euclaise/mathqa_programs huggingface dataset:
Problem: 6 bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none
Rationale: l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d
Answer: d
Python program:
a = 30 * const_60
b = math.lcm(12, 10)
c = math.lcm(b, 8)
d = a / c
e = d + 1
Problem: a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 200 , what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 8 , c ) 12 , d ) 4 , e ) 2
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 200 x = 64 - y 3 ( 64 - y ) + 4 y = 200 192 - 3 y + 4 y = 200 y = 8 answer : b"
Answer: b
Python program:
a = 64 * 3
b = 200 - a
Problem: when average age of 24 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 23 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 24 numbers = 0 . sum of 24 numbers ( 0 x 24 ) = 0 . it is quite possible that 23 of these numbers may be positive and if their sum is a then 24 th number is ( - a ) answer is 23 ( b )"
Answer: b
Python program:
a = 24 - 1
Problem: a shopkeeper sold an article at $ 100 with 15 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 87 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 115 = $ 87 ( approximately ) answer is d"
Answer: d
Python program:
a = 100 + 15 
b = 100 / a
c = 100 * b
Problem: marcella has 26 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 26 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 26 pairs of shoes minus the 5 ' destroyed ' pairs yields 21 pairs that still fulfill the requirements . answer : a"
Answer: a
Python program:
a = 9 / 2
b = math.floor(a)
c = b + 1 
d = 26 - c
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 4 hours ?
Options: a ) 675 , b ) 900 , c ) 1,800 , d ) 5,900 , e ) 7,500
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 4 hours ) = 900 cans . the answer is b ."
Answer: b
Python program:
a = 4 * 360
b = 5 * 360
c = 4 + 4 
d = b / c
e = 4 * d
f = a - e
Problem: the probability that event a occurs is 0.4 , and the probability that event b occurs is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b and event b will occur ?
Options: a ) 0.25 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( a n b ) + 0.45 p ( b ) = 0.25 ans : a"
Answer: a
Python program:
a = 0 + 6 
b = a - 0
Problem: 60 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 90 , d ) 30 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 60 + 50 % ( 60 ) = 60 + 30 = 90 . answer c"
Answer: c
Python program:
a = 50 / 100
b = 60 * a
c = 60 + b
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 30 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 70 * 1 + 40 * 2 ) / 3 = 50 % are men total = 120 * 100 / 50 = 240 no . of women = 240 - 120 = 120 d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 3
c = 20 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 30 / 100
i = g * h
j = e + i 
k = 120 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 30 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price q of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price q = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Python program:
a = 90 * 20
b = a / 100
c = 90 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: what is the 28 th digit to the right of the decimal point in the decimal form of 5 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 11 = 0.45454545 . . . the even numbered positions in the decimal expansion are all 5 . the answer is c ."
Answer: c
Python program:
a = 5 / 11
Problem: a large box contains 16 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 450 , d ) 400 , e ) 650
Rationale: "the number of chocolate bars is equal to 16 * 25 = 400 correct answer d"
Answer: d
Python program:
a = 16 * 25
Problem: the sum of 4 consecutive even numbers is 52 , find the third number ?
Options: a ) 14 , b ) 10 , c ) 12 , d ) 16 , e ) 20
Rationale: let the first number be n let the second number be n + 2 let the third number be n + 4 let the third number be n + 6 n + n + 2 + n + 4 + n + 6 = 52 combine like terms : 4 n + 12 = 52 4 n + 12 = 52 4 n = 52 - 12 4 n = 40 n = 10 n + 2 = 12 n + 4 = 14 n + 6 = 16 the third number is 14 answer : a
Answer: a
Python program:
a = 52 / 4
b = a + 1
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 99 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?
Options: a ) 126 sq . ft
b ) 64 sq . ft
c ) 100 sq . ft
d ) 120 sq . ft
e ) 140 sq . ft
Rationale: explanation : solution 1 length = 9 feet breadth = 37 − 9 / 2 = 14 feet area = 9 × 14 = 126 square feet answer : option a
Answer: a
Python program:
a = 3 * 3
b = 37 - a
c = b / 2
d = 3 * 3
e = c * d
Problem: the ratio between the presents of the a and b is 6 : 7 . if b is 4 years older than a , what will be the ratio of the ages of a and b after 4 years ?
