euclaise/mathqa_programs huggingface dataset:
Problem: a batsman in his 12 th innings makes a score of 48 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 26 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 48 ∴ x = 26 answer a"
Answer: a
Python program:
a = 12 * 2
b = 48 - a
c = b + 2
Problem: the average of 1 st 3 of 4 numbers is 7 and of the last 3 are 5 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 3.5 , d ) 7 , e ) 8
Rationale: "a + b + c = 21 b + c + d = 15 a + d = 13 a – d = 6 a + d = 13 2 d = 7 d = 3.5 answer : c"
Answer: c
Python program:
a = 3 * 7
b = 13 - 7
c = b + 3 
d = a - c
e = d - 7
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 24 - inch flat - screen television than a square 17 - inch flat - screen television ?
Options: a ) 143.5 , b ) 154 , c ) 160 , d ) 148.75 , e ) 142.25
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 24 - inch flat - screen television the diagonal ( hypotenuse ) = 24 so , we can apply the pythagorean theorem to get x ² + x ² = 24 ² simplify : 2 x ² = 24 ² divide both sides by 2 to get : x ² = 24 ² / 2 since the area of the square = x ² , we can see that the area of this square is 24 ² / 2 square 17 - inch flat - screen television the diagonal ( hypotenuse ) = 17 so , we can apply the pythagorean theorem to get x ² + x ² = 17 ² simplify : 2 x ² = 17 ² divide both sides by 2 to get : x ² = 17 ² / 2 since the area of the square = x ² , we can see that the area of this square is 17 ² / 2 difference in areas = 24 ² / 2 - 17 ² / 2 = 288 - 144.5 i . e = 143.5 a"
Answer: a
Python program:
a = 24 ** 2
b = a / 2
c = 17 ** 2
d = c / 2
e = b - d
Problem: the average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 85 kg , d ) 90 kg , e ) none
Rationale: "sol . total weight increased = ( 8 × 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer c"
Answer: c
Python program:
a = 8 * 2
b = 65 + a
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 6 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 8 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 6 / 8 * c : ( b + c ) / 2 = ( 6 / 8 ) * c b = ( 1 / 2 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 2 * c ) / 2 = ( 1 / 4 ) * c median = ( a + c ) / 2 = ( 1 / 4 * c + c ) / 2 = ( 5 / 4 ) * c / 2 = ( 5 / 8 ) * c ( answer d )"
Answer: d
Python program:
a = 6 / 8
b = a * 2
c = b - 1
d = 3 / 4
e = d * 2
f = e - 1
g = 1 / f
h = c / g
i = 1 + h 
j = i / 2
Problem: line q has the equation 5 y – 3 x = 75 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 48 , b ) 52 , c ) 56 , d ) 60 , e ) 64
Rationale: "5 y - 3 x = 75 and so y = 3 x / 5 + 15 when x = 0 , then y = 15 . when y = 0 , then x = - 25 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 25 , 0 ) , 0 = - 5 ( - 25 ) / 3 + c the y - intercept is c = - 125 / 3 < - 41 . thus the perpendicular line s can have y - intercepts from - 41 up to 14 . the number of possible lines is 41 + 14 + 1 = 56 the answer is c ."
Answer: c
Python program:
a = 75 / 5
b = a - 2
c = 75 / 3
d = 75 / 5
e = c + d 
f = b + e
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1100 , b ) $ 1240 , c ) $ 1360 , d ) $ 1480 , e ) $ 1550
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 5 + 2 * 5 ) = 62 square feet the total cost is 62 * $ 20 = $ 1240 the answer is b ."
Answer: b
Python program:
a = surface_rectangular_prism * (
Problem: two concentric circles form a ring . the inner and outer circumference of the ring are 352 / 7 m and 528 / 7 m respectively . find the width of the ring .
