euclaise/mathqa_programs huggingface dataset:
Problem: a major airplane manufacturer announced the sale of 150 small airliners at $ 125 million each , 75 medium sized airliners at $ 175 million each , and 60 large airliners at $ 220 million each . what percentage of the company ' s income came from large and medium airliners ?
Options: a ) 29 % , b ) 41 % , c ) 58 % , d ) 69 % , e ) 70 %
Rationale: answer is ( money from mid and large plane ) / ( total money from all the planes ) x 100 = ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 = 58.4 % you could just multiply add divide to get answer . however sometimes its much better to make it easy we should see if we have any common terms 125 * 150 = ( 5 * 5 * 5 ) * ( 2 * 3 * 5 * 5 ) 175 * 75 = ( 5 * 5 * 7 ) * ( 3 * 5 * 5 ) 220 * 60 = ( 2 * 2 * 11 * 5 ) * ( 2 * 2 * 3 * 5 ) 3 * 5 * 5 is common cancel it ans becomes ( 175 + 176 ) / ( 176 + 175 + 250 ) * 100 = ~ = ~ 350 / 600 * 100 = ~ = ~ 7 / 12 * 100 = 60 % > > > 58 % is closest . answer : c
Answer: c
Python program:
a = 75 * 175
b = 60 * 220
c = a + b 
d = 75 * 175
e = 60 * 220
f = d + e 
g = 150 * 125
h = f + g 
i = c / h
j = i * 100
Problem: if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a"
Answer: a
Python program:
a = 75 + 30 
b = a + 20 
c = b - 100
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 4 ?
Options: a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a"
Answer: a
Python program:
a = 1 / 4
b = a ** 4
Problem: ( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ?
Options: a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7
Rationale: ( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b
Answer: b
Python program:
a = 5 / 10
Problem: 85 % of the population of a city is 85000 . the total population of the city is ?
Options: a ) 95000 , b ) 97500 , c ) 100000 , d ) 105000 , e ) 102500
Rationale: "x * ( 85 / 100 ) = 85000 x = 1000 * 100 x = 100000 answer : c"
Answer: c
Python program:
a = 100 / 85
b = a * 85000
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25
Rationale: it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 = 25 e
Answer: e
Python program:
a = 24 + 26 
b = a / 2
Problem: what is the perimeter of a square with area 9 p ^ 2 / 64 ?
Options: a ) 3 p / 2
b ) 3 p ^ 2 / 4
c ) 3 p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a .
Answer: a
Python program:
a = math.sqrt(9)
b = math.sqrt(64)
c = a / b
d = c * 4
Problem: 14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4
Rationale: x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 â € “ 4 xy ( x - y ) 2 = 625 â € “ 576 = > ( x â € “ y ) = 7 answer : a
Answer: a
Python program:
a = 25 ** 2
b = 144 * 2
c = a - b
d = 144 * 2
e = c - d
f = 25 ** 2
g = 144 * 2
h = f - g
i = 144 * 2
j = h - i
k = j - 4
l = k - 3
m = e - l
Problem: ( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x
Options: a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521
Rationale: "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c"
Answer: c
Python program:
a = 90510 + 7819 
b = a - 9011
c = b - 1789
d = const_60 / 2
e = c * d
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2500 , what will be the difference between q and r ' s share ?
Options: a ) 2225 , b ) 2325 , c ) 2425 , d ) 2625 , e ) 2525
Rationale: "4 - - - 2100 5 - - - ? = > 2625 answer : d"
Answer: d
Python program:
a = 12 - 7
b = 7 - 3
c = 2500 / b
d = a * c
Problem: a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a"
Answer: a
Python program:
a = 15 / 0
Problem: if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 + x - 20 = 0 , then x =
Options: a ) 1 , b ) - 4 , c ) 4 , d ) - 5 , e ) 5
Rationale: x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 + x - 20 = ( x - 4 ) ( x + 5 ) = 0 then x = 4 or x = - 5 . thus x = - 5 . the answer is d .
Answer: d
Python program:
a = 4 * 4
Problem: the rate at which a sum becomes 4 times of itself in 15 years at s . i . , will be :
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) none
Rationale: sol . let sum = x . then , s . i . = 3 x ∴ rate = [ 100 * s . i . / p * t ] = [ 100 * 3 x / x * 15 ] % = 20 % . answer c
Answer: c
Python program:
a = 3 * 100
b = a / 15
Problem: 20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 330 , d ) 390 , e ) 445
Rationale: "there are 20 business exec and in each handshake 2 business execs are involved . hence 20 c 2 = 190 also , each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake . total = 190 + 140 = 330 ans : c"
Answer: c
Python program:
a = 20 - 1
b = 20 * a
c = b / 2
d = 20 * 7
e = c + d
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 9 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 11 / 20 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: x * 6 / 100 * 1 + ( 20000 - x ) * 9 / 100 * 1 = 1440 6 x - 8 x = 144000 - 180000 = > - 2 x = - 18000 = > x = 9000 so 11000 / 20000 = 11 / 20 answer - a
Answer: a
Python program:
a = 1 + 4 
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d 
f = 1 + 4 
g = 2 * f
h = 4 * g
i = e + h 
j = i / 20
k = j / 9
l = k + 9 
m = l - 6
n = m / 20
Problem: in a school of 850 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 163 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 850 * 18 / 100 = 153 answer : c"
Answer: c
Python program:
a = 44 + 28 
b = a + 10 
c = 100 - b
d = 850 * c
e = d / 100
Problem: 109 × 109 + 91 × 91 = ?
