euclaise/mathqa_programs huggingface dataset:
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 7 , so ( x - 7 ) / x = 7 / 9 = > 9 x - 63 = 7 x = > 2 x = 63 = > x = 31.5 so sachin age is 31.5 - 7 = 24.5 answer : b"
Answer: b
Python program:
a = 9 - 7
b = 7 / a
c = b * 7
Problem: the present population of a town is 500 . population increase rate is 10 % p . a . find the population of town before 2 years ?
Options: a ) 512 , b ) 615 , c ) 810 , d ) 413 , e ) 123
Rationale: "p = 500 r = 10 % required population of town = p / ( 1 + r / 100 ) ^ t = 500 / ( 1 + 10 / 100 ) ^ 2 = 500 / ( 11 / 10 ) ^ 2 = 413 ( approximately ) answer is d"
Answer: d
Python program:
a = 500 * 10
b = a / 100
c = 500 + b
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 5,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 . the answer is c ."
Answer: c
Python program:
a = 4 + 2 
b = a / 1
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 90 = $ 1.10 cents on commodity y , which will take 11 years . the answer is c .
Answer: c
Python program:
a = 90 / 100
b = 4 - 4
c = a + b 
d = 30 / 100
e = 4 - 4
f = d - e
g = c / f
h = 2001 + g
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 650 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 725 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 1000 , b ) 1,250 , c ) 2,250 , d ) 3,250 , e ) 4,250
Rationale: so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 325 , thus 0.2 x = $ 325 - - > x = $ 1625 since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,625 = $ 3,250 answer d
Answer: d
Python program:
a = 650 / 2
b = 650 / 2
c = a * b
d = 725 - 650
e = c / d
f = e * 2
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 70 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 29 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 70 % of 60 = 42 total new books = 58 fraction = 16 / 58 = 8 / 29 ans : b"
Answer: b
Python program:
a = 40 * 40
b = a / 100
c = 40 * 40
d = c / 100
e = 100 - 40
f = 70 * e
g = f / 100
h = d + g 
i = b / h
Problem: 10 years ago , the age of anand was one - third the age of bala at that time . the present age of bala is 10 years more than the present age of anand . find the present age of anand ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let the present ages of anand and bala be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 10 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 0 ) = > 3 a - 30 = a = > 2 a = 30 = > a = 15 . answer : d
Answer: d
Python program:
a = 10 * 3
b = 3 - 1
c = a / b
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 17 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.3 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 17 = 403 hence , new average = 403 ⁄ 10 = 40.3 answer a"
Answer: a
Python program:
a = 40 * 2
b = 13 + 17 
c = a + b 
d = c - 31
e = d / 10
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 4 screws and 2 nails ?
Options: a ) 4 , b ) 5 / 2 , c ) 2 , d ) 3 / 2 , e ) 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 4 s and 2 n = 4 s + 2 * 4 s = 12 s . . ratio = 15 s / 12 s = 15 / 12 = 5 / 4 answer : e"
Answer: e
Python program:
a = 3 * 4
b = a + 3 
c = b / 10
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1200 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 24750 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1200 × 20.625 ) = 24750 . answer c"
Answer: c
Python program:
a = 5 * 5
b = 1200 * a
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 6 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 6 * ( 2 / 3 ) ) days = > 30 days answer : a
Answer: a
Python program:
a = 15 * 21
b = a * 8
c = 21 * 6
d = 2 / 3
e = c * d
f = b / e
Problem: 4 brothers adam , bill , charles and david together contributed certain amount of money and purchased a car . the contribution made by adam is half that of the total contribution made by the other 3 brothers , contribution made by bill is one - fourth of the total contribution made by the other 3 brothers and the contribution made by charles is two - third of the total contribution made by the other 3 brothers . if the total price of the car is $ 9750 , find the contribution made by david .
Options: a ) $ 540 , b ) $ 580 , c ) $ 600 , d ) $ 650 , e ) $ 680
Rationale: given that a : ( b + c + d ) = 1 : 2 . hence a contributed 1 / 3 rd of the total price . given b : ( a + c + d ) = 1 : 4 hence b contributed 1 / 5 th of the total price . given c : ( a + b + d ) = 2 : 3 hence c contributed 2 / 5 th of the total price . thus the contribution made by a , b and c = 1 / 3 + 1 / 5 + 2 / 5 = 14 / 15 so , the remaining 1 / 15 th of the price is contributed by david . hence david ' s contribution = 1 / 15 × 9750 = $ 650 . the answer is d .
