euclaise/mathqa_programs huggingface dataset:
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party a . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "assume the total pool of registered voters = 100 , so 35 of the country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and 20 had a favorable impression only of party a let x = # of voters with a favorable impression of both parties let 2 x = # of voters with a favorable impression only of party b so unfavorable a and favorable b # of voters = 2 x - x = x 35 + x = number of unfavorable a 20 + 35 + x = 100 55 + x = 100 x = 45 answer : e"
Answer: e
Python program:
a = 35 + 20 
b = 100 - a
c = b / 3
Problem: the length of a rectangle is reduced by 30 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 42.8 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 30 * 100 ) / ( 100 - 30 ) = 42.8 % a"
Answer: a
Python program:
a = 100 - 30
b = a / 100
c = 1 - b
d = 100 - 30
e = d / 100
f = c / e
g = f * 100
Problem: what is the remainder if 7 ^ 4 is divided by 100 ?
Options: a ) 5 , b ) 4 , c ) 1 , d ) 2 , e ) 10
Rationale: "7 * 7 * 7 * 7 / 100 = 2401 / 100 = 24 reminder 1 answer : c"
Answer: c
Python program:
a = 100 / 2
b = 7 * 7
c = a - b
Problem: how many positive factors do 120 and 80 have in common ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 120 and 80 is 40 number of factors of 40 = 8 answer : a"
Answer: a
Python program:
a = 80 - 10
b = a / 10
Problem: find value of x : ( 422 + 404 ) ^ 2 − ( 4 × 422 × 404 ) = x .
Options: a ) 234 , b ) 267 , c ) 324 , d ) 356 , e ) 577
Rationale: given equation is in the form ( a + b ) 2 − 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 − 4 ab = ( a − b ) 2 = ( 422 − 404 ) 2 = 182 = 324 c
Answer: c
Python program:
a = 422 + 404 
b = a ** 2
c = 4 * 422
d = c * 404
e = b - d
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6400 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9357 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6400 1 = 6400 / 68.4 100 = ( 6400 * 100 ) / 68.4 = rs . 9357 . answer : option d"
Answer: d
Python program:
a = 6400 * 100
b = 100 - 20
c = 100 - 20
d = c * 10
e = d / 100
f = b - e
g = 100 - 20
h = 100 - 20
i = h * 10
j = i / 100
k = g - j
l = k * 5
m = l / 100
n = f - m
o = a / n
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14080 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 4096
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14080 ã — 16 / 55 = rs . 4096 . share of z in the profit is rs . 4096 . option e"
Answer: e
Python program:
a = 3 * 4
b = a - 4
c = 48000 * b
d = 3 * 4
e = 36000 * d
f = 3 * 4
g = 42000 * f
h = e + g 
i = 3 * 4
j = i - 4
k = 48000 * j
l = h + k 
m = 14080 / l
n = c * m
Problem: 6 ) a marketing firm determined that , of 160 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 5
Rationale: "80 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 120 = > 4 x = 20 = > x = 5 answer - e"
Answer: e
Python program:
a = 160 - 80
b = a - 60
c = b / 4
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 54 , how many more green disks than blue disks are in the bag ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 54 - - > x = 3 . g - b = 8 x - 3 x = 5 x = 15 . the answer is a ."
Answer: a
Python program:
a = 3 + 7 
b = a + 8 
c = 54 / b
d = 8 - 3
e = c * d
Problem: what will be the fraction of 6 %
Options: a ) 1 / 20 , b ) 3 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 6 * 1 / 100 = 3 / 50 . option b"
Answer: b
Python program:
a = 6 / 2
b = circle_area / (
Problem: among 250 viewers interviewed who watch at least one of the 3 tv channels namely a , bc . 116 watch a , 127 watch c , while 107 watch b . if 90 watch exactly two channels . how many watch exactly one channel ?
