euclaise/mathqa_programs huggingface dataset:
Problem: the average of 7 consecutive numbers is 20 . the largest of these numbers is :
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c"
Answer: c
Python program:
a = 20 * 7
b = 1 + 2 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = 1 + f 
h = g + 1 
i = h + 1 
j = 1 + 2 
k = j + 1 
l = k + 1 
m = l + 1 
n = m + 1 
o = 1 + n 
p = o + 1 
q = p + 1 
r = q + 1 
s = i + r 
t = a - s
u = t / 7
v = 1 + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = u + y
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 5 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 1 and - 5 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 5 i . e x ^ 2 + 4 x - 5 = 0 is the quadratic equation which needs to be solved . ( x - 1 ) ( x + 5 ) = 0 hence x = 1 . c = - 5 imo d"
Answer: d
Python program:
a = 5 ** 2
b = a / 4
Problem: 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height . what is the diameter of each sphere ?
Options: a ) 2 cm , b ) 4 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 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 1 cm ^ 3 r = 1 cm d = 2 cm the answer is a ."
Answer: a
Python program:
a = 8 / 2
b = volume_cylinder / (
c = b * math.pi
d = c / 3
e = d / 4
f = e / 12
g = f / 4
h = g * 4
Problem: 9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ?
Options: a ) 690.48 , b ) 690.49 , c ) 690.5 , d ) 690.51 , e ) 690.52
Rationale: if the bill was $ 690.47 dollars , how much money should be removed with 1 cent as the smallest unit ? this is equivalent to finding the first number that is divisible by 9 that occurs after 690.47 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 6 + 9 + 0 + 4 + 7 = 26 . if you add 1 , the number is divisible by 9 ( 26 + 1 ) . 27 is divisible by 9 . hence , we need to add 1 cent from this number for it to be divisible by 9 . correct option : a
Answer: a
Python program:
a = min(690)
Problem: evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 )
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13"
Answer: e
Python program:
a = 6 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 11 + d
Problem: 16 people can write 52 book in 12 days working 8 hour a day . then in how many day 206 can be written by 64 people ?
Options: a ) 309 / 26 , b ) 309 / 28 , c ) 309 / 22 , d ) 319 / 26 , e ) 339 / 26
Rationale: "work per day epr hour per person = 52 / ( 12 * 8 * 16 ) / / eq - 1 people = 64 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 206 / ( p * 8 * 64 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 309 / 26 answer : a"
Answer: a
Python program:
a = 52 * 12
b = 64 / 2
c = a / b
Problem: total dinning bill for 7 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 ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c"
Answer: c
Python program:
a = 15 * 211
b = a / 100
c = 211 + 0 
d = c / 7
Problem: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 812 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 9.6 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 12 miles per hour time = t 2 = distance / speed = x / 12 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : d"
Answer: d
Python program:
a = 8 + 812 
b = a / 2
Problem: in a survey of 345 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 40 / 69
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 291 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 345 we have to find not part time and not uninsured . in other words not part time and insured = x / 345 = ( 291 - 104 + 13 ) / 345 = 40 / 69 answer is e ."
Answer: e
Python program:
a = 12 * 5
b = 1 * 100
c = a / b
d = 54 - c
e = d + 104 
f = 345 - e
g = f / 345
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team w . if team a ' s average speed was 5 mph greater than team w ' s , what was team w ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team w ' s speed was s . then team w ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team w . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team w is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Python program:
a = 300 / 5
b = a / 3
Problem: if a ( a - 5 ) = 6 and b ( b - 5 ) = 6 where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 9 , e ) 5
Rationale: "i . e . if a = - 1 then b = 6 or if a = 6 then b = - 1 but in each case a + b = - 1 + 6 = 5 answer : option e"
Answer: e
Python program:
a = 5 + 6 
b = 5 - 6
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: how many positive integers less than 100 have a remainder of 6 when divided by 13 ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 9 , e ) 10
Rationale: "we have to include 6 also . as 13 * 0 + 6 = 6 if somebody says to divide 6 by 13 , we will be telling we have 0 quotient and remainder as 6 . answer is c"
Answer: c
Python program:
a = 4 + 6 
b = a - 1
c = math.factorial(b)