Options: a ) 20162 , b ) 18322 , c ) 13032 , d ) 18662 , e ) none of these
Rationale: "explanation : ( a + b ) 2 + ( a − b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1092 + 912 = ( 100 + 9 ) 2 + ( 100 − 9 ) 2 = 2 ( 1002 + 92 ) = 2 ( 10000 + 81 ) = 20162 . answer : option a"
Answer: a
Python program:
a = 109 * 109
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price q per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: if x = 3 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.02 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de answer : b"
Answer: b
Python program:
a = 2 / 2
b = a / 1000
Problem: last year , for every 100 million vehicles that travelled on a certain highway , 98 vehicles were involved in accidents . if 3 billion vehicles travelled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 100000000 )
Options: a ) 288 , b ) 320 , c ) 2,940 , d ) 3,200 , e ) 28,800
Rationale: to solve we will set up a proportion . we know that “ 100 million vehicles is to 98 accidents as 3 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 98 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 98 x = 30 * 98 = 2,940 correct answer is c .
Answer: c
Python program:
a = 3 * 100000000
b = a * 10
c = b / 100000000
d = c * 98
e = d / 1000
f = math.floor(e)
Problem: in what time will a train 125 m long cross an electric pole , it its speed be 130 km / hr ?
Options: a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 130 * 5 / 18 = 36 m / sec time taken = 125 / 36 = 3.5 sec . answer : a"
Answer: a
Python program:
a = 130 * const_0_2778
b = 125 / a
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 80 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 80 - { both correctly } + 5 { both correctly } = 70 . answer : c ."
Answer: c
Python program:
a = 85 + 80 
b = a + 5 
c = b - 100
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 71
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 71 answer : e"
Answer: e
Python program:
a = 43 * 23
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 9.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 30 = 10 * 2 = 20 time difference = 9.1 ans : d"
Answer: d
Python program:
a = 55 + 10 
b = a - 1
c = 10 / 30
d = 10 / 55
e = c - d
f = b * e
g = max(f)
Problem: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 77 , c ) 42 , d ) 88 , e ) 12
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 96 = 42 . answer : c"
Answer: c
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 96
f = e / 2
Problem: the length of a side of a hexagon is 8 inches . what is the perimeter ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 38
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 8 ) = 48 inches answer c"
Answer: c
Python program:
a = 3 * 2
b = 8 * a
Problem: when positive integer n is divided by positive integer j , the remainder is 11 . if n / j = 724.04 , what is value of j ?
Options: a ) 140 , b ) 150 , c ) 260 , d ) 275 , e ) 280
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 724.04 here 724 is the quotient . given that remainder = 11 so , 724.04 = 724 + 11 / j so , j = 275"
Answer: d
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 724 - 4
e = 11 / d
Problem: a can complete the job in 2 hours and b can complete the same job in 4 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 6
Answer: a
Python program:
a = 2 - 1
b = a - 4
c = 2 * 4
d = b / c
Problem: if a ' s income is 25 % less than b ' s . by what % b ' s income is greater than a ?
Options: a ) 11 , b ) 12 , c ) 33 , d ) 15 , e ) 36
Rationale: if b ' s income is rs 100 , a ' s income = rs 75 % b ' s income is greater than a = 100 * 25 / 75 = 33.33 % answer : c
Answer: c
Python program:
a = 100 - 25
b = 100 / a
c = b - 1
d = c * 100
Problem: x starts a business with rs . 56000 . y joins in the business after 4 months with rs . 44000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 21 : 11 , b ) 11 : 21 , c ) 22 : 23 , d ) 25 : 23 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 56000 * 12 : 44000 * 8 = 56 * 12 : 44 * 8 = 7 * 3 : 11 = 21 : 11 . answer : option a"
Answer: a
Python program:
a = 56000 * 12
b = 4 + 3 
c = 44000 * b
d = a / c
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 965 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"
Answer: c
Python program:
a = 8 * 70
b = 9 * 45
c = a + b
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is theprobability that the extracted ball would turn onto be white , if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ?
Options: a ) 3 / 5 , b ) 5 / 8 , c ) 6 / 7 , d ) 7 / 8 , e ) 6 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Python program:
a = 1 / 2
b = 1 + 3 
c = 1 / b
d = 1 + 3 
e = 3 / d
f = c + e 
g = a + f 
h = 1 + g 
i = 1 + 3 
j = h / i
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 36 meter head start . if cristina runs at a pace of 6 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 36 for cristina = c = 6 * t @ t = 12 , n = 72 c = 72 right answer ans : e"
Answer: e
Python program:
a = 6 - 3
b = 36 / a
Problem: 587 * 999 = ?
