euclaise/mathqa_programs huggingface dataset:
Problem: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 4 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 15 , d ) 18 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = 18 . answer : d ."
Answer: d
Python program:
a = 0 * 6
b = 0 - 60
c = 0 - 8
d = b / c
Problem: three solid cubes of sides 1 cm , 6 cm and 8 cm are melted to form a new cube . find the surface area of the cube so formed
Options: a ) 486
b ) 366
c ) 299
d ) 278
e ) 1888
Rationale: explanation : volume of new cube = = edge of new cube = = 9 cm surface area of the new cube = ( 6 x 9 x 9 ) = 486 answer : a ) 486
Answer: a
Python program:
a = 1 ** 3
b = 6 ** 3
c = a + b 
d = 8 ** 3
e = c + d 
f = e ** const_0_33
g = f ** 2
h = 3 * g
i = h * 2
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 12 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 21 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 12 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 22 / 25 = ( 1 + p % ) profit % = 21 % b"
Answer: b
Python program:
a = 100 + 10 
b = 100 - 20
c = 12 + b 
d = a - c
e = d * 2
Problem: in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 2 of the absentee ballets were thrown out and 1 / 2 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "1 / 2 * 1 / 2 ( total absentee votes ) = 1 / 4 ( total votes ) = 1 / 4 * 12000 = 3000 answer is b"
Answer: b
Python program:
a = 3 * 4
b = a * 1000
c = 1 * 4
d = c * 1000
e = 1 / 2
f = d * e
g = b - f
h = 1 * 4
i = h * 1000
j = 1 * 4
k = j * 1000
l = 1 / 2
m = k * l
n = i - m
o = 1 / 2
p = n * o
q = g - p
r = q / 1000
s = r / 4
t = s * 1
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is
Options: a ) rs . 500 , b ) rs . 515 , c ) rs . 550 , d ) rs . 600 , e ) none
Rationale: "solution 110 % of s . p . = 616 ‹ = › s . p . = ( 616 x 100 / 110 ) . ‹ = › rs . 560 . c . p . ‹ = › rs . ( 100 / 112 x 560 ) ‹ = › rs . 500 . answer a"
Answer: a
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 12 
g = e / f
Problem: a man swims downstream 45 km and upstream 25 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 17 , b ) 24 , c ) 7 , d ) 24 , e ) 20
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = ( 9 + 5 ) / 2 = 14 / 2 = 7 answer : c"
Answer: c
Python program:
a = 25 / 5
b = 45 / 5
c = a + b 
d = c / 2
Problem: the length of a bridge in meters , which a train 90 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 145 , b ) 215 , c ) 265 , d ) 285 , e ) 375
Rationale: 45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 90 = 375 meters x = 285 meters the answer is d .
Answer: d
Python program:
a = 45 * 1000
b = a / 3600
c = b * 30
d = c - 90
Problem: if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b .
Answer: b
Python program:
a = 8 - 3
b = a - 1
Problem: a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 2 boys ?
Options: a ) 3 / 8 , b ) 1 / 4 , c ) 3 / 16 , d ) 1 / 8 , e ) 1 / 16
Rationale: "no of ways of getting p ( ggbb ) is 4 ! / 2 ! * 2 ! ; total no of ways is 2 ^ n = 2 ^ 4 = 16 ; 6 / 16 = 3 / 8 ; we can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads . p ( all out comes ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ; p ( favorable outcomes ) = 4 ! / ( 2 ! * 2 ! ) = 6 / 16 = 3 / 8 ; answer : a"
Answer: a
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = a / b
d = 2 / 2
e = d ** 4
f = c * e
g = 2 - f
Problem: p can lay railway track between two stations in 16 days . q can do the same job in 12 days . with the help of r , they completes the job in 4 days . how much days does it take for r alone to complete the work ?
