euclaise/mathqa_programs huggingface dataset:
Problem: linda spent 2 / 3 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 750 , b ) $ 350 , c ) $ 650 , d ) $ 550 , e ) $ 850
Rationale: "if linda spent 2 / 3 of her savings on furniture , the rest 3 / 3 - 2 / 3 = 1 / 3 on a tv but the tv cost her $ 250 . so 1 / 3 of her savings is $ 250 . so her original savings are 3 times $ 250 = $ 750 correct answer a"
Answer: a
Python program:
a = 2 / 3
b = 1 - a
c = 250 / b
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 188 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 470 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 188 = > 4 x / 10 = 188 = > 4 x = 1880 = > x = 470 . answer : d"
Answer: d
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 188 / c
Problem: in a classroom , 12 students brought apples and 8 students brought bananas . if exactly 10 students brought only one of the two types of fruits , how many students brought both types of fruits ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: say x students brought both fruits . ( 12 - x ) + ( 8 - x ) = 10 - - > x = 5 . answer : a .
Answer: a
Python program:
a = 12 + 8 
b = a / 4
Problem: the average ( arithmetic mean ) of the even integers from 20 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 10 to 140 inclusive ?
Options: a ) 40 , b ) 15 , c ) 35 , d ) 20 , e ) 25
Rationale: so , according to a mean of a set of even numbers from 20 to 60 = ( 20 + 60 ) / 2 = 40 and mean of a set of even numbers from 10 to 140 = ( 10 + 140 ) / 2 = 75 difference = 75 - 40 = 35 answer : c .
Answer: c
Python program:
a = 140 + 10 
b = a / 2
c = 60 + 20 
d = c / 2
e = b - d
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 option b"
Answer: b
Python program:
a = 26 - 6
b = a * 3
c = b / 4
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 38 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 205 , b ) 245 , c ) 285 , d ) 325 , e ) 365
Rationale: after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 8 miles per hour . the time to catch up is 60 / 8 = 7.5 hours . in 7.5 hours , train a travels another 30 * 7.5 = 225 miles for a total of 285 miles . the answer is c .
Answer: c
Python program:
a = 30 * 2
b = 38 - 30
c = a / b
d = c * 38
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 100 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?
Options: a ) 12.25 , b ) 44 , c ) 18 , d ) 16 , e ) 14
Rationale: let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 100 / 2 = 50 sq m l b = 50 i . e . , l * l / 3 = 150 l 2 = 150 = > l = 12.25 answer : a
Answer: a
Python program:
a = 100 / 2
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: if | x + 10 | = 10 what is the sum of all the values of x .
Options: a ) 20 , b ) 40 , c ) - 20 , d ) 0 , e ) - 40
Rationale: "there will be two cases x + 10 = 10 and x + 10 = - 10 solve for x = > x = 10 - 10 = > x = 0 or x = - 10 - 10 = > x = - 20 the sum of both values will be 0 + - 20 = - 20 answer is c"
Answer: c
Python program:
a = 10 + 10
Problem: anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 12 coconut doughnuts , and 10 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 34 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 12 + 12 + 10 = 34 . answer is b ."
Answer: b
Python program:
a = 12 + 12 
b = a + 10
Problem: a bowl was filled with 10 ounces of water , and 0.014 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 7 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 014 * 50 = . 014 * 100 / 2 = 1.4 / 2 = . 7 percent of the original amount of water evaporated during this period = ( . 7 / 10 ) * 100 % = 7 % answer d"
Answer: d
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: a and b play a game where each is asked to select a number from 1 to 16 . if the two numbers match , both of them win a prize . find the probability that they will not win a prize in a single trial .