Answer: d
Python program:
a = 1 + 2 
b = 9750 / a
c = 4 + 1 
d = 9750 / c
e = b + d 
f = 3 / 2
g = f + 1 
h = 9750 / g
i = e + h 
j = 9750 - i
Problem: share rs . 6000 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 2000
Rationale: "amount received by sanjay . 4 / 12 x 6000 = 2000 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2000 . e"
Answer: e
Python program:
a = 6000 / 2
b = 6000 / 6
c = a - b
Problem: a worker makes a toy in every 2 h . if he works for 120 h , then how many toys will he make ?
Options: a ) 40 , b ) 60 , c ) 45 , d ) 39 , e ) none
Rationale: "no . of toys = 120 / 2 = 60 answer : b"
Answer: b
Python program:
a = 120 / 2
Problem: find the sum of all odd numbers up to 100 .
Options: a ) 2500 , b ) 2400 , c ) 2300 , d ) 2200 , e ) 2100
Rationale: "the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 . required sum = n / 2 ( first term + last term ) = 50 / 2 ( 1 + 99 ) = 2500 . answer is a ."
Answer: a
Python program:
a = 100 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 100 / e
g = f / 2
h = 100 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 100 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: there are , in a certain league , 20 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 450 , b ) 760 , c ) 110 , d ) 180 , e ) 400
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 760 option b ."
Answer: b
Python program:
a = 20 - 1
b = a * 4
c = 20 / 2
d = b * c
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 12 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 6
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 12 / 15 ) / ( 2 / 15 ) = 6 . e"
Answer: e
Python program:
a = 12 / 15
b = 2 / 15
c = a / b
Problem: the water level in a rectangular swimming pool measuring 20 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100
b ) 250
c ) 1875
d ) 1200
e ) 5625
Rationale: 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 20 * 25 * 1 / 2 = 250 feet ^ 3 of water must be removed , which equals to 250 * 7.5 = 1875 gallons . answer : c .
Answer: c
Python program:
a = 10 + 2 
b = 6 / a
c = volume_rectangular_prism * (
Problem: a man buys rs . 20 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 ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 18
Rationale: dividend on rs 20 = 9 / 100 * 20 = 9 / 5 is 12 income 100 9 / 5 is an income on rs ( 100 / 12 * 9 / 5 ) = rs 15 answer d
Answer: d
Python program:
a = 100 / 12
b = 9 / 100
c = b * 20
d = a * c
Problem: a car travels first 160 km at 75 km / hr and the next 160 km at 90 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 81.81
Rationale: "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 90 km / hr time taken to travel next 160 km = distancespeed = 160 / 90 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 90 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 90 ) = 81.81 km / hr answer : e"
Answer: e
Python program:
a = 160 / 75
b = 160 / 90
c = a + b 
d = 1 / c
e = 320 * d
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 360 . how much does c have ?
Options: a ) 60 , b ) 78 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 360 - - - - - - - - - - - - - - a + b + 2 c = 560 a + b + c = 500 - - - - - - - - - - - - - - - - c = 60 answer : a"
Answer: a
Python program:
a = 200 + 360 
b = a - 500
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 190 games will be played during the tournament . what is the number of participants ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 190 n * ( n - 1 ) = 380 = 20 * 19 ( trial and error ) the answer is d ."
Answer: d
Python program:
a = 190 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: a certain number of men can finish a piece of work in 10 days . however , if there were 10 less men it will take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 10 men , b ) 30 men , c ) 40 men , d ) 20 men , e ) none of these
Rationale: "let x be the number of men originally thus , 10 x = ( 10 + 10 ) ( x - 10 ) 10 x = 20 ( x - 10 ) x = 2 ( x - 10 ) x = 20 answer : d"
Answer: d
Python program:
a = 10 + 10 
b = 10 / a
c = 1 - b
d = 10 / c
Problem: find the average of all numbers between 4 and 34 which are divisible by 5
Options: a ) 20 , b ) 21 , c ) 25 , d ) 30 , e ) 55
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 5 = 105 / 5 = 21 option b"
Answer: b
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: how can a cake ( circular ) be cut into 8 pieces by making just 3 cuts ?