d = math.factorial(6)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 1 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "explanations we have the function f ( x ) = 3 x – 5 , and we want to some sophisticated algebra with it . let ’ s look at the two sides of the prompt equation separately . the left side says : 2 * [ f ( x ) ] – 1 — - this is saying : take f ( x ) , which is equal to its equation , and multiply that by 2 and then subtract 1 . 2 * [ f ( x ) ] – 1 = 2 * ( 3 x – 5 ) – 1 = 6 x – 10 – 1 = 6 x – 11 the right side says f ( 3 x – 6 ) — this means , take the algebraic expression ( 3 x – 6 ) and plug it into the function , as discussed above in the section “ how a mathematician things about a function . ” this algebraic expression , ( 3 x – 6 ) , must take the place of x on both sides of the function equation . f ( 3 x – 6 ) = 3 * [ 3 x – 6 ] – 5 = 9 x – 18 – 5 = 9 x – 23 now , set those two equal and solve for x : 9 x – 23 = 6 x – 11 9 x = 6 x – 11 + 23 9 x = 6 x + 12 9 x – 6 x = 12 3 x = 12 x = 4 answer = b"
Answer: b
Python program:
a = 2 * 5
b = a + 1 
c = 3 * 3
d = c + 5 
e = b - d
f = 2 * 3
g = 3 * 1
h = f - g
i = e / h
Problem: in n is a positive integer less than 200 , and 18 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 18 n / 60 must be an integer . = > 3 n / 10 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
Answer: a
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is :
Options: a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98
Rationale: let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b
Answer: b
Python program:
a = 3 * 8
b = 4 * 8
c = math.lcm(a, b)
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 59000 ?
Options: a ) 81000 , b ) 81007 , c ) 74671.875 , d ) 81066 , e ) 81022
Rationale: "59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c"
Answer: c
Python program:
a = 1 / 8
b = a * 59000
c = 59000 + b 
d = 1 / 8
e = 1 / 8
f = e * 59000
g = 59000 + f 
h = d * g
i = c + h
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 650 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a"
Answer: a
Python program:
a = 30 / 100
b = 500 * a
c = 500 + b
Problem: if the sum and difference of two numbers are 20 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c"
Answer: c
Python program:
a = 20 + 8 
b = a / 2
c = b ** 2
d = 20 + 8 
e = d / 2
f = 20 - e
g = f ** 2
h = c - g
Problem: raja complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 200 km , b ) 250 km , c ) 224 km , d ) 255 km , e ) 260 km
Rationale: consider x - - > ( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 = = > x / 21 + x / 24 = 20 15 x = 168 * 20 = = > 224 km answer c
Answer: c
Python program:
a = 10 / 2
b = a * 24
c = 10 / 2
d = c * 21
e = b + d
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is :
Options: a ) 44 % , b ) 46 % , c ) 48 % , d ) 50 % , e ) 51 %
Rationale: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a"
Answer: a
Python program:
a = 100 + 20 
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a person travels equal distances with speeds of 2 km / hr , 4 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 4 ) + ( x / 6 ) = 11 / 60 x = 0.2 total distance = 3 * 0.2 = 0.6 km = 600 meters correct option is c"
Answer: c
Python program:
a = 11 / const_60
b = 1 / 2
c = 1 / 4
d = b + c 
e = 1 / 6
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: the ratio of the radius of two circles is 1 : 9 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 81
Rationale: "r 1 : r 2 = 1 : 9 π r 12 : π r 22 r 12 : r 22 = 1 : 81 answer : e"
Answer: e
Python program:
a = circle_area / (
Problem: the average salary of all the workers in a workshop is rs . 9000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e"
Answer: e
Python program:
a = 12000 - 9000
b = 6 * a
c = 9000 - 6000
d = b / c
e = 6 + d
Problem: the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation
Options: a ) 6 , b ) 7 , c ) 9 , d ) 4 , e ) 11
Rationale: the following approach might be the easiest one and less error prone . we need on - time departure rate to be higher than 6 / 10 , so it should be at least 7 / 11 , which means that 7 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 7 - 3 = 4 subsequent flights need to depart on - time . answer : d
Answer: d
Python program:
a = 60 / 100
b = a * 10
c = b + 1 
d = c - 3
Problem: 6 ) a marketing firm determined that , of 300 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 ) 45
Rationale: "220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d"
Answer: d
Python program:
a = 300 - 80
b = a - 60
c = b / 4
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 8 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 7 / 15 , b ) 11 / 25 , c ) 17 / 35 , d ) 23 / 45 , e ) 27 / 55
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 15 / 24 ) = 8 / 15 hours peter worked for 23 / 15 hours so he painted 23 / 15 * 1 / 3 = 23 / 45 of the room . the answer is d ."