Options: a ) 15 / 16 , b ) 1 / 16 , c ) 7 / 8 , d ) 9 / 8 , e ) none of these
Rationale: explanation : a and b win a prize , only if both a and b select the number . so , if a chooses a number , b has to select the same number . hence , it is problem on dependent event . let a select a number . , then p ( a ) = 1 / 16 = probability of a . now , b selects the same number after a has already selected that number . then , p ( b / a ) = 1 / 1 = dependent probability of b given a has occurred . p ( ab ) = probability of winning a prize by both a and b is : - = > p ( a ) x p ( ab ) . = > ( 1 / 16 ) x 1 = 1 / 16 . hence , the probability of not winning a prize is : - = 1 - ( 1 / 16 ) . = 15 / 16 . answer : a
Answer: a
Python program:
a = 16 - 1
b = a / 16
Problem: a family pays $ 700 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,500 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 700 + $ 400 = $ 1100 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 500 when the medical expenses are $ 1500 . the answer is c ."
Answer: c
Python program:
a = 1 - 0
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.50 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 30 + 90 = $ 1.20 cents on commodity y , which will take 12 years . the answer is d ."
Answer: d
Python program:
a = 90 / 100
b = 4 - 50
c = a + b 
d = 30 / 100
e = 4 - 50
f = d - e
g = c / f
h = 2001 + g
Problem: there are 20 poles with a constant distance between each pole . a car takes 20 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 34.4543 , b ) 34.5455 , c ) 34.45128 , d ) 34.51288 , e ) 34.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 20 seconds 1 pole ( 20 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 20 / 11 ) seconds = 34.5455 seconds answer : b"
Answer: b
Python program:
a = 20 / 12
b = a * 20
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: firstly calculate the number of even integers between 99 and 301 : no of even integers = ( 300 - 100 ) / 2 + 1 = 101 avg of the even integers is ( 100 + 300 ) / 2 = 200 . the sum would be = no of even integers * avg . = = > 101 * 202 = 20,200 answer b .
Answer: b
Python program:
a = 301 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: what percent of 500 is 125 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "500 * x / 100 = 125 x = 125 / 5 x = 25 ans : c"
Answer: c
Python program:
a = 500 / 125
b = a * 100
Problem: a number is increased by 40 % and then decreased by 40 % . find the net increase or decrease per cent .
Options: a ) 19 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: "let the number be 100 . increase in the number = 40 % = 40 % of 100 = ( 40 / 100 × 100 ) = 40 therefore , increased number = 100 + 40 = 140 this number is decreased by 40 % therefore , decrease in number = 40 % of 140 = ( 40 / 100 × 140 ) = 5600 / 100 = 56 therefore , new number = 140 - 56 = 84 thus , net decreases = 100 - 84 = 16 hence , net percentage decrease = ( 16 / 100 × 100 ) % = ( 1600 / 100 ) % = 16 % answer : e"
Answer: e
Python program:
a = 40 + 100 
b = 100 - 40
c = a * b
d = c / 100
Problem: a man buys an article for $ 20 . and sells it for $ 25 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %
Rationale: "c . p . = $ 20 s . p . = $ 25 gain = $ 5 gain % = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Python program:
a = 20 / 100
b = 25 / a
c = b - 100
Problem: add 20 % of 40 and 25 % of 60 .
Options: a ) 9.5 , b ) 23 , c ) 25 , d ) 22 , e ) 15
Rationale: "20 % of 40 + 25 % of 60 40 * 20 / 100 + 60 * 25 / 100 8 + 15 = 23 answer b"
Answer: b
Python program:
a = 20 * 40
b = a / 100
c = 25 * 60
d = c / 100
e = b + d
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 800 , e ) 400
Rationale: we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 40 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 800 = 20 t 19 t + 800 = 20 t 800 = t there are a total of 800 students in the math class . answer is d .