Options: a ) 155 , b ) 160 , c ) 175 , d ) 190 , e ) 195
Rationale: 250 = n ( exactly 1 channel ) + n ( exactly 2 channels ) + n ( exactly 3 channels ) 250 = n ( exactly 1 channel ) + 90 + n ( exactly 3 channels ) let ' s find the value of n ( exactly 3 channels ) = x 250 = n ( a ) + n ( b ) + n ( c ) - n ( a and b ) - n ( b and c ) - n ( c and a ) + n ( a and b and c ) note that each of n ( a and b ) is the sum of ' number of people watching exactly two channels a and b ' and ' number of people watching all three channels ' . 250 = 116 + 127 + 107 - n ( exactly 2 channels ) - 3 x + x 250 = 116 + 127 + 107 - 90 - 2 x x = 25 250 = n ( exactly 1 channel ) + 90 + 25 n ( exactly 1 channel ) = 155 answer ( a )
Answer: a
Python program:
a = 250 - 90
b = 116 + 127 
c = b + 107 
d = c - 90
e = d - 250
f = e / 2
g = a - f
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "let total paint = 1 let amount replaced = x 50 ( 1 - x ) + 25 x = 30 x = 4 / 5 answer : e"
Answer: e
Python program:
a = 30 / 100
b = 50 / 100
c = a - b
d = 25 / 100
e = 50 / 100
f = d - e
g = c / f
Problem: 9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height . what is the diameter of each sphere ?
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 9 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 12 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c ."
Answer: c
Python program:
a = 8 / 2
b = volume_cylinder / (
c = b * math.pi
d = c / 3
e = d / 4
f = e / 9
g = f / 4
h = g * 4
Problem: working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 5 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 4 x units of product p in 10 days ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 18
Rationale: "the rate of 6 machines is rate = job / time = x / 5 units per day - - > the rate of 1 machine 1 / 6 * ( x / 5 ) = x / 30 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 30 ) = 4 x - - > m = 12 . answer : c ."
Answer: c
Python program:
a = 6 * 4
b = 5 / 10
c = a * b
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 220 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "answer d ( a + b ) ( a - b ) = 220 6 cases for ( a + b ) , ( a - b ) 220 , 1 110 , 2 55 , 4 44,5 22 , 10 20,11 answer d"
Answer: d
Python program:
a = math.log(220)
b = 4 + 1 
c = math.log(b)
d = a / c
Problem: a boat goes 100 km downstream in 4 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 35 , e ) 15
Rationale: "100 - - - 10 ds = 25 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 25 - 5 ) / 2 = 10 kmph . answer : a"
Answer: a
Python program:
a = 100 / 4
b = 75 / 15
c = a - b
d = c / 2
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 10 ) ?
Options: a ) 0 , b ) 5 , c ) 2 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 10 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , and - 10 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 = 30 - 30 = 0 hence the correct answer choice is a ."
Answer: a
Python program:
a = 6 - 8
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 60,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 2 a * 1 + a * 5 ) / 6 = 7 a / 6 = 35000 answer is a . $ 35,000"
Answer: a
Python program:
a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g 
i = 75 + 15 
j = h / i
Problem: along a road lie an odd number of stones placed at intervals of 10 m . these stones have to be assembled around the middle stone . a person can carry only one stone at a time . a man carried out the job starting with the stone in the middle , carrying stones in succession , thereby covering a distance of 4.8 km . then the number of stones is
Options: a ) 35 , b ) 15 , c ) 29 , d ) 31 , e ) 29
Rationale: explanation : if he travels 10 m for the first stone he has to travel that dist back as well . . . so he travels 2 * 10 m dist for the first stone and so on . = > 2400 = 2 * ( 10 + 20 + 30 . . . . 10 n ) using formula for ap = > 2400 = 2 * n / 2 * ( 2 * 10 + ( n - 1 ) * 10 ) . = > 2400 = 10 n 2 + 10 n . on solving this , we get n = 15 as the positive root , so total numer of stones on both sides = 30 . and including the one which he was at = 31 . answer : d
Answer: d
Python program:
a = 4 * 8
b = 2 * 2
c = b * 10
d = a / c
e = d * 2
f = 4 * 4
g = e / f
h = g * 2
i = h + 1
Problem: 850 - ( 1500 ÷ ? ) × 8 / 15 = 770
Options: a ) a ) 31 , b ) b ) 10 , c ) c ) 15 , d ) d ) 26 , e ) e ) 17
Rationale: "explanation : = > 850 - ( 1500 ÷ ? ) × 8 / 15 = 770 = > 850 - 770 = ( 1500 ÷ ? ) × 8 / 15 = > 80 = ( 1500 ÷ ? ) × 8 / 15 = > 80 × 15 / 8 = ( 1500 ÷ ? ) = 150 = > 1 / ? = 150 / 1500 = 1 / 10 = > ? = 10 answer : option b"
Answer: b
Python program:
a = 1500 / 8
b = 850 - a
Problem: the contents of two vessels containing copper and tin in the ratio 2 : 3 and 5 : 7 are mixed in the ratio 3 : 5 . the resulting mixture will have copper and tin in the ratio ?