Options: a ) 21
b ) 787
c ) 37
d ) 26
e ) 01
Rationale: explanation : cut the cake using three mutually perpendicular planes . it leaves 8 pieces , one each in each octant . answera
Answer: a
Python program:
a = 8 / 3
b = a * 8
Problem: the bankers discount of a certain sum of money is rs . 72 and the true discount on the same sum for the same time is rs . 60 . the sum due is :
Options: a ) rs . 360 , b ) rs . 432 , c ) rs . 540 , d ) rs . 1080 , e ) rs . 1280
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 72 * 60 ) / 72 - 60 ; 360 answer : a"
Answer: a
Python program:
a = 60 * 72
b = 72 - 60
c = a / b
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1000 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 15,600 , d ) rs . 20,625 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1000 x 20.625 ) = rs . 20625 . answer d"
Answer: d
Python program:
a = 5 * 5
b = 1000 * a
Problem: find the value of x in [ ( 17.28 / x ) / ( 3.6 * 0.2 ) ] = 2
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 17.28 / x ) = 2 * 3.6 * 0.2 x = ( 17.28 / 1.44 ) = ( 1728 / 14 ) = 12 . option b
Answer: b
Python program:
a = 3 * 6
b = a * 2
c = 17 / 28
Problem: set a contains all the even numbers between 22 and 70 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1400
Rationale: "each term in set b is 40 more than the corresponding term in set a . the difference of the sums = 25 * 40 = 1000 . the answer is c ."
Answer: c
Python program:
a = 62 - 22
b = 70 - 22
c = b / 2
d = c + 1 
e = a * d
Problem: a person travels from p to q a speed of 40 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 27 , b ) 87 , c ) 48 , d ) 77 , e ) 51
Rationale: "speed on return trip = 150 % of 40 = 60 km / hr . average speed = ( 2 * 40 * 60 ) / ( 40 + 60 ) = 48 km / hr . answer : c"
Answer: c
Python program:
a = 50 / 100
b = 1 + a 
c = 40 * b
d = c + 40 
e = d / 2
Problem: the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 2 , the average of the numbers increases to 9.2 . what number is multiplied by 2 ?
Options: a ) 12.0 , b ) 30.0 , c ) 30.9 , d ) 40.0 , e ) 60.0
Rationale: the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 2 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 2 be n then , 2 n = n + 12 or n = 12 answer : - a
Answer: a
Python program:
a = 9 * 2
b = 6 * 8
c = a - b
Problem: the sale price sarees listed for rs . 345 after successive discount is 12 % and 25 % is ?
Options: a ) 321 , b ) 276 , c ) 342 , d ) 228 , e ) 245
Rationale: "explanation : 345 * ( 88 / 100 ) * ( 75 / 100 ) = 228 answer : d"
Answer: d
Python program:
a = 345 * 12
b = a / 100
c = 345 - b
d = 345 * 12
e = d / 100
f = 345 - e
g = f * 25
h = g / 100
i = c - h
Problem: the length and breadth of the floor of the room are 20 feet and 10 feet respectively . square tiles of 2 feet length of different colours are to be laid on the floor . black tiles are laid in the first row on all sides . if white tiles are laid in the one - third of the remaining and blue tiles in the rest , how many blue tiles will be there ?