Options: a ) 586411 , b ) 586413 , c ) 486411 , d ) 486413 , e ) none of these
Rationale: "explanation : trick : 587 * ( 1000 - 1 ) = 587000 - 587 = 586413 option b"
Answer: b
Python program:
a = 587 / 999
b = a * 100
Problem: it takes 35 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "35 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 6 / 7 * 1 / 12 = 1 / 14 of the job each hour . the answer is a ."
Answer: a
Python program:
a = 1000 / 2
b = a * 1000
c = 1000 / 2
d = c * 1000
e = d / 35
f = e / 12
g = f * 30
h = b / g
Problem: a sum was put at si at certain rate for 2 years . had it been put at 3 % higher rate , it would have fetched rs . 300 more . find the sum
Options: a ) rs 4000 , b ) rs 5000 , c ) rs 6000 , d ) rs 7000 , e ) rs 8000
Rationale: let p be the sum . and x be the interest rate . ( 2 * ( x + 3 ) * p / 100 ) - ( 2 * x * p / 100 ) = 300 therefore 6 p / 100 = 300 p = rs 5000 answer : b
Answer: b
Python program:
a = 3 / 100
b = a * 2
c = 300 / b
Problem: 9 people decided to split the restaurant bill evenly . if the bill was $ 314.16 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: this is equivalent to finding the first number that is divisible by 9 that occurs after 31416 . 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 31416 = 15 and 18 is divisible by 9 . hence , we need to add 3 to this number for it to be divisible by 9 correct option : d
Answer: d
Python program:
a = 3 / 100
b = 314 + 16
Problem: 1395 x 1395 = ?
Options: a ) a ) 1951609 , b ) b ) 1946025 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1395 x 1395 = ( 1395 ) 2 = ( 1400 - 5 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 2 x 1400 x 5 ) = 1960000 + 25 - 14000 = 1960025 - 14000 = 1946025 . answer : b"
Answer: b
Python program:
a = 1395 / 1395
b = a * 100
Problem: x ÷ 4 × 5 + 10 – 12 = 48 , then x =
Options: a ) 60 , b ) 40 , c ) 100 , d ) 28 , e ) 50
Rationale: follow reverse process 48 + 12 = 60 – 10 = 50 ÷ 5 = 10 × × 4 = 40 option b
Answer: b
Python program:
a = 48 - 10
b = a + 12 
c = b * 4
d = c / 5
Problem: - 84 x 29 + 365 = ?
Options: a ) 2071 , b ) 2436 , c ) 2801 , d ) - 2801 , e ) - 2071
Rationale: "e given exp . = - 84 x ( 30 - 1 ) + 365 = - ( 84 x 30 ) + 84 + 365 = - 2520 + 449 = - 2071"
Answer: e
Python program:
a = 1 - 2
b = 84 * 29
c = b - 365
d = a * c
Problem: 5 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 267 , e ) 6400
Rationale: "( 5 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 20 x = 320 x = 6400 answer : e"
Answer: e
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 5
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 3 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 12 : 15 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 3 - - > e : l = 5 : 3 = 20 : 12 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 12 : 15 . answer : a ."
Answer: a
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 3 * 4
f = d / e
g = c / f
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 168 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 168 km time taken = distance / speed = 168 / 28 = 6 hours answer : option d"
Answer: d
Python program:
a = 24 + 4 
b = 168 / a
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 10 x + 5 = 0 ?
Options: a ) 6 , b ) 42 , c ) 24 , d ) 18 , e ) 95
Rationale: a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 10 / 1 = - 10 ab = 5 / 1 = 5 hence a / b + b / a = [ ( - 10 ) 2 - 2 ( 5 ) ] / 5 = 90 / 5 = 18 . d )
Answer: d
Python program:
a = negate ** (
b = a / 2
c = b - 5
Problem: jim is able to sell a hand - carved statue for $ 750 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 555.56 , d ) $ 574.90 , e ) $ 588.20
Rationale: "750 = 1.35 * x x = 750 / 1.35 = 555.5555556 . . . which rounds to $ 555.56 , which is ( c ) ."
Answer: c
Python program:
a = 35 / 100
b = a + 1 
c = 750 / b
Problem: in a fuel station the service costs $ 4.25 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 309.85 $
Rationale: "service cost of 3 van and 2 truck = 4.25 * ( 3 + 2 ) = 21.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 21.25 = 309.85 answer is e"
Answer: e
Python program:
a = 65 * 120
b = a / 100
c = 65 + b 
d = c * 2
e = d * 0
f = 65 * 3
g = f * 0
h = e + g
Problem: a cistern is normally filled in 10 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 60 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 10 - 1 / x = 1 / 12 , solving 1 / x = 1 / 60 so in 60 hours full cistern will be empty . answer : c"
Answer: c
Python program:
a = 1 / 10
b = 10 + 2 
c = 1 / b
d = a - c
e = 1/(d)