euclaise/mathqa_programs huggingface dataset:
Problem: the equation of line s is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line s ?
Options: a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100
Rationale: this can be solve in two steps and without any complex calculation . given : equation of line s as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 75,0 ) . this can be considered a right angle triangle with right angle at ( 0,0 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 0,0 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c
Answer: c
Python program:
a = 100 * 3
b = 4 ** 2
c = 3 ** 2
d = b + c 
e = math.sqrt(d)
f = a / e
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.0 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 5.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2 + ( 3.6 / . 4 ) * . 35 = 2 + 9 * . 35 = 5.15 $ answer a"
Answer: a
Python program:
a = 2 / 5
b = 3 / 6
c = b * 0
d = c + 2
Problem: to a sugar solution of 10 liters containing 50 % sugar , 10 liter of water is added . the percentage of sugar in the new solution is ?
Options: a ) 25 % , b ) 30 % , c ) 15 % , d ) 20 % , e ) 18 %
Rationale: "quantity of sugar = 50 * 10 / 100 = 5 kg new percentage = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Python program:
a = 50 / 100
b = a * 10
c = 10 + 1 
d = b / c
e = d * 100
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 2 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 175 , d ) 216 , e ) 264
Rationale: total paint initially = 360 gallons paint used in the first week = ( 2 / 3 ) * 360 = 240 gallons . remaning paint = 120 gallons paint used in the second week = ( 1 / 5 ) * 120 = 24 gallons total paint used = 264 gallons . option e
Answer: e
Python program:
a = 360 / 3
b = a * 2
c = 360 / 3
d = c * 2
e = 360 - d
f = e / 5
g = b + f
Problem: a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 9
Rationale: let the ten ' s and unit digit be x and 8 respectively . x then , 10 x + 8 + 18 = 10 x 8 + x x x 10 x 2 + 8 + 18 x = 80 + x 2 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 option b
Answer: b
Python program:
a = 10 - 1
b = 18 / a
Problem: how many numbers from 10 to 47 are exactly divisible by 3 ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 , . 12 numbers . 10 / 3 = 3 and 47 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits a )"
Answer: a
Python program:
a = 47 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1
Problem: a 7 % stock yields 10 % . the market value of the stock is :
Options: a ) rs 60 , b ) rs 70 , c ) rs 90 , d ) rs 75 , e ) rs 50
Rationale: "explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 7 , investment = rs . 100 / 10 x 7 = rs 70 market value of rs . 100 stock = rs . 70 answer is b"
Answer: b
Python program:
a = 100 / 10
b = a * 7
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 360 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 298 , e ) 930
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 360 62 % - - - - - - - - ? = > 930 answer : e"
Answer: e
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 360 / c
e = d * 62
f = e / 100
Problem: a light flashes every 6 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 6 sec for 1 min = 10 flashes so for 1 hour = 10 * 60 = 600 flashes . answer : b"
Answer: b
Python program:
a = 3600 / 6
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 6 : 4 . if 60 % of the toyota bought and 40 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 60 and honda 40 , so total number of suv ' s bought for toyota and honda respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d"
Answer: d
Python program:
a = 6 * 4
b = 4 * 6
c = a + b 
d = 100 - c
Problem: a clothing store purchased a pair of pants for $ 81 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 5.4 , c ) $ 4.4 , d ) $ 1.2 , e ) $ 5.0
Rationale: "sale price ( sp ) = 81 + markup ( mp ) - - > mp = sp - 81 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 81 3 sp / 4 = 81 sp = 108 now a discount of 20 % is given so new sp is . 8 * 108 = 86.4 profit = 86.4 - 81 = 5.4 $ answer is b"
Answer: b
Python program:
a = 100 - 20
b = 81 / 3
c = b + 81 
d = a * c
e = d / 100
f = e - 81
Problem: find the average of all prime numbers between 80 and 100
Options: a ) 88 , b ) 60 , c ) 80 , d ) 89.6 , e ) 92
Rationale: "prime numbers between 80 and 100 are 83 , 89 , 97 required average = ( 83 + 89 + 97 ) / 3 = 269 / 3 = 89.6 answer is d"
Answer: d
Python program:
a = 80 + 1 
b = 80 + 1 
c = b + 2 
d = a + c 
e = 100 - 80
f = 100 - 2
g = e + f 
h = d + g 
i = h / 80
Problem: a train 240 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 9 , e ) 13
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 240 * 3 / 55 ] sec = 13 sec answer : e"
Answer: e
Python program:
a = 240 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 70 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 31 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.7 * 10 = 17 percentage by which wage earned by charles is more than that earned by robin = ( 17 - 13 ) / 13 * 100 % = 4 / 13 * 100 % = 31 % answer d"
Answer: d
Python program:
a = 100 + 70 
b = 100 + 30 
c = a - b
d = 100 + 30 
e = c / d
f = e * 100
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 3 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 3 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 3 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 3 / 7 x 1 / 5 = 3 / 35 answer : a"
Answer: a
Python program:
a = 3 / 7
b = 1 / 5
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 60 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 767 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 60 km more than the other , 25 x – 20 x = 60 5 x = 60 x = 12 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 12 = 540 km . answer : a"
Answer: a
Python program:
a = 20 + 25 
b = 25 - 20
c = 60 / b
d = a * c
Problem: a set consists of 18 numbers , all are even or multiple of 5 . if 6 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: { total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 18 = 6 + 12 - { both } + 0 ; { both } = 0 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : a .