Options: a ) 16
b ) 24
c ) 32
d ) 48
e ) none of these
Rationale: area left after laying black tiles = [ ( 20 – 4 ) × ( 10 – 4 ) ] sq . ft . = 96 sq . ft . area under white tiles = ( 1 ⁄ 3 × 96 ) sq . ft = 32 sq . ft . area under blue tiles = ( 96 – 32 ) sq . ft = 64 sq . ft . number of blue tiles = 64 / 2 × 2 = 16 . answer a
Answer: a
Python program:
a = 20 * 10
b = 20 + 20 
c = 3 + 3 
d = b + c 
e = 3 + 3 
f = d + e 
g = f * 2
h = a - g
i = 20 * 10
j = 20 + 20 
k = 3 + 3 
l = j + k 
m = 3 + 3 
n = l + m 
o = n * 2
p = i - o
q = p / 3
r = h - q
s = r / 4
Problem: in a group of 89 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 27 , d ) 26 , e ) 31
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 89 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 89 - 59 = 30 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 89 = 36 + 32 + 30 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - c"
Answer: c
Python program:
a = 36 + 32 
b = a - 59
c = 36 - b
Problem: the workforce of company x is 60 % female . the company hired 22 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 264 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 22 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 22 ) 0.05 x = 12.1 x = 242 - this is quantity of employees before adding 22 men so after adding it will be 264 answer is c"
Answer: c
Python program:
a = 55 / 100
b = a * 22
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 22
Problem: a fruit seller sells mangoes at the rate of rs . 8 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.5 , b ) rs 9.5 , c ) rs 10.5 , d ) rs 11.5 , e ) none of these
Rationale: explanation : 80 : 8 = 105 : x x = ( 8 × 105 / 80 ) = rs 10.5 option c
Answer: c
Python program:
a = 100 + 5 
b = 8 * a
c = 100 - 20
d = b / c
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 21 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 2 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 21 = = > 27 x + 17 y = 21 x + 21 y = = > 6 x = 4 y = = > x / y = 2 / 3 . answer : c"
Answer: c
Python program:
a = 27 - 21
b = 21 - 17
c = a / b
Problem: if n = 9 ^ 11 – 9 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 9 ^ 3 - 9 . now 9 ^ 3 has last digit 9 . , we subtract 9 from 9 , thus 9 - 9 = 0 is the answer . option a
Answer: a
Python program:
a = math.log(9)
b = 9 ** 11
c = math.log(b)
d = a / c
Problem: two trains each 210 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 90 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 3 sec , b ) 2.6 sec , c ) 3.6 sec , d ) 8.6 sec , e ) 7.6 sec
Rationale: "explanation : d = 210 m + 210 m = 420 m rs = 90 + 85 = 175 * 5 / 18 = 243 / 5 t = 420 * 5 / 243 = 8.6 sec answer : option d"
Answer: d
Python program:
a = 210 + 210 
b = a / 1000
c = 90 + 85 
d = b / c
e = 3600 * d
Problem: b completes a work in 8 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.44 days , c ) 5 days , d ) 6.44 days , e ) 7 days
Rationale: "1 / 8 + 1 / 10 = 9 / 40 40 / 9 = 4.44 days answer : b"
Answer: b
Python program:
a = 10 * 8
b = 8 + 10 
c = a / b
Problem: a sum fetched a total simple interest of rs . 1000 at the rate of 10 p . c . p . a . in 4 years . what is the sum ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 1900 , e ) 1500
Rationale: sol . principal = rs . [ 100 * 1000 / 10 * 4 ] = rs . [ 100000 / 40 ] = rs . 2500 . answer a
Answer: a
Python program:
a = 1000 * 100
b = a / 10
c = b / 4
Problem: p and q are the only two applicants qualified for a short - term research project that pays 360 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 6 , c ) $ 9 , d ) $ 12 , e ) $ 15
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 360 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 360 / 30 = $ 12 p ' s hourly wage is 360 / ( t - 10 ) = $ 18 which is $ 6 per hour more . the answer is b ."
Answer: b
Python program:
a = 3 / 2
b = a - 1
c = 10 / b
d = 360 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10 
i = 360 / h
j = d - i
Problem: a cylinder of height h is 7 / 8 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 69 % , d ) 80 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 7 / 8 new cylinder 3 / 5 so 3 / 5 / 7 / 8 = 3 / 5 * 8 / 7 = 0.69 or 69 % . answer c"
Answer: c
Python program:
a = 3 / 5
b = 7 / 8
c = a / b
d = c * 100
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 1000
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 250 . so 1 / 4 of her savings is $ 250 . so her original savings are 4 times $ 250 = $ 1000 correct answer e"
Answer: e
Python program:
a = 3 / 4
b = 1 - a
c = 250 / b
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 7 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 39.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.93 * 150 x = 139.5 x hence total profit = 39.5 % option d"
Answer: d
Python program:
a = 100 - 7
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100