Options: a ) 9 days , b ) 9 ( 3 / 5 ) days , c ) 11 1 / 5 days , d ) 13 days , e ) 13 1 / 7
Rationale: amount of work p can do in 1 day = 1 / 16 amount of work q can do in 1 day = 1 / 12 amount of work p , q and r can together do in 1 day = 1 / 4 amount of work r can do in 1 day = 1 / 4 - ( 1 / 16 + 1 / 12 ) = 3 / 16 – 1 / 12 = 5 / 48 = > hence r can do the job on 48 / 5 days = 9 ( 3 / 5 ) days b )
Answer: b
Python program:
a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / 16
e = c - d
f = 1/(e)
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 20 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 10 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 20 = 10 hours answer is b"
Answer: b
Python program:
a = 12 - 10
b = a / 20
Problem: in a games hour 4 different types of players came to the ground ? cricket 16 , hokey 12 , football 18 , softball 13 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 59 , e ) 50
Rationale: "total number of players = 16 + 12 + 18 + 13 = 59 answer is d"
Answer: d
Python program:
a = 16 + 12 
b = 18 + 13 
c = a + b
Problem: in a class of 69 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b"
Answer: b
Python program:
a = 41 + 22 
b = a - 9
c = 69 - b
Problem: the charge for a single room at hotel p is 50 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 50 % , b ) 60 % , c ) 75 % , d ) 80 % , e ) 90 %
Rationale: "p = 0.5 r = 0.8 g r = 0.8 g / 0.5 = 1.6 * g thus r is 60 % greater than g . the answer is b ."
Answer: b
Python program:
a = 100 - 50
b = 100 - 20
c = a / b
d = c * 100
e = 100 - d
f = 100 - 50
g = 100 - 20
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 18 kmph and prasanna moves southward at a speed of 27 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 28 , d ) 45 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 18 kmph x 1 hr = 18 km total southward prasanna ' s distance = 27 kmph x 1 hr = 27 km total distance between prasanna and laxmi is = 18 + 27 = 45 km . answer : d"
Answer: d
Python program:
a = 18 + 27
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 894 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 578
Rationale: "s . i . for 1 year = rs . ( 894 - 815 ) = rs . 79 . s . i . for 3 years = rs . ( 79 x 3 ) = rs . 237 . principal = rs . ( 815 - 237 ) = rs . 578 . answer : option e"
Answer: e
Python program:
a = 894 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: tom traveled the entire 80 miles trip . if he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 55 mph , b ) 50 mph , c ) 40 mph , d ) 60 mph , e ) 70 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 30 + 50 ) / ( ( 30 / 30 ) + ( 50 / 50 ) ) = 80 / 2 = 40 mph c"
Answer: c
Python program:
a = 80 - 30
b = 50 / a
c = 30 / 30
d = b + c 
e = 80 / d
Problem: there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches and roses were planted ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 2 , e ) 9
Rationale: let xx be the number of roses . then the number of birches is 24 − x 24 − x , and the number of boys is 3 × ( 24 − x ) 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 x + 216 − 9 x = 72 216 − 72 = 8 x 216 − 72 = 8 x 1448 = x 1448 = x x = 18 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . answer : a
Answer: a
Python program:
a = 3 * 24
b = a - 24
c = 3 * 3
d = c - 1
e = b / d
Problem: having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 1.20 , b ) $ 1.50 , c ) $ 1.80 , d ) $ 2.00 , e ) $ 2.50
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 40 cents ( 4 / 15 ) x = 40 x = $ 1.50 the answer is b ."
Answer: b
Python program:
a = 3 * 5
b = a * 0
c = b / 4
Problem: 3 / 4 of 5 / 7 of a number is greater than 2 / 3 of 4 / 7 of the same number by 26 . what is half of that number ?
Options: a ) 32 , b ) 78 , c ) 92 , d ) 84 , e ) 96
Rationale: "let no . be x 3 / 4 * 5 / 7 * x - 2 / 3 * 4 / 7 * x = 26 by further solving 15 x / 28 - 8 x / 21 = 26 13 x / 84 = 26 x = 168 we have to find x / 2 = 168 / 2 = 84 answer : d"
Answer: d
Python program:
a = 3 / 4
b = 5 / 7
c = a * b
d = 4 / 5
e = 3 / 3
f = d * e
g = c - f
h = 26 / g
i = h / 4
Problem: robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert earned a performance incentive rs . 7280 / - from company . but robert forgot that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the bonus amount given to robert ?
Options: a ) a ) 9500 , b ) b ) 12500 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600
Rationale: total salary = rs . 15000 / - incentive earned earlier = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - bonus = 18500 - 7720 = 10780 / - answer is c
Answer: c
Python program:
a = 18500 - 7280
Problem: if a and b run on a circular path in opposite directions of constant speeds with different velocities from p and q . first time they meet 800 mts away from p and second time they meet 700 mts away from p , what is the lenght of the circular path .