Options: a ) 210 : 283 , b ) 312 : 433 , c ) 178 : 213 , d ) 197 : 283 , e ) 145 : 256
Rationale: the ratio of copper and tin the new vessel = ( 2 / 5 * 3 / 8 + 5 / 12 * 5 / 8 ) : ( 3 / 5 * 3 / 8 + 7 / 12 * 5 / 8 ) = 197 / 480 : 283 / 480 = 197 : 283 answer is d
Answer: d
Python program:
a = 2 * 3
b = 5 * 5
c = a + b 
d = 3 * 3
e = 7 * 5
f = d + e 
g = c / f
Problem: a and b together can do a work in 8 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 24 days , e ) 25 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 8 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 8 ) - ( 1 / 12 ) = 24 days answer : option d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 12
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: x and y are positive integers . when x is divided by 15 , the remainder is 2 , and when x is divided by 10 , the remainder is 7 . when y is divided by 9 , the remainder is 5 , and when y is divided by 7 , the remainder is 2 . what is the least possible value of x * y ?
Options: a ) 389 , b ) 390 , c ) 388 , d ) 391 , e ) 392
Rationale: "when x is divided by 15 , the remainder is 2 : so , the possible values of x are : 2 , 17 , 32 , 47 , etc . when x is divided by 10 , the remainder is 7 : so , the possible values of x are : 7,17 . . . stop . since both lists include 17 , the smallest possible value of x is 17 . when y is divided by 9 , the remainder is 5 : so , the possible values of y are : 5 , 14 , 23,32 etc . when y is divided by 7 , the remainder is 2 : so , the possible values of y are : 2 , 9 , 16 , 23 . . . stop . since both lists include 23 , the smallest possible value of y is 23 since the smallest possible values of x and y are 17 and 23 respectively , the smallest possible value of x * y is 391 . so , d is the correct answer to the original question ."
Answer: d
Python program:
a = 9 * 2
b = a + 5 
c = 2 + 15 
d = b - c
Problem: what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Rationale: mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d .
Answer: d
Python program:
a = 2 * 100
b = a / 2
Problem: marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 20 laps around the track per hour and nick completes 10 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 8 , c ) 24 , d ) 15 , e ) 20
Rationale: "maria ' s rate - 20 laps per hour - - > 20 / 60 laps / min nick ' s rate - 10 laps per hour - - > 10 / 60 laps / min lets set equations : 20 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 10 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 20 / 60 - 10 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 24 min needed maria to run 4 laps answer : c"
Answer: c
Python program:
a = 10 + 1 
b = a * 20
c = 20 / b
d = 10 + 1 
e = d * 20
f = 10 / e
g = c - f
h = 4 / g
Problem: in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 129,500 , b ) 129,600 , c ) 129,700 , d ) 129,800 , e ) 129,900
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 6 - 3 = 3 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 3 = 129,600 . hence b ."
Answer: b
Python program:
a = 6 - 3
b = a * 3600
c = b * 12
Problem: how many times in a day , are the hands of a clock in straight line but opposite in direction ?
Options: a ) 21 , b ) 22 , c ) 17 , d ) 26 , e ) 25
Rationale: b 22 the hands of a clock point in opposite directions ( in the same straight line ) 11 times in every 12 hours . ( because between 5 and 7 they point in opposite directions at 6 o ' clcok only ) . so , in a day , the hands point in the opposite directions 22 times .
Answer: b
Python program:
a = 2 * 12
b = 2 * a
c = b - 4
d = c / 2
Problem: add 11 % of 36 and 12 % of 64 .
Options: a ) 9.5 , b ) 10.5 , c ) 11.5 , d ) 12 , e ) 15
Rationale: "11 % of 36 + 12 % of 64 36 * 11 / 100 + 64 * 12 / 100 3.9 + 7.6 = 11.5 answer c"
Answer: c
Python program:
a = 11 * 36
b = a / 100
c = 12 * 64
d = c / 100
e = b + d
Problem: if the cost price of 55 articles is equal to the selling price of 50 articles , then what is the percent profit ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 50 y = 55 x y = 1.1 x the answer is b ."
Answer: b
Python program:
a = 100 * 50
b = a / 55
c = 100 - b
d = 100 * 50
e = d / 55
f = c / e
g = 100 * f
Problem: in a certain quiz that consists of 8 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 360 points , how many points is the third question worth ?
