euclaise/mathqa_programs huggingface dataset:
Problem: in a school with 652 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 250 , d ) 163 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 652 - x ) . then , ( 11 3 / 4 × 652 ) ⇔ 11 x + 12 ( 652 - x ) ⇔ x = 7824 - 7661 ⇔ 163 . answer d"
Answer: d
Python program:
a = 12 * 652
b = 9 / 12
c = 11 + b 
d = c * 652
e = a - d
Problem: ( 35423 + 7164 + 41720 ) - ( 317 x 89 ) = ?
Options: a ) 28213 , b ) 84307 , c ) 50694 , d ) 54094 , e ) none of them
Rationale: "= ( 84307 ) - 317 x 89 = 84307 - ( 317 x ( 90 - 1 ) ) = 84307 - ( 317 x 90 - 317 ) = 84307 - 28213 = 54094 answer is d"
Answer: d
Python program:
a = 35423 + 7164 
b = a / 41720
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 2 / 3 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 2 / 3 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 3 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 1 / 3 * 1 / 2 = 1 / 6 , or a ."
Answer: a
Python program:
a = 2 / 3
b = 1 - a
c = 1 / 2
d = b * c
Problem: how many words , with or without meaning , can be formed using all letters of the word beautiful using each letter exactly once ?
Options: a ) 388,620 , b ) 388,260 , c ) 362,880 , d ) 352,880 , e ) 342,880
Rationale: "the word beautiful has exactly 9 letters which are all different . therefore the number of words that can be formed = number of permutations of 9 letters taken all at a time . = p ( 9 , 9 ) = 9 ! = 9 x 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 362,880 answer : c"
Answer: c
Python program:
a = math.factorial(3)
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams . find the profit percent .
Options: a ) 7.38 , b ) 5.38 , c ) 4.38 , d ) 6.38 , e ) 3.38
Rationale: explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 940 100 + g / 100 + 0 = 1000 / 940 100 + g = 100 / 94 * 100 g = 6.38 answer : d
Answer: d
Python program:
a = 4 + 1 
b = 4 + 1 
c = a + b 
d = c * 100
e = d - 940
f = e / 940
g = f * 100
Problem: the average of first six multiples of 4 is :
Options: a ) 14 , b ) 9 , c ) 12 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 84 / 6 = 14 answer a"
Answer: a
Python program:
a = 4 + 1
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 20 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 96 km , d ) 12 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 20 2 x + 3 x = 480 x = 96 km answer is c"
Answer: c
Python program:
a = 10 - 2
b = 10 + 2 
c = a * b
d = c * 20
e = 10 - 2
f = 10 + 2 
g = e + f 
h = d / g
Problem: during a sale , the price of a pair of shoes is marked down 20 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 25 %
Rationale: "assume the price = 100 price during sale = 80 price after sale = 100 percent increase = 20 / 80 * 100 = 25 % approx . correct option : e"
Answer: e
Python program:
a = 20 * 100
b = 100 - 20
c = a / b
Problem: in what time will a train 320 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 8.0 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 320 / 40 = 8.0 sec . answer : b"
Answer: b
Python program:
a = 144 * const_0_2778
b = 320 / a
Problem: among 200 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 172 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 60 using your analysis : we see that the total number of students who study either maths or sociology = 88 + 112 - 60 = 140 so , in the image we know that the number of students in the zone with the black boundary = 140 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 200 , we can write : 140 + b + w = 200 or , b + w = 200 - 140 = 60 that is , b = 60 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 60 a"
Answer: a
Python program:
a = 200 / 100
b = a * 56
c = 200 / 100
d = c * 44
e = b + d 
f = 200 / 100
g = f * 30
h = e - g
i = 200 - h
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Rationale: speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 5 2 x + 3 x = 120 x = 24 km answer is a
Answer: a
Python program:
a = 10 - 2
b = 10 + 2 
c = a * b
d = c * 5
e = 10 - 2
f = 10 + 2 
g = e + f 
h = d / g
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 70 / 10 sq . metre , whose base & perpendicular distance from the other side being 84 m & 24 m respectively ?