Answer: a
Python program:
a = 18 - 12
Problem: what is the units digit of 17 ^ 83 × 13 ^ 52 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 5 correct option : b"
Answer: b
Python program:
a = math.factorial(17)
b = math.factorial(83)
c = a * b
d = math.factorial(17)
e = math.factorial(52)
f = d * e
g = c + f 
h = g / 17
Problem: during a certain two - week period , 50 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 9 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 ) 5 a , b ) 10 a , c ) 20 a , d ) 25 a , e ) 28 a
Rationale: "movies : 50 % comedies . 50 % remaining genre . now in this 50 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 9 x . total 10 x . 10 x = 50 ; x = 5 action movies : 5 % drama movies : 45 % we can say that out of 100 z , : comedies : 50 z action : 5 z drama : 45 z now action movies were a this means : a = 5 z . z = ( a / 5 ) comedies : 50 z = 50 * ( a / 5 ) 10 a b is the answer ."
Answer: b
Python program:
a = 9 + 1 
b = 50 / a
c = math.floor(b)
Problem: a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250
Rationale: "let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b"
Answer: b
Python program:
a = 3 + 4 
b = a * 1000
c = 2 + 3 
d = c * 100
e = b + d 
f = 320 * 20
g = e - f
h = 2 + 3 
i = 2 + 3 
j = h * i
k = g / j
l = 320 - k
Problem: a and b can do a work in 4 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 78
Rationale: "work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 4 + 1 / 12 = 1 / 3 . total time required to complete the work = 2 * 3 = 6 days . answer : d"
Answer: d
Python program:
a = 1/(4)
b = 1/(12)
c = a + b 
d = 1/(c)
e = d * 2
Problem: john had a stock of 1300 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 69.0 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1300 - n = 1300 - 402 = 898 percentage books not sold / total number of books = 898 / 1300 = 0.69 = 69 % correct answer d"
Answer: d
Python program:
a = 75 + 50 
b = 64 + 78 
c = a + b 
d = c + 135 
e = 1300 - d
f = e / 1300
g = f * 100
Problem: a farm is made up of brown and white goats . the number of male brown goats is 35 % less than the total number of brown goats . the total number of female goats is 20 times more than the number of female brown goats . if the total population of male goats is half the population of the female goats , what percentage of male goats are brown ?
Options: a ) 30.1 , b ) 20.5 , c ) 15.2 , d ) 10.2 , e ) 28.6
Rationale: since we are dealing in percentage let us pick 100 as the number of brown male goats . that means that the total number of brown goats is = 135 ( number of male brown goats is 35 % less than the total number of brown goats ) , therefore the number of brown female goats is 35 . the total number of female goats is 15 x the number of brown female goats = 35 * 20 = 700 female goats . male goats total population is half the population of the female goats = 700 / 2 = 350 therefore percentage of male horses goats that are brown = 100 / 350 * 100 = 28.6 correct option is e
Answer: e
Python program:
a = 35 / 100
b = a * 20
c = b * 4
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 4 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 4 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 4 = 3 / 4 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 3 / 4 = 3 / 8 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 3 / 4 * 5 / 8 = 1 / 2 ans d"
Answer: d
Python program:
a = 2 / 0
b = 1 - a
c = 1 / 4
d = 1 - c
e = d / 1
f = 1 - e
g = b * f
Problem: the average of 7 consecutive numbers is 20 . the largest of these numbers is
Options: a ) 12 , b ) 27 , c ) 23 , d ) 28 , e ) 11
Rationale: 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: ( 128.5 x 25 ) + ( 13.8 x 50 ) = ? x 50
Options: a ) 78.05 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 25 ) + ( 13.8 x 50 ) / 50 = 3212.5 + 690 / 50 = 78.05 answer : option a"
Answer: a
Python program:
a = 4 + 1 
b = a ** 4
c = 128 * 5
Problem: a bookseller sells his books at a 15 % markup in price . if he sells a book for $ 23.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 21.00 , d ) $ 19.60 , e ) $ 20.00
Rationale: "let the cost price of book = x selling price of book = 23 $ markup % = 15 ( 115 / 100 ) x = 23 = > x = 20 answer e"
Answer: e
Python program:
a = 15 / 100
b = a * 23
c = 23 - 0
Problem: there are 20 poles with a constant distance between each pole . a car takes 24 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 41.4543 , b ) 41.4545 , c ) 41.45128 , d ) 41.41288 , e ) 41.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 24 seconds 1 pole ( 24 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 24 / 11 ) seconds = 41.4545 seconds answer : b"
Answer: b
Python program:
a = 24 / 12
b = a * 20
Problem: a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 50 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 63 , b ) 66 , c ) 69 , d ) 72 , e ) 75
Rationale: let v be the speed of the person and let x be the speed of the walkway . 50 ( v + x ) = 100 then 150 ( v + x ) = 300 150 ( v - x ) = 100 when we add the two equations : 300 v = 400 v = 4 / 3 time = 100 / ( 4 / 3 ) = 75 seconds the answer is e .