Options: a ) 2
b ) 4
c ) 5
d ) 6
e ) 78
Rationale: explanation : let the inner and outer radii be r and r meters then , \ inline { \ color { black } 2 \ prod r } = 352 / 7 = > r = ( 352 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 8 m \ inline { \ color { black } 2 \ prod r } = 528 / 7 = > r = ( 528 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 12 m width of the ring = r - r = 12 - 8 = 4 m answer : b ) 4
Answer: b
Python program:
a = 528 / 7
b = a / 2
c = b / math.pi
d = 352 / 7
e = d / 2
f = e / math.pi
g = c - f
Problem: a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2300
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 12 %
Rationale: "explanation : gain % = ( 264.36 * 100 / 2300 ) = 11.49 % = 12 % approx option e"
Answer: e
Python program:
a = 2564 - 36
b = a / 2300
c = 100 * b
d = math.floor(c)
Problem: in a recent election , geoff received 0.5 percent of the 6000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 50.5 , c ) 56 , d ) 60 , e ) 63
Rationale: word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b
Answer: b
Python program:
a = 6000 * 0
b = a / 100
c = 3000 + b 
d = c / 6000
e = d * 100
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates w apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates w / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Python program:
a = 24 / 2
b = 2 + 3 
c = a * b
d = 24 * 2
e = c + d 
f = 3 + 4 
g = 24 * f
h = e / g
Problem: the sum of two consecutive number is 115 . which is the larger number ?
Options: a ) 42 , b ) 58 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 115 2 x + 1 = 115 2 x = 114 x = 57 therefore larger number is x + 1 = 58 answer : b"
Answer: b
Python program:
a = 115 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 115 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 115 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 115 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
Options: a ) 3 / 8 , b ) 2 / 8 , c ) 6 / 7 , d ) 3 / 5 , e ) 2 / 5
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by a in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : a"
Answer: a
Python program:
a = 3 / 30
b = 1 / 30
c = 1 / 20
d = 1 / 20
e = c + d 
f = b + e 
g = 3 * f
h = 1 / g
i = a * h
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 36 then sum is
Options: a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 3600
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 36 3600 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 10 / 100
c = a * b
d = 36 / c
Problem: the ratio of ducks and frogs in a pond is 31 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 169 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 31 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 70 = 169 . answer : option d"
Answer: d
Python program:
a = 31 + 39 
b = a + 2 
c = b / 2
d = 152 / c
e = 39 * d
Problem: x is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number . find value of x ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 a
Answer: a
Python program:
a = negate + ( 
b = 17 ** 2
c = 1 * negate
d = 4 * c
e = b - d
f = math.sqrt(e)
g = a / f
Problem: a man invests rs . 6,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 3000 , e ) none of these
Rationale: "explanation : interest on rs . 6000 at 5 % per annum = ( 6000 × 5 × 1 ) / 100 = rs . 300 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 6000 + x ) × 6 × 1 / 100 . = > 300 + 2 x / 25 = ( 6000 + x ) × 6 × 1 / 100 . = > 30000 + 8 x = ( 6000 + x ) × 6 . = > 30000 + 8 x = 36000 + 6 x . = > 2 x = 6000 . = > x = 3000 . answer : d"
Answer: d
Python program:
a = 8 * 1000
b = 6 - 5
c = 8 - 6
d = b / c
e = a * d
Problem: the lcm of two numbers is 2310 and hcf is 47 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 582 , e ) 517
Rationale: first number * second number = lcm * hcf other number = 2310 * 47 / 210 = 11 * 47 = 517 answer : e
Answer: e
Python program:
a = 2310 * 47
b = a / 210
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 70 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 42 , d ) 19 , e ) 50
Rationale: "answer : d = 19 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 70 % increase makes retail price = 170 . now 30 % decrease - > ( 1 - 30 / 100 ) * 170 = 119 . now compared to the wholesale price of 100 , 19 % increase is what will have the same effect as increasing the wholesale price ."
Answer: d
Python program:
a = 70 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: machine p and machine q are each used to manufacture 220 sprockets . it takes machine p 10 hours longer to produce 220 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 2 , c ) 55 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 220 / x = 220 / 1.1 x + 10 1.1 ( 220 ) = 220 + 11 x 11 x = 22 x = 2 the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = a + 1 
c = 220 / b
d = 220 - c
e = d / 10
Problem: the diagonal of a square is twice the side of equilateral triangle then the ratio of area of the triangle to the area of square is ?