Options: a ) s . 2400 , b ) s . 2016 , c ) s . 1400 , d ) s . 3480 , e ) s . 2000
Rationale: "area of the parallelogram = length of the base * perpendicular height = 84 * 24 = 2016 m . total cost of levelling = rs . 2016 b"
Answer: b
Python program:
a = 84 * 24
b = 70 / 10
c = a * b
Problem: during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) a / 14 , b ) 5 a / 7 , c ) 7 a / 5 , d ) 14 a , e ) 35 a
Rationale: "total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 5 * action = 30 - - > action = a = 5 . comedies = 70 = 14 a . answer : d ."
Answer: d
Python program:
a = 5 + 1 
b = 70 / a
c = math.floor(b)
Problem: country x taxes each of its citizens an amount equal to 11 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 58,000 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.11 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,400 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,600 - - > x = 58,000 . answer : d ."
Answer: d
Python program:
a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 11 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
Problem: list k consists of 14 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: answer = d = 8 if least = - 4 , then largest = 9 range = 9 - 1 = 8
Answer: d
Python program:
a = 14 - 4
b = a - 1
c = b - 1
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 40 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 2.55 km
Rationale: "e 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 40 / 60 47 x / 60 = 40 / 60 = > x = 0.85 . total distance = 3 * 0.85 = 2.55 km ."
Answer: e
Python program:
a = 40 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: the average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results ?
Options: a ) 30 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 85 result = sum of 20 result + sum of 65 result . = 20 x 65 + 65 x 20 = 2600 correct option : a"
Answer: a
Python program:
a = 20 * 65
b = 65 * 20
c = a + b 
d = 20 + 65 
e = c / d
Problem: by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at
Options: a ) 46 , b ) 96 , c ) 35 , d ) 87 , e ) 13
Rationale: "to earn rs . 135 , investment = rs . 1620 . to earn rs . 8 , investment = rs . 96 . market value of rs . 100 stock = rs . 96 . answer : b"
Answer: b
Python program:
a = 1620 / 135
b = 8 / 100
c = a * b
d = c * 100
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 192 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 480 , 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 = 192 = > 4 x / 10 = 192 = > 4 x = 1920 = > x = 480 . answer : d"
Answer: d
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 192 / c
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ?
Options: a ) 45 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 20 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 20 x = 30 since you need a 15 l solution , you must evaporate 45 of the original 50 l solution to get a 20 % solution . answer is a ."
Answer: a
Python program:
a = 50 / 100
b = a * 20
c = 50 - b
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Python program:
a = 10 * 2
b = a - 10
c = b * 1000
d = c / 10
e = d / 1000
Problem: find the average of all the numbers between 6 and 34 which is divisible by 5
Options: a ) 15 , b ) 18 , c ) 13 , d ) 19 , e ) 20
Rationale: "avg = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = > 20 answer e"
Answer: e
Python program:
a = 6 + 4 
b = 34 - 4
c = a + b 
d = c / 2
Problem: . 3 + 33 + 333 + 3.33 = ?
Options: a ) 369.63 , b ) 372.33 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: . 3 33 333 3.33 - - - - - - - - - - 369.63 - - - - - - - - - - answer is a
Answer: a
Python program:
a = 33 + 333 
b = a + 3 
c = 3 / 10
d = b + c
Problem: an woman swims downstream 45 km and upstream 25 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 2.1
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - - 5 us = 5 ? - - - - 1 s = ? s = ( 9 - 5 ) / 2 = 2 answer : a"
Answer: a
Python program:
a = 45 / 5
b = 25 / 5
c = a - b
d = c / 2
Problem: find a sum for first 6 prime number ' ss ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 41
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option e
Answer: e
Python program:
a = 6 + 6 
b = a * 4
c = 6 + 1 
d = b - c
Problem: a computer factory produces 8400 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 8400 / ( 28 * 24 * 2 ) = 6.25 answer e"
Answer: e
Python program:
a = 8400 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: what least number should be subtracted from 3,381 so that the remainder when divided by 9 , 11 , and 17 will leave in each case the same remainder 8 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 15
Rationale: "the lcm of 9 , 11 and 17 is 1,683 . the next multiple is 2 * 1,683 = 3,366 . 3,366 + { remainder } = 3,366 + 8 = 3,374 , which is 7 less than 3,381 . answer : b ."
