b = a - 21
c = 50 - b
Problem: a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ?
Options: a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3
Rationale: let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d
Answer: d
Python program:
a = 3 / 5
b = 4 / a
c = b - 4
Problem: set a of 8 positive integers may have the same element and have 37 . and set b of 8 positive integers must have different elements and have 37 . when m and n are the greatest possible differences between 37 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 37 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 30 and 37 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 9 . so , 30 - 9 = 21 . the correct answer is b .
Answer: b
Python program:
a = 8 + 2 
b = a + 8 
c = 37 - b
Problem: if 6 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 6 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 3 * 2 * 2 * 2 = 5 * n / 4 must be an integer for this to be true n must multiple of 4 , thus min of n = 4 hence b"
Answer: b
Python program:
a = math.lcm(6, 8)
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters q long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Python program:
a = 4 * 2
b = 4 * 1
c = a + b 
d = 15 - c
Problem: if the average of 8 x and 8 y is greater than 120 , and x is twice y , what is the least integer value of x ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 42
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 8 x and 4 x is greater than 120 . average of 8 x and 4 x is 6 x . so , 6 x > 120 x > 20 answer : a"
Answer: a
Python program:
a = 8 * 2
Problem: the batting average of a particular batsman is 61 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 202 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 – 2552 = 254 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer b"
Answer: b
Python program:
a = 61 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is ?
Options: a ) 377 , b ) 126 , c ) 111 , d ) 727 , e ) 121
Rationale: "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"
Answer: c
Python program:
a = 2 * 4107
b = 37 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 4107
f = d + e 
g = math.sqrt(f)