Options: a ) 3 √ 9
b ) 3 √ 8
c ) 3 √ 7
d ) 3 √ 5
e ) 3 √ 1
Rationale: let the side of equilateral triangle = 1 unit . we know that area of an equilateral triangle = 3 – √ 4 a 234 a 2 as side = 1 unit area of the equilateral triangle = 3 – √ 434 now diagonal of the square = 2 ( side of the equilateral triangle ) = 2 we know that area of the square = 12 d 212 d 2 where d = diagonal so area of the square = 12 ( 22 ) = 212 ( 22 ) = 2 ratio of the areas of equilateral triangle and square = 3 – √ 434 : 2 ⇒ ⇒ 3 √ 8 answer : b
Answer: b
Python program:
a = triangle_area_three_edges / (
Problem: the average mark of the students of a class in a particular exam is 65 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 14 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 75 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 65 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 25 x = > x = 14 answer : a"
Answer: a
Python program:
a = 90 * 5
b = 5 * 20
c = a - b
d = 90 - 65
e = c / d
Problem: there are 24 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1250 , b ) 1800 , c ) 2024 , d ) 3256 , e ) 2864
Rationale: "24 c 3 = 24 * 23 * 22 / 6 = 2024 the answer is c ."
Answer: c
Python program:
a = 3 / 24
b = 1 - a
c = b * 24
Problem: fred and sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 2 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: relative distance = 35 miles relative speed = 2 + 5 = 7 miles per hour time taken = 35 / 7 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c
Answer: c
Python program:
a = 2 + 5 
b = 35 / a
c = 5 * b
Problem: a camera lens filter kit containing 5 filters sells for $ 72.50 . if the filters are purchased individually , 2 of them are priced at $ 12.45 each , 2 at $ 14.05 each , 1 at $ 11.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 10.03 % , b ) 11.03 % , c ) 12.03 % , d ) 13.03 % , e ) 11 %
Rationale: cost of kit = $ 72.50 if filters are purchased individually - $ 12.45 * 2 + $ 14.05 * 2 + $ 11.50 = $ 64.50 amount saved = $ 72.50 - $ 64.50 = $ 8 required % age = ( $ 8 / $ 72.50 ) * 100 = 11.03 % so , the correct answer is b .
Answer: b
Python program:
a = 2 * 12
b = 2 * 14
c = a + b 
d = 11 + 5 
e = 72 - 5
f = e * 100
g = f / 72
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 2 of the juniors is equal to 2 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 4 / 7 , b ) 1 / 3 , c ) 5 / 3 , d ) 12 / 7 , e ) 17 / 20
Rationale: let total number of juniors = j total number of seniors = s ( 1 / 2 ) j = ( 2 / 3 ) s = > s = 3 / 4 j total number of students = j + s = ( 7 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 4 ) j ] = 4 / 7 answer a
Answer: a
Python program:
a = 2 * 2
b = 2 * 2
c = 3 + b 
d = a / c
Problem: in a certain alphabet , 10 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 6 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 10 + 24 = 34 ; next , we find the total # of letters without line : 40 - 34 = 6 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 6 - 0 = 6 . a
Answer: a
Python program:
a = 10 + 24 
b = 40 - a
Problem: a certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price . if the new selling price was $ 92.00 and the cost of the product remained the same , what was the old selling price ?
Options: a ) $ 77.40 , b ) $ 80.00 , c ) $ 83.64 , d ) $ 87.40 , e ) $ 88.00
Rationale: given that { cost of the product } * 1.15 = $ 92 - - > { cost of the product } = $ 80 . the old price was $ 80 * 1.1 = $ 88 . answer : e .
Answer: e
Python program:
a = 10 + 100 
b = 15 + 100 
c = a / b
d = c * 92
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 65 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 47 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.65 = 39 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 39 + 8 = 47 registered voters are expected to vote for candidate a , which is 47 % of the total number of registered voters . answer : e ."