Answer: d
Python program:
a = 4 * 8
b = a + 1 
c = 4 / b
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .
Answer: d
Python program:
a = 4 + 2 
b = a / 1
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 5
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 40 % of 60 = 24 total new books = 24 + 16 = 40 fraction = 16 / 40 = 2 / 5 ans : e"
Answer: e
Python program:
a = 40 * 40
b = a / 100
c = 40 * 40
d = c / 100
e = 100 - 40
f = 40 * e
g = f / 100
h = d + g 
i = b / h
Problem: the price of lunch for 15 people was $ 209.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.66 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"
Answer: b
Python program:
a = 100 + 15 
b = 209 / 0
c = b * 100
d = 1 / 15
e = c * d
Problem: the average of 50 numbers id 44 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 11.35 , e ) 43.75
Rationale: "explanation : total of 50 numbers = ( 50 × 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e"
Answer: e
Python program:
a = 50 * 44
b = 45 + 55 
c = a - b
d = 50 - 2
e = c / d
Problem: mike earns $ 14 per hour and phil earns $ 12 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 14 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 14 is 12 let it be x % less , then = 14 ( 1 - x / 100 ) = 12 1 - x / 100 = 12 / 14 x = 100 / 7 x = 14 % ans c"
Answer: c
Python program:
a = 12 / 14
b = a * 100
Problem: what is the remainder when 45 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 45 * 49 ) / 8 } } = remainder of ( 45 / 8 ) * remainder of ( 49 / 8 ) = 5 * 1 = 7 answer : d"
Answer: d
Python program:
a = 8 / 2
b = 45 * 45
c = a - b
Problem: 6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?
Options: a ) 3 / 10 , b ) 1 / 70 , c ) 3 / 14 , d ) 1 / 10 , e ) 11 / 14
Rationale: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a
Answer: a
Python program:
a = 6 ** 2
b = 6 - 1
c = 6 * b
d = 6 - 1
e = d - 1
f = c * e
g = a / f
Problem: solution x is 80 % chemical a and 20 % chemical b by volume . solution y is 50 % chemical a and 50 % chemical b by volume . if a mixture of x and y is 68 % chemical a , what percent of the mixture is solution x ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the volume of the mixture be x + y . 0.8 x + 0.5 y = 0.68 ( x + y ) 0.12 x = 0.18 y x = 3 y / 2 x / ( x + y ) = ( 3 y / 2 ) / ( 5 y / 2 ) = 3 / 5 = 40 % . the answer is e ."
Answer: e
Python program:
a = 50 - 68
b = 68 - 80
c = a / b
d = 50 - 68
e = 68 - 80
f = d / e
g = f + 1 
h = c / g
i = h * 100
Problem: what number has a 5 : 1 ratio to the number 11 ?
Options: a ) 22 , b ) 50 , c ) 55 , d ) 52 , e ) 12
Rationale: "5 : 1 = x : 10 x = 55 answer : c"
Answer: c
Python program:
a = 11 * 5
Problem: in a class , if 50 % of the boys were girls , then there would be 50 % more girls than boys . what percentage of the overall class is girls ?
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 20 % , e ) 10 %
Rationale: detailed solution for questions of this type , it is best to go from the final step . in the final state , the number of girls should be 1.5 * the number of boys . when 50 % of the boys are taken as girls , let the number of boys = x number of girls = 1.5 x total number of students = 2.5 x original number of boys = 2 x ( 50 % of boys = x ) original number of girls = 0.5 x girls form 20 % of the overall class . correct answer d .
Answer: d
Python program:
a = 50 / 100
b = 1 + a 
c = 50 / 100
d = b * c
e = 50 / 100
f = d - e
g = 50 / 100
h = 1 + g 
i = 50 / 100
j = h * i
k = 50 / 100
l = j - k
m = l + 1 
n = f / m
o = n * 100
Problem: a man can row downstream at the rate of 30 kmph and upstream at 10 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 10 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 30 + 10 ) = 20 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 30 - 10 ) = 1 / 2 ( 20 ) = 10 kmph answer is a ."
Answer: a
Python program:
a = 30 - 10
b = a / 2
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 192,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Python program:
a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg , what is his percent ?
Options: a ) 11.11 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
Rationale: "900 - - - 100 100 - - - ? = > 11.11 % answer : a"
Answer: a
Python program:
a = 100 / 900
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 75
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 5 * 180 / 12 = 75 ounces of water e"
Answer: e
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 5