Options: a ) 1 : 2 , b ) 9 : 11 , c ) 7 : 8 , d ) 6 : 7 , e ) 3 : 4
Rationale: let a and b ages will be 6 x and 7 x 7 x - 6 x = 4 x = 4 required ratio = 6 x + 4 : 7 x + 4 = 28 : 32 = 7 : 8 answer is c
Answer: c
Python program:
a = 7 * 4
b = a - 4
c = b + 4 
d = 7 * 4
e = d + 4 
f = c / e
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 8000 , the number of valid votes that the other candidate got , was :
Options: a ) 3500 , b ) 3600 , c ) 3270 , d ) 3700 , e ) 4000
Rationale: "number of valid votes = 80 % of 8000 = 6400 . valid votes polled by other candidate = 45 % of 8000 = ( 45 / 100 ) x 8000 = 3600 answer = b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 8000
Problem: a certain city with a population of 72,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 6,000 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 72 k x = 6,000 answer : a"
Answer: a
Python program:
a = 4 * 2
b = a * 100
Problem: joe drives 420 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 54 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 420 / 60 = 7 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 10 hours avg speed = total distance / t = 540 / 10 = 54 mph = b"
Answer: b
Python program:
a = 420 + 120 
b = 420 / 60
c = 120 / 40
d = b + c 
e = a / d
Problem: in a caravan , in addition to 60 hens , there are 35 goats and 6 camels with some keepers . if the total number of feet be 193 more than the number of heads in the caravan , the number of keepers is
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: explanation : let number of keepers be x . then , total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2 x = 2 x + 284 . total number of heads = 60 + 35 + 6 + x = 101 + x . therefore ( 2 x + 284 ) = ( 101 + x ) + 193 or x = 10 . answer : b
Answer: b
Python program:
a = 60 + 35 
b = a + 6 
c = b + 193 
d = 2 * 60
e = 4 * 35
f = d + e 
g = 4 * 6
h = f + g 
i = c - h
Problem: 100 liter solution of cool - drink is made from 10 % jasmine water . if 5 liters of jasmine and 10 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 3 / 31 , d ) 4 / 15 , e ) 2 / 3
Rationale: denominator 100 + 5 + 10 115 numerator 100 * 0.1 = 10 - - - > jasmine water 10 + 5 = 15 - - - > new content of jasmine water in new solution ratio 3 / 23 answer is b
Answer: b
Python program:
a = 100 + 10 
b = 5 + a 
c = 10 / b
Problem: a box contain red , blue and green colored balls . the number of red balls is 80 and the number of blue balls is 60 . the number of green balls subtracted from the number of red balls is the same as the number of green balls added with the number of blue balls . then the number of green balls is ?
Options: a ) 80 , b ) green balls = 70 , c ) 60 , d ) 85 , e ) 140
Rationale: answer let the number of green balls be x . then , x - 60 = 80 - x â ‡ ’ 2 x = 80 + 60 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : b
Answer: b
Python program:
a = 80 - 60
b = a / 2
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 25 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 25 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Python program:
a = 25 * 4
b = a / 2
c = 25 + 5 
d = b + c
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 80 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 16 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 80 = 0.9375 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.9375 + t » 100 / 40 = 0.9375 + t » 2.5 = 0.9375 + t » t = 1.5625 back to 2 nd part of the trip formula : 25 / s = 1.5625 » s = 16 ans a"
Answer: a
Python program:
a = 40 + 80 
b = a - 75
c = 40 + 80 
d = c / 40
e = 75 / 80
f = d - e
g = b / f
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 4 or 15 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 15 , e ) 11 / 30
Rationale: number of multiples of 4 from 1 through 30 = 30 / 4 = 7 number of multiples of 15 from 1 through 30 = 30 / 15 = 2 number of multiples of 4 and 15 both from 1 through 30 = number of multiples of 15 * 4 ( = 60 ) = 0 total favourable cases = 7 + 2 - 0 = 9 probability = 9 / 30 = 3 / 10 answer : option c
Answer: c
Python program:
a = 30 / 4
b = math.floor(a)
c = 30 / 15
d = b + c 
e = d / 30
Problem: a car gets 28 miles to the gallon . if it is modified to use a solar panel , it will use only 80 percent as much fuel as it does now . if the fuel tank holds 15 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 85 , b ) 90 , c ) 95 , d ) 100 , e ) 105
Rationale: "originally , the distance the car could go on a full tank was 15 * 28 = 420 miles . after it has been modified , the car can go 28 / 0.8 = 35 miles per gallon . on a full tank , the car can go 15 * 35 = 525 miles , thus 105 miles more . the answer is e ."
Answer: e
Python program:
a = 28 / 80
b = a * 100
c = b * 15
d = 28 * 15
e = c - d
Problem: how many of the positive factors of 63 , 84 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 63 - 1,3 , 7,9 , 21,63 factors of 84 - 1,2 , 3,4 , 6,7 , 12,14 , 21,28 , 42,84 comparing both , we have three common factors of 63 and 84 - 1,3 , 7,21 answer ( b )"
Answer: b
Python program:
a = 84 / 63
Problem: a cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm . the total area of the wet surface is :
Options: a ) 120 m 2 , b ) 136 m 2 , c ) 128 m 2 , d ) 130 m 2 , e ) 134 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.50 + 10 x 1.50 ) + 8 x 10 ] m 2 = 134 m 2 . answer : e"
Answer: e
Python program:
a = 50 / 100
b = a + 1 
c = b * 8
d = 50 / 100
e = d + 1 
f = e * 10
g = c + f 
h = 2 * g
i = 8 * 10
j = h + i
Problem: jim and cara begin running at the same time and they start at the same place on a straight path . jim runs at 6 miles per hour , and cara runs at 5 miles per hour . after 30 minutes , jim stops to stretch . if it takes jim 18 minutes to stretch and cara continues to run during this time , how many minutes will it take jim to catch up to cara ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: in 30 minutes , jim runs 3 miles . in 48 minutes , cara runs 4 miles . jim can catch cara at a rate of 1 mile per hour . since cara is ahead by 1 mile , it will take jim 1 hour = 60 minutes to catch cara . the answer is c .