Options: a ) 2300 mtrs , b ) 2400 mtrs , c ) 2500 mtrs , d ) 2600 mtrs , e ) 2700 mtrs
Rationale: 800 + 800 + 700 = 2300 mtrs answer : a
Answer: a
Python program:
a = 800 * 2
b = a + 700
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 11 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 %
Rationale: "let us suppose the interest rate last year is x , this year the interest rate is increased by 10 % . hence this year interest rate would be 1.1 * x . setting up the equation - - - - - > 11 = 1.1 * x x = 10 % answer : d"
Answer: d
Python program:
a = 11 * 100
b = 11 + 100 
c = a / b
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ?
Options: a ) rs . 692 , b ) rs . 768 , c ) rs . 876 , d ) rs . 972 , e ) none
Rationale: "solution surface area of the cube = ( 6 × 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg ‹ = › 24 kg . cost of painting = rs . ( 36.50 × 24 ) = rs . 876 . answer c"
Answer: c
Python program:
a = surface_cube / (
b = a * 16
Problem: express a speed of 84 kmph in meters per second ?
Options: a ) 13.33 mps , b ) 23.33 mps , c ) 33.33 mps , d ) 25.33 mps , e ) 43.33 mps
Rationale: "84 * 5 / 18 = 23.33 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 84
Problem: a shopkeeper sells 300 metres of cloth for rs . 9000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 36 , d ) s . 46 , e ) s . 13
Rationale: "sp per metre = 9000 / 300 = rs . 30 loss per metre = rs . 6 cp per metre = 30 + 6 = rs . 36 answer : c"
Answer: c
Python program:
a = 9000 / 300
b = a + 6
Problem: the h . c . f . of two numbers is 42 and the other two factors of their l . c . m . are 12 and 14 . the larger of the two numbers is :
Options: a ) 588 , b ) 642 , c ) 567 , d ) 344 , e ) 789
Rationale: "explanation : clearly , the numbers are ( 42 x 12 ) and ( 42 x 14 ) . { \ color { blue } \ therefore } larger number = ( 42 x 14 ) = 588 . answer : a ) 588"
Answer: a
Python program:
a = 42 * 14
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that all three will make a basket ?
Options: a ) 1 / 336 , b ) 5 / 336 , c ) 11 / 336 , d ) 1 / 168 , e ) 1 / 84
Rationale: "the probability that all three will make a basket is 1 / 6 * 1 / 7 * 1 / 8 = 1 / 336 . the answer is a ."
Answer: a
Python program:
a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e
Problem: how much is 75 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 67 , c ) 10 , d ) 12 , e ) 66
Rationale: "( 75 / 100 ) * 40 – ( 4 / 5 ) * 25 = 10 answer : c"
Answer: c
Python program:
a = 75 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 105 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 15 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 105 6 x + 15 = 105 6 x = 90 x = 15 answer : d"
Answer: d
Python program:
a = 3 * 5
b = 105 - a
c = 3 * 2
d = b / c
Problem: 10 play kabadi , 35 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 35 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 35 + 5 = 40 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 40 - 5 = 45 answer : e"
Answer: e
Python program:
a = 35 + 5 
b = 10 + a 
c = b - 5
Problem: if the average of 12 x and 8 y is greater than 200 , and x is twice y , what is the least integer value of x ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 25 , e ) 35
Rationale: substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 12 x and 4 x is greater than 200 . average of 12 x and 4 x is 8 x . so , 8 x > 200 x > 25 answer : d
Answer: d
Python program:
a = 12 * 2
Problem: i sold a book at a profit of 10 % . had i sold it for $ 150 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 150 5 % of cost = $ 150 cost = 150 * 100 / 5 = $ 3000 answer is c"
Answer: c
Python program:
a = 150 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: 8 / 7 * 24 = 27.4 the answer is b .
Answer: b
Python program:
a = 24 * 8
b = a / 7
c = math.floor(b)
Problem: add 8 % of 24 and 10 % of 40 .