Options: a ) 39 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 8 x + 112 = 360 8 x = 248 x = 31 3 rd question = 31 + 8 = 31 + 8 = 39 answer a
Answer: a
Python program:
a = 360 / 10
b = 8 - 4
c = b - 1
d = a + c
Problem: line l passes through the points ( - 2,0 ) and ( 0 , a ) . line ll passes through the points ( 4,0 ) and ( 6,2 ) . what value of a makes the two lines parallel ?
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: find slopes first slope of l = ( a - 0 ) / ( 0 - ( - 2 ) ) = a / 2 slope of ll = ( 2 - 0 ) / ( 6 - 4 ) = 1 for l and ll to be parallel , their slopes must be equal a / 2 = 1 , a = 2 correct answer b
Answer: b
Python program:
a = 2 - 0
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 6 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 72 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 6 books / month = 72 books a year total number of books = 72 cs"
Answer: c
Python program:
a = 6 * 12
Problem: debony normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debony averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: debony normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Python program:
a = 40 * 45
b = a / const_60
c = 40 * 2
d = b * c
e = d / 100
f = e * const_60
g = f / 12
h = g - 45
Problem: if the average ( arithmetic mean ) of a and b is 40 and the average of b and c is 60 , what is the value of c − a ?
Options: a ) 25 , b ) 40 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 80 ) b + c = 120 c - a = 40 b . 40"
Answer: b
Python program:
a = 60 * 2
b = 40 * 2
c = a - b
Problem: a 6 - liter solution is 25 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3
Rationale: "let x be the amount of pure alcohol required . 0.25 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.5 x = 3 liters the answer is d ."
Answer: d
Python program:
a = 6 * 25
b = a / 100
c = b * 2
d = 6 - c
Problem: a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 5 : 12 , e ) 7 : 3
Rationale: "container 1 has 9 ounces in the ratio 1 : 2 or , x + 2 x = 9 gives x ( alcohol ) = 3 and remaining water = 6 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 3 + 2 and water = 6 + 6 ratio thus alcohol / water = 5 / 12 answer d"
Answer: d
Python program:
a = 1 + 2 
b = 1 / a
c = 9 * b
d = 1 + 3 
e = 1 / d
f = 8 * e
g = c + f 
h = 9 + 8 
i = 1 + 2 
j = 1 / i
k = 9 * j
l = 1 + 3 
m = 1 / l
n = 8 * m
o = k + n 
p = h - o
q = g / p
Problem: if the ratio of apples to bananas is 3 to 2 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 2 : 3 , b ) 1 : 2 , c ) 3 : 5 , d ) 2 : 5 , e ) 5 : 6
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6 . the ratio of apples to bananas to cucumbers is 3 to 2 to 6 . the ratio of apples to cucumbers is 3 to 6 which equals 1 : 2 . the answer is b ."
Answer: b
Python program:
a = 3 / 2
b = a / 3
Problem: if k and w are the dimensions of a rectangle that has area 60 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 60 = 60 * 1 = 30 * 2 = 15 * 4 = 20 * 3 = 12 * 5 = 10 * 6 - - > k can take 6 values answer : e"
Answer: e
Python program:
a = 3 * 1
Problem: a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 60 marks and failed by 20 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 190
Rationale: "he secured 60 marks nd fail by 20 marks so total marks for pass the examinatn = 80 let toal marks x x * 42 / 100 = 80 x = 190 answer : e"
Answer: e
Python program:
a = 60 + 20 
b = 42 / 100
c = a / b
Problem: the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800
Rationale: "market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 30 / 100 ) = 8000 - 2400 = $ 5600 market value in 1984 = market value in 1983 - ( 30 % of $ 8000 ) = 5600 - 2400 = $ 3200 answer : c"
Answer: c
Python program:
a = 100 * 10
b = 2 * 4
c = a * b
d = 100 * 30
e = 2 * 4
f = d * e
g = 30 / 100
h = g * 2
i = f * h
j = c - i
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : 2550 + ( 100 * 50 ) = 7550 ; answer : b
Answer: b
Python program:
a = 200 + 102 
b = a / 2
c = 200 - 102
d = c / 2
e = d + 1 
f = b * e
Problem: ratio between rahul and deepak is 4 : 3 , after 22 years rahul age will be 26 years . what is deepak present age
Options: a ) 10 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 22 = 26 = > x = 1 so deepak age is = 3 ( 1 ) = 3 answer : option b"
Answer: b
Python program:
a = 26 - 22
b = a * 3
c = b / 4