Answer: d
Python program:
a = 1 / 5
b = 1 / 4
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 40 / f
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 8 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: to get 40 points as end of season we need another 32 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 hence option d - 9
Answer: d
Python program:
a = 40 - 8
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 12
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : on dividing 427398 by 12 we get the remainder 6 , so 6 should be subtracted answer : option c
Answer: c
Python program:
a = 427398 / 12
b = math.floor(a)
c = b * 12
d = 427398 - c
Problem: charges made by two companies for the same a / c company xcompany y price $ 575 $ 530 surcharge as a percent of price 4 % 3 % installation charge $ 82.50 $ 93.00 the table above shows the various charges made by two companies for the same air conditioner . what is the total amount that can be saved on the purchase and installation of the air conditioner by dealing with the company that offers the lower total charge ?
Options: a ) $ 41.60 , b ) $ 45.00 , c ) $ 50.75 , d ) $ 55.75 , e ) $ 61.25
Rationale: looking at the values / percentage , its clear that company x costlier than company y just observed the oa ; they have 4 distinct numbers after decimal point total calculation of company x gives . 00 + . 00 + . 50 = . 50 at the decimal total calculation of company y gives . 00 + . 90 + . 00 = . 90 at the decimal there difference provides . 60 at the decimal ; only 41.60 fits in answer = a
Answer: a
Python program:
a = 4 / 100
b = a * 575
c = 575 + b 
d = c + 82 
e = 3 / 100
f = e * 530
g = 530 + f 
h = g + 93 
i = d - h
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 49 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 5 : 7 , c ) 4 : 5 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 49 = 5 : 7 answer : b"
Answer: b
Python program:
a = math.sqrt(25)
b = math.sqrt(49)
c = a / b
Problem: total dinning bill for 6 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 40.44 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 6 = 40.44 answer : b"
Answer: b
Python program:
a = 15 * 211
b = a / 100
c = 211 + 0 
d = c / 6
Problem: there are 7 baskets numbered from 1 to 7 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 90 , b ) 120 , c ) 250 , d ) 720 , e ) 910
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 = 7 * 8 / 2 = 28 apples . the total number of apples taken by 10 children is 10 * 28 = 280 the number of apples left in the end is 1000 - 280 = 720 apples . the answer is d ."
Answer: d
Python program:
a = 1 + 7 
b = 10 / 2
c = a * b
d = 10 / 2
e = c + d 
f = e + 1 
g = f * 10
h = 1000 - g
Problem: there are 400 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 400 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 400 = 2 / 5 t , or 2 / 5 ( t - m ) = 400 , from here we get that t - m = 1000 , that would be total number of female employees and the answer ( c )
Answer: c
Python program:
a = 2 / 5
b = 400 / a
Problem: a and b together can do a work in 6 days . if a alone can do it in 42 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 7 , c ) 8 , d ) 20 , e ) 25
Rationale: "b 7 1 / 6 â € “ 1 / 42 = 1 / 7 = > 7"
Answer: b
Python program:
a = 1 / 6
b = 1 / 42
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: in one hour , the crow eats 1 / 40 of the nuts . ( 1 / 4 ) / ( 1 / 40 ) = 10 hours the answer is b .
Answer: b
Python program:
a = 1 / 4
b = 2 + 3 
c = 1 / b
d = c / 8
e = a / d
Problem: if all the numbers between 11 and 100 are written on a piece of paper . how many times will the number 4 be used ?
Options: a ) 87 , b ) 267 , c ) 68 , d ) 26 , e ) 21
Rationale: we have to consider the number of 4 ' s in two digit numbers . _ _ if we fix 4 in the 10 th place , unit place be filled with 10 ways . if we fix 4 in units place , 10 th place be filled with 9 ways ( 0 is not allowed ) so total 19 ways . alternatively : answer : a
Answer: a
Python program:
a = 100 - 11
Problem: the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ?