Answer: b
Python program:
a = 9 * 11
b = a * 17
c = b * 2
d = c + 8 
e = 3 - 381
Problem: a trader marked the selling price of an article at 40 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 7.8 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: sol . let c . p . = rs . 100 . then , marked price = rs . 140 , s . p . = rs . 99 . ∴ discount % = [ 11 / 140 * 100 ] % = 7.8 % answer b
Answer: b
Python program:
a = 2 + 3 
b = a * 2
c = b + 1 
d = 100 + 40 
e = c / d
f = 100 * e
Problem: diana is painting statues . she has 7 / 16 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 7 / 16 ÷ 1 / 16 = 7 / 16 * 16 / 1 = 7 / 1 = 7 answer is a ."
Answer: a
Python program:
a = 7 / 16
b = 1 / 16
c = a / b
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1300 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6500
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1300 20 x / 100 = 1300 x = 1300 * 100 / 20 = 6500 answer is e"
Answer: e
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 1300 / c
Problem: fresh grapes contain 60 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 30 kg of fresh grapes ?
Options: a ) 10 kg , b ) 15 kg , c ) 20 kg , d ) 25 kg , e ) 40 kg
Rationale: "from the question we know : 30 kg * 60 % = 18 kg of water in the fresh grapes 30 kg - 18 kg of water = 12 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 20 % of the weight of the dry graps is water and we know that 12 kg is non - water mass we can set up the following equation : x = 1 / 5 ( x ) + 12 kg 4 / 5 ( x ) = 12 kg x = 15 kg answer - b"
Answer: b
Python program:
a = 100 - 60
b = a * 30
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: without stoppages , a train travels certain distance with an average speed of 80 km / h , and with stoppages , it covers the same distance with an average speed of 60 km / h . how many minutes per hour the train stops ?
Options: a ) 15 , b ) 18 , c ) 10 , d ) 16 , e ) none of these
Rationale: "due to stoppages , it covers 20 km less . time taken to cover 20 km = 20 ⁄ 80 h = 1 ⁄ 4 h = 1 ⁄ 4 × 60 min = 15 min answer a"
Answer: a
Python program:
a = 60 / 80
b = a * const_60
c = const_60 - b
Problem: if 5 / ( 4 + 1 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 5 / ( 4 + 1 / x ) = 1 should have been equal to something . if 5 / ( 4 + 1 / x ) = 1 = > 5 x / ( 4 x + 1 ) = 1 = > 5 x = 4 x + 1 = > x = 1 correct option : b"
Answer: b
Python program:
a = 5 - 4
b = 1 / a
Problem: the average age of a class of 22 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 44 , b ) 48 , c ) 45 , d ) 43 , e ) 50
Rationale: "total age = 22 * 21 tot age of all stu + age of the teacher = 23 * 22 age of the teacher = 23 * 22 - 22 * 21 = 44 answer a"
Answer: a
Python program:
a = 22 + 1 
b = 21 + 1 
c = a * b
d = 22 * 21
e = c - d
Problem: by selling 88 pens , a trader gains the cost of 22 pens . find his gain percentage ?