Options: a ) 9.5 , b ) 10.5 , c ) 5.5 , d ) 5.9 , e ) 8.5
Rationale: "8 % of 24 + 10 % of 40 24 * 8 / 100 + 40 * 10 / 100 1.9 + 4 = 5.9 answer d"
Answer: d
Python program:
a = 8 * 24
b = a / 100
c = 10 * 40
d = c / 100
e = b + d
Problem: in a certificate by mistake a candidate gave his height as 20 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 13 , b ) 20 , c ) 30 , d ) 43 , e ) 50
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.20 - 1 ) = 13 a"
Answer: a
Python program:
a = const_0_25 + const_0_25 
b = 20 + a 
c = b - 5
d = const_0_25 + const_0_25 
e = 20 + d 
f = e - 5
g = 100 + f 
h = c / g
i = h * 100
Problem: if 2 men or 3 women can reap a field in 12 days how long will 4 men and 5 women take to reap it ?
Options: a ) 12 / 16 , b ) 11 / 36 , c ) 14 / 24 , d ) 18 / 36 , e ) 2 / 24
Rationale: "explanation : 2 men reap 1 / 12 field in 1 day 1 man reap 1 / ( 2 x 12 ) 3 women reap 1 / 12 field in 1 day 1 woman reap 1 / ( 12 x 3 ) 4 men and 5 women reap ( 4 / ( 2 x 12 ) + 5 / ( 3 x 12 ) = 11 / 36 in 1 day 4 men and 5 women will reap the field in 11 / 36 days answer : option b"
Answer: b
Python program:
a = 12 / 2
b = 4 * a
c = 12 / 3
d = 5 * c
e = b + d 
f = 12 / e
Problem: one pack of cake mix is being stirred before being poured into two separate baking trays . the first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first . if the total number of cups poured is 500 , how many cups of batter does the second tray hold ?
Options: a ) 250 , b ) 260 , c ) 500 , d ) 280 , e ) 240
Rationale: tray one as t 1 and tray two as t 2 . t 2 = t 1 - 20 cups as equation a . t 1 + t 2 = 500 cups in total as equation b . substitute equation a into equation b , resulting in t 1 + ( t 1 - 20 ) = 500 transpose like terms , 2 * t 1 = 500 + 20 ( 2 * t 1 ) / 2 = 520 / 2 t 1 = 260 , thus t 2 is t 1 less 20 cups , which is 240 cups . answer is e .
Answer: e
Python program:
a = 500 - 20
b = a / 2
Problem: a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got $ 242 . what is the share of c ?
Options: a ) $ 25 , b ) $ 48 , c ) $ 44 , d ) $ 49 , e ) $ 40
Rationale: "c $ 44 the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = $ 44"
Answer: c
Python program:
a = 1/(14)
b = 1/(21)
c = 1/(7)
d = 1/(14)
e = c + d 
f = b + e 
g = a / f
h = 242 * g
Problem: a certain no . when divided by 95 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 95 + 25 = 120 / 15 = 8 ( remainder ) d"
Answer: d
Python program:
a = 95 - 25
b = a - 4
c = b - 2
Problem: during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 10 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . c"
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = 20 / 100
d = 1 - c
e = 20 - 14
f = e / 20
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 14 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 14 + 13 = 27 . the answer is b ."
Answer: b
Python program:
a = 14 * 2
b = a - 1
Problem: the length of a train and that of a platform are equal . if with a speed of 180 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 1500 , b ) 266 , c ) 299 , d ) 750 , e ) 261
Rationale: "speed = [ 180 * 5 / 18 ] m / sec = 50 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 50 = > x = 50 * 60 / 2 = 1500 answer : a"
Answer: a
Python program:
a = 180 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: running at the same constant rate , 8 identical machines can produce a total of 240 pens per minute . at this rate , how many pens could 5 such machines produce in 5 minutes ?
Options: a ) 114 , b ) 108 , c ) 192 , d ) 750 , e ) 777
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 240 / 8 = 30 pens per minute per machine . 5 machines = 150 per minute . 5 minutes worth = 750 pens . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."
Answer: d
Python program:
a = 240 / 8
b = a * 5
c = b * 5
Problem: the product of the squares of two positive integers is 81 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : c - 2 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 81 [ square root both sides ] xy = 9 9 = 1 x 9 , 9 x 1 , 3 x 3 cancel the repeats this leaves us with exactly 2 options . hence , c"
Answer: c
Python program:
a = 2 + 3 
b = a - 2