Options: a ) 82 %
b ) 78 %
c ) 80 %
d ) 90 %
e ) none of these
Rationale: since side 1 x side 2 = area therefore , net % change in area = ( x + y + xy / 100 ) % = [ 40 + 30 + ( 40 x 30 ) / 100 ] % or 82 % . therefore , area is increased by 82 % . answer : a
Answer: a
Python program:
a = 40 / 100
b = 1 + a 
c = 30 / 100
d = 1 + c 
e = b * d
f = e - 1
g = f * 100
Problem: when asked what the time is , a person answered that the amount of time left is 2 / 6 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 6 pm , e ) 7 pm
Rationale: a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 2 / 6 x ⇒ x = 18 time is 6 pm answer : d
Answer: d
Python program:
a = 2 * 12
b = 2 * 12
c = 2 / 6
d = c + 1 
e = b / d
f = a - e
Problem: a walks at 10 kmph and 7 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 140 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 7 hours . x / 10 - x / 20 = 7 x = 140 km answer is b"
Answer: b
Python program:
a = 7 * 20
Problem: the length of a rectangualr hll is 5 m more than its breadth . the area of the hall is 750 m . the length of the hall is
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none
Rationale: solution let the length = xmetres . then length = ( x + 5 ) metres . then , x ( x + 5 ) = 750 = x ² + 5 x - 750 = 0 ( x + 30 ) ( x - 25 ) = 0 x = 25 . answer c
Answer: c
Python program:
a = 750 * 4
b = 5 ** 2
c = a + b 
d = math.sqrt(c)
e = d + 5 
f = e / 2
g = f - 5
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 2 | ≤ 12 ?
Options: a ) 15 , b ) 16 , c ) 12 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 2 < = 12 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . c"
Answer: c
Python program:
a = 3 * 2
b = a + 1
Problem: if a = 105 and a ^ 3 = 21 * 35 * 45 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 5 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 2 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 2 * 7 ^ 2 b = 5 * 7 = 35 correct answer a ."
Answer: a
Python program:
a = 105 ** 3
b = 21 * 35
c = b * 45
d = a / c
Problem: a thief is spotted by a policeman from a distance of 175 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 700 m , e ) none of them
Rationale: relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 175 m / 1000 ) x 1 / 2 hr = 7 / 80 hr . in 7 / 80 hrs , the thief covers a distance of 8 x 7 / 80 km = 7 / 10 km = 700 m answer is d .
Answer: d
Python program:
a = 175 * 8
b = 10 - 8
c = a / b
Problem: in an election between two candidates , one got 60 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 1200 , b ) 750 , c ) 800 , d ) 600 , e ) 900
Rationale: "number of valid votes = 80 % of 2000 = 1600 . valid votes polled by other candidate = 40 % of 2000 = ( 40 / 100 ) x 2000 = 800 answer = c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 60 / 100
d = 1 - c
e = b * d
f = e * 2000
Problem: a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ?
Options: a ) 50 , b ) 25 , c ) 86 , d ) 75 , e ) 102
Rationale: "circumference of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 20 + 2 * 20 = 102.8 approximately 102 answer e"
Answer: e
Python program:
a = circumface / (
b = a + 2
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.5 km ?
Options: a ) 375 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "a 375 m distance covered by amar = 18 / 4.8 ( 1.5 km ) = 3 / 8 ( 1500 ) = 375 m"
Answer: a
Python program:
a = 1 * 5
b = 18 * a
c = b / 48
Problem: a prize of $ 400 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 100 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 400 number of people = 20 2 / 5 of 400 ( = $ 160 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 400 - 160 = $ 240 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 240 - 140 = $ 100 , hence a is the correct answer ."
Answer: a
Python program:
a = 400 * 2
b = a / 5
c = 400 - b
d = 20 * 3
e = d / 5
f = 20 - e
g = f - 1
h = g * 20
i = c - h
Problem: the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 179.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
Answer: b
Python program:
a = 35 * 181
b = a - 166
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: if 10 typists can type 20 letters in 20 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 220 , b ) 210 , c ) 200 , d ) 240 , e ) 260
Rationale: "no . of letters typing by 10 typists in 20 minutes = 20 no . of letters typing by 10 typists in 60 minutes = 20 * 3 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : d"
Answer: d
Python program:
a = 20 * 3
b = a / 10
c = b * 40