Options: a ) 25 % , b ) 26 % , c ) 27 % , d ) 28 % , e ) 29 %
Rationale: let the cp of each pen be rs . 1 . cp of 88 pens = rs . 88 profit = cost of 22 pens = rs . 22 profit % = 22 / 88 * 100 = 25 % answer : a
Answer: a
Python program:
a = 22 / 88
b = a * 100
Problem: the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 13 days , how large is the colony today ?
Options: a ) 512 , b ) 1024 , c ) 768 , d ) 2048 , e ) 4096
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : b"
Answer: b
Python program:
a = 9 + 1 
b = 2 ** a
c = b - 1
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 35 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 ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 24
Rationale: "9 / 35 - 9 / 55 = 9 / 5 * ( 11 - 7 ) / 77 = 9 / 5 * 4 / 77 * 60 min = 9 * 12 * 4 / 77 = 432 / 77 ~ 5.6 answer - b"
Answer: b
Python program:
a = 55 + 9 
b = a - 1
c = 9 / 35
d = 9 / 55
e = c - d
f = b * e
g = max(f)
Problem: if k is a non - negative integer and 18 ^ k is a divisor of 624,938 then 6 ^ k - k ^ 6 =
Options: a ) 0 , b ) 1 , c ) 36 , d ) 118 , e ) 420
Rationale: "6 + 2 + 4 + 9 + 3 + 8 = 32 , so this number is not divisible by 3 and thus not divisible by 18 . therefore , k = 0 6 ^ k - k ^ 6 = 1 - 0 = 1 the answer is b ."
Answer: b
Python program:
a = 1 - 1
b = 6 ** a
c = 1 - 1
d = c ** 6
e = b - d
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 3 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 18 , b ) 3 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 4 : 9
Rationale: m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 1 / 9 + 2 / 9 = 1 / 3 losses = 1 - 1 / 3 = 2 / 3 the ratio of wins to losses is 1 : 2 . the answer is c .
Answer: c
Python program:
a = 1 + 2 
b = 3 + 3 
c = a / b
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 55 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 495 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 55 km more than the other , 25 x â € “ 20 x = 55 5 x = 55 x = 11 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 11 = 495 km . answer : b"
Answer: b
Python program:
a = 20 + 25 
b = 25 - 20
c = 55 / b
d = a * c
Problem: the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 2 , d ) 1 : 1 , e ) 1 : 7
Rationale: "5 / 6 * 3 / 2 * 4 / 5 = 1 / 1 1 : 1 answer : d"
Answer: d
Python program:
a = 5 * 3
b = 6 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 146 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 17 = 35 5 * quotient = 35 quotient = 7 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 7 ) + 6 = 146 . b )"
Answer: b
Python program:
a = 6 * 3
b = a + 17 
c = 6 * 3
d = c + 17 
e = d / 5
f = b * e
g = f + 6
Problem: if albert ’ s monthly earnings rise by 36 % , he would earn $ 495 . if , instead , his earnings rise by only 25 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 454 , d ) 460 , e ) 490
Rationale: "= 495 / 1.36 ∗ 1.25 = 454 = 454 answer is c"
Answer: c
Python program:
a = 36 / 100
b = 1 + a 
c = 495 / b
d = 25 / 100
e = 1 + d 
f = c * e
Problem: lilly has 10 fish and rosy has 9 fish . in total , how many fish do they have in all ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "10 + 9 = 19 the answer is d ."
Answer: d
Python program:
a = 10 + 9
Problem: after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options: a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Rationale: "cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c"
Answer: c
Python program:
a = 100 / 30
b = 1000 / a
c = 1000 + b 
d = c + 100 
e = d - 1000
f = e / 1000
Problem: of the goose eggs laid at a certain pond , 1 / 3 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1025 , b ) 1075 , c ) 1125 , d ) 1175 , e ) 1225
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 3 ) x = 120 ( 8 / 75 ) x = 120 x = 1125 the answer is c ."
Answer: c
Python program:
a = 3 / 5
b = 1 - a
c = 120 / b
d = 3 / 5
e = c / d
f = 1 / 3
g = e / f