Answer: c
Python program:
a = 18 / const_60
b = 5 * a
c = 30 / const_60
d = 5 * c
e = b + d 
f = 30 / const_60
g = 6 * f
h = e - g
i = h * const_60
Problem: what is the value of 4 ^ 4 + 4 ^ 6 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 17 ( 4 ^ 4 )
Rationale: "4 ^ 4 + 4 ^ 6 = 4 ^ 4 ( 1 + 4 ^ 2 ) = 4 ^ 4 * 17 answer e"
Answer: e
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 35000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1450 , d ) $ 900 , e ) $ 1000
Rationale: "30 sec approach - solve it using approximation 35000 sheet at full price , 5 cent = 1750 35000 sheet at max discount price , 4 cent = 1400 your ans got to be between these two . ans c it is ."
Answer: c
Python program:
a = 10000 - 2000
b = 1 / 10
c = 1 - b
d = 1 / 10
e = c * d
f = a * e
Problem: a rectangular floor that measures 6 meters by 8 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 12 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 ) $ 960 , e ) $ 144
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 ( 8 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 8 / 2 ) = 12 . the total cost is 12 * 12 = $ 144 the answer is , therefore , e ."
Answer: e
Python program:
a = 12 * 6
Problem: in a public show 50 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 300 , e ) 150
Rationale: "50 % of 600 = 50 / 100 × 600 = 300 therefore , the number of vacant seats = 600 - 300 = 300 . answer : d"
Answer: d
Python program:
a = 100 - 50
b = 600 * a
c = b / 100
Problem: how many even number in the range between 10 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 46 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 46 - 15 = 31 . hence , answer c"
Answer: c
Python program:
a = 100 - 10
b = a - 2
c = b / 2
d = 100 - 2
e = 3 * 4
f = d - e
g = f - 3
h = g - 3
i = h / 3
j = i / 2
k = c - j
Problem: a and b are partners in a business . a contributes 1 / 4 of the capital for 15 months and b received 2 / 3 of the profit . for how long b ’ s money was used ?
Options: a ) 4 months , b ) 6 months , c ) 8 months , d ) 10 months , e ) none
Rationale: "sol . let the total profit be rs . z . then , b ’ share = rs . 2 z / 3 , a ’ s share = rs . [ z - 2 z / 3 ] = rs . z / 3 ∴ a : b = z / 3 : 2 z / 3 = 1 : 2 . let the total capital be rs . x and suppose b ’ s money was used for x months . then , [ 1 / 4 x * 15 ] / [ 3 / 4 x * y ] = 1 / 2 ⇔ y = [ 15 * 2 / 3 ] = 10 . thus , b ’ s money was used for 10 months . answer d"
Answer: d
Python program:
a = 10 + 1 
b = a - 1
Problem: a man buys rs . 52 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 39
Rationale: "dividend on rs . 52 = rs . 9 / 100 x 52 = rs . 4.68 . rs . 12 is an income on rs . 100 . rs . 4.68 is an income on rs . 100 / 12 x 4.68 = rs . 39 . answer : option e"
Answer: e
Python program:
a = 100 / 12
b = 9 / 100
c = b * 52
d = a * c
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 32 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 13 , c ) 15 , d ) 16 , e ) 18
Rationale: "in 32 liters , red = 5 / 8 * 32 = 20 and blue = 12 so , 20 / ( 12 + x ) = 4 / 5 or , x = 13 ( answer b )"
Answer: b
Python program:
a = 5 + 3 
b = 5 / a
c = 32 * b
d = 5 + 3 
e = 4 / d
f = c / e
g = 5 + 3 
h = 5 / g
i = f * h
j = 5 + 3 
k = 5 / j
l = 32 * k
m = 32 - l
n = i - m
Problem: if 5 / w + 5 / x = 5 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 5 / w + 5 / x = 5 / ywx = y find : ( w + x ) / 2 = ? 5 ( 1 / w + 1 / x ) = 5 ( 1 / y ) - divide both sides by 5 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Python program:
a = 5 + 5 
b = 5 / a
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 e 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: jerry went to a shop and bought things worth rs . 45 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 29.5 , e ) 39.7
Rationale: "total cost of the items he purchased = rs . 45 given that out of this rs . 45 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 45 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 45 − 0.3 − x ) = 30 ⇒ ( 45 − 0.3 − x ) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 e )"
Answer: e
Python program:
a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d 
f = 45 - e
Problem: in an examination , 25 % of total students failed in hindi , 48 % failed in english and 27 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 54 , c ) 28 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 48 â € “ 27 = 46 therefore students who passed = 100 â € “ 46 = 54 . answer : b"
Answer: b
Python program:
a = 25 + 48 
b = a - 27
c = 100 - b