Answer: e
Python program:
a = 65 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e
Problem: the smallest number when increased by ` ` 2 ` ` is exactly divisible by 12 , 30 , 48 , 74 and 100 is :
Options: a ) 14439 , b ) 44398 , c ) 44400 , d ) 44402 , e ) 15005
Rationale: "lcm = 44400 44400 - 2 = 44398 answer : b"
Answer: b
Python program:
a = math.lcm(12, 30)
b = math.lcm(48, 74)
c = math.lcm(a, b)
d = math.lcm(c, 100)
e = d + 2
Problem: how many integers between 1 and 1400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e
Answer: e
Python program:
a = math.lcm(25, 35)
b = 1400 / a
Problem: a semicircular cubicle has a radius of 14 . what is the approximate perimeter of the cubicle ?
Options: a ) 55
b ) 86
c ) 25
d ) 72
e ) 35
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 14 + 2 * 14 = 71.96 approximately 72 answer d
Answer: d
Python program:
a = math.pi * 14
b = 2 * 14
c = a + b
Problem: a works thrice as much as b . if a takes 60 days less than b to do a work then find the number of days it would take to complete the work if both work together ?
Options: a ) 22.5 days , b ) 21.5 days , c ) 23.5 days , d ) 24.5 days , e ) 25.5 days
Rationale: if a finishes the job in x days b finishes it in 3 x days 3 x = x + 60 thus x = 30 in one hour 1 / t = 1 / 30 + 1 / 90 = 4 / 90 where t is the number of days they finish the job together . t = 90 / 4 = 22.5 days answer : a
Answer: a
Python program:
a = 3 - 1
b = 60 / a
c = 3 * b
d = 1/(c)
e = 3 - 1
f = 60 / e
g = 1/(f)
h = d + g 
i = 1/(h)
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 t 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 t = $ 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: 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 40 % of the workers who do have a retirement plan are men . if 128 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 112 , e ) 210
Rationale: "set up equation : x = total number of workers 128 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 128 = 16 / 30 x x = 240 240 - 128 = 112 answer 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 = 40 / 100
i = g * h
j = e + i 
k = 128 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: calculate the number of urns of water needed to fill a tank of dimensions of 10 x 10 x 5 m to 90 % full , if the volume of the urn is 0.8 m 3 and can only be filled to 80 % .
Options: a ) 520 , b ) 650.2 , c ) 685.5 , d ) 703.1 , e ) 712.2
Rationale: volume of the tank that needed to be filled = 10 x 10 x 5 x 0.9 = 450 volume of the urn that can be filled = 0.8 x 0.8 = 0.64 no . of urns of water needed to fill the tank = 450 / 0.64 = 703.1 answer : d
Answer: d
Python program:
a = 10 * 10
b = a * 5
c = b * 90
d = c / 100
e = 0 * 8
f = e / 100
g = d / f
Problem: a batsman makes a score of 92 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 44 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 92 = 17 x or x = ( 92 – 48 ) = 44 . answer d"
Answer: d
Python program:
a = 17 * 3
b = 92 - a
c = b + 3
Problem: a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half .
Options: a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) 35 mins
Rationale: explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 x 1 / 40 + x / 2 x 1 / 24 = 1 x = 30 mins answer is d
Answer: d
Python program:
a = 40 * 3
b = a * 2
c = 4 + 4 
d = b / c
Problem: in a division sum , the quotient is 65 , the divisor 24 and the remainder 5 , find the dividend ?
Options: a ) 1595 , b ) 1569 , c ) 1265 , d ) 1555 , e ) 1565
Rationale: "explanation : 65 * 24 + 5 = 1565 answer : e"
Answer: e
Python program:
a = 65 * 24
b = a + 5
Problem: the principal that amounts to rs . 3913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 3913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 3096 . answer : a"
Answer: a
Python program:
a = 1 / 4
b = 6 + a 
c = b / 100
d = 1 + c 
e = d ** 3
f = 3913 / e