Answer: e
Python program:
a = 100 / 50
b = 100 / 150
c = a + b 
d = c / 2
e = 100 / d
Problem: what will be the compound interest on a sum of rs . 23,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 9313.34 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 23000 * ( 1 + 12 / 100 ) 3 ] = 23000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 32313.34 c . i . = ( 32313.34 - 23000 ) = rs . 9313.34 answer : a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: the radius of a wheel is 16.8 cm . what is the distance covered by the wheel in making 300 resolutions ?
Options: a ) 754 m , b ) 316.512 m , c ) 311.512 m , d ) 311.518 m , e ) 313.512 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 16.8 = 31651.2 cm = 316.512 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 16
g = f * 2
h = g * 300
i = h / 100
Problem: evaluate : 6302.5 + 630.25 + 63.025 + 6.3025 + 0.63025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 7002.70775
Rationale: "6302.5 630.25 63.025 6.3025 + 0.63025 - - - - - - - - - - - - - - - 7002.70775 answer is e ."
Answer: e
Python program:
a = 630 * 25
b = a * 6
c = 6302 - 5
Problem: what is the sum of all the prime numbers from 20 to 40 ?
Options: a ) 279 , b ) 100 , c ) 278 , d ) 120 , e ) 191
Rationale: "explanation : 23 + 29 + 31 + 37 = 120 answer : d"
Answer: d
Python program:
a = 40 - 20
b = a - 2
c = b / 2
d = c + 20 
e = 40 - 20
f = e + 2 
g = f / 2
h = d * g
Problem: evaluate 30 ! / 28 !
Options: a ) 720 , b ) 600 , c ) 870 , d ) 910 , e ) 650
Rationale: "we have 30 ! / 28 ! = 30 * 29 * 28 ! / 28 ! = 30 * 29 = 870 answer is c"
Answer: c
Python program:
a = 28 / 30
b = 30 / a
Problem: at present the ratio between the ages of arun and deepak is 2 : 5 . after 10 years arun ' s age will be 30 years . what is the age of the deepak ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 45
Rationale: "let the present age of arun and deepak be 4 x and 3 x 2 x + 10 = 30 2 x = 20 x = 10 deepak ' s age = 5 x = 50 years answer is c"
Answer: c
Python program:
a = 30 - 10
b = a * 5
c = b / 2
Problem: 100 liters of a mixture contains milk and water in the ratio 4 : 1 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 7 : 5 , b ) 9 : 2 , c ) 6 : 1 , d ) 5 : 4 , e ) 11 : 4
Rationale: "quantity of milk in 100 liters if mix = 100 * 4 / 5 = 80 liters quantity of milk in 110 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 110 - 90 = 20 liters ratio of milk and water in new mix = 90 : 20 = 9 : 2 answer is b"
Answer: b
Python program:
a = 10 - 1
b = a * 1
c = 4 * 1
d = b / c
Problem: there are 8 baskets numbered from 1 to 8 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 640 , b ) 680 , c ) 720 , d ) 760 , e ) 800
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 8 * 9 / 2 = 36 apples . the total number of apples taken by 10 children is 10 * 36 = 360 the number of apples left in the end is 1000 - 360 = 640 apples . the answer is a ."
Answer: a
Python program:
a = 1 + 8 
b = 10 / 2
c = a * b
d = 10 / 2
e = c + d 
f = e + 1 
g = f * 10
h = 1000 - g
Problem: a rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 15 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 225 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 6 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 10 / 2 ) = 15 . the total cost is 15 * 15 = $ 225 . the answer is , therefore , d ."
Answer: d
Python program:
a = 15 * 15
Problem: on multiplying a numberz by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number z is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Python program:
a = 100 * 4
b = 100 * 4
c = a + b 
d = c - 100
e = 3 * 4
f = e + 3 
g = d + f 
h = g * 153
Problem: the average age of 40 passengers in a ferry is 35 . what is the average age of the new group formed when combining the passengers with the 5 crew members of ferry whose average age is 25 ?
Options: a ) 36.45 , b ) 38.89 , c ) 39.67 , d ) 40.12 , e ) 41.88
Rationale: sum of ages of passengers = 40 x 35 = 1400 sum of ages of crew = 25 x 5 = 125 sum of ages of new group formed = 1525 average = 1525 / 45 = 38.89 answer : b
Answer: b
Python program:
a = 35 * 40
b = 5 * 25
c = a + b 
d = 35 + 5 
e = c / d