euclaise/mathqa_programs huggingface dataset:
Problem: a can do a work in 20 days , b in 30 days . a alone start the work after 10 days he left work . in how many days b can finish the work ?
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 10 days , e ) 15 days
Rationale: "10 days work of a = 10 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 b can finish 1 / 2 work = 30 * 1 / 2 = 15 days answer is e"
Answer: e
Python program:
a = 1 / 20
b = 10 * a
c = 1 - b
d = 1 / 30
e = c / d
Problem: there are 24 students in chad â € ™ s class . he brought 27 cookies to pass out for his birthday . how many cookies will each student get ? will there be any cookies left over ?
Options: a ) 1 - 9 , b ) 1 - 7 , c ) 2 - 8 , d ) 1 - 3 , e ) 3 - 10
Rationale: 27 / 24 = 1 r 3 chad will give each student 1 cookie and there will be 3 cookies left over correct answer d
Answer: d
Python program:
a = 27 / 24
Problem: a shopkeeper sells 450 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 45 , e ) 21
Rationale: sp per metre = 18000 / 450 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
Answer: d
Python program:
a = 18000 / 450
b = a + 5
Problem: a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 55 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 37 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a"
Answer: a
Python program:
a = 20 / 100
b = a * 2
c = 55 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: a man goes from a to b at a speed of 35 kmph and comes back to a at a speed of 28 kmph . find his average speed for the entire journey ?
Options: a ) 38.9 kmph , b ) 38.8 kmph , c ) 38.1 kmph , d ) 37.1 kmph , e ) 37.8 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 35 ) + ( d / 28 ] = ( 2 d ) / [ 11 d / 140 ) = > 38.1 kmph . answer : c"
Answer: c
Python program:
a = 35 + 28 
b = a / 2
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 23.56 , b ) 33.0 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 20 ) = 84 cm parameter of the square = 84 cm i . e . 4 a = 84 a = 21 diameter of the semicircle = 21 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) 21 = 1 / 2 ( 22 / 7 ) ( 21 ) = 66 / 2 = 33 cm answer : b"
Answer: b
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 5 of the mice are brown . if there are 12 white mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 18 , e ) 16
Rationale: "let total number of mice = m number of brown mice = 2 / 5 m number of white mice = 3 / 5 m = 12 = > m = 20 answer a"
Answer: a
Python program:
a = 2 / 5
b = 12 / a
c = b - 12
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length and width of this rectangle .
Options: a ) w = 15 and l = 20
b ) w = 25 and l = 30
c ) w = 35 and l = 40
d ) w = 45 and l = 50
e ) w = 55 and l = 60
Rationale: l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer a
Answer: a
Python program:
a = 70 / 2
b = 70 / 2
c = b ** 2
d = 4 * 300
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.6 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.6 ( x ) + 0.5 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.5 x = 0.25 / 0.1 x = 1 / 4 therefore the answer is a : 1 / 4 ."
Answer: a
Python program:
a = 0 - 75
b = 0 - 6
c = a / b
Problem: the total number of digits used in numbering the pages of a book having 346 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 930 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 247 ) = ( 9 + 180 + 741 ) = 930 . answer : d"
Answer: d
Python program:
a = 346 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
Problem: a light has a rating of 110 watts , it is replaced with a new light that has 30 % higher wattage . how many watts does the new light have ?
Options: a ) 143 , b ) 145 , c ) 156 , d ) 134 , e ) 100
Rationale: "final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a"
Answer: a
Python program:
a = 30 / 100
b = 1 + a 
c = 110 * b
Problem: a train 150 m long crosses a platform 100 m long in 10 sec ; find the speed of the train ?
Options: a ) 100 , b ) 70 , c ) 95 , d ) 90 , e ) 85
Rationale: "d = 150 + 100 = 250 t = 10 s = 250 / 10 * 18 / 5 = 90 kmph . answer : d"
Answer: d
Python program:
a = 100 * const_0_2778
b = 10 * a
c = b - 150
Problem: calculate the time it will take for a train that is 240 meter long to pass a bridge of 130 meter length , if the speed of the train is 50 km / hour ?
Options: a ) 21.64 seconds , b ) 22.64 seconds , c ) 23.64 seconds , d ) 26.64 seconds , e ) 35.64 seconds
Rationale: "speed = 35 km / hr = 50 * ( 5 / 18 ) m / sec = 13.89 m / sec total distance = 240 + 130 = 370 meter time = distance / speed = 370 * ( 1 / 13.89 ) = 26.64 seconds answer : d"
Answer: d
Python program:
a = 240 + 130 
b = 50 / const_3_6
c = a / b
Problem: there are 200 doctors and nurses at a hospital . if the ratio of doctors to nurses is 4 to 6 , how many nurses are at the hospital ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "the number of nurses at the hospital is ( 6 / 10 ) * 200 = 120 . the answer is b ."
Answer: b
Python program:
a = 4 + 6 
b = 200 / a
c = b * 6
Problem: milk contains 5 % water . what content of pure milk should be added to 10 liters of milk to reduce this to 2 % ?
Options: a ) 10 liters , b ) 15 liters , c ) 20 liters , d ) 18 liters , e ) 22 liters
Rationale: "quantity of water in 10 liters = 5 % of 10 liters = 0.5 liters let x liters of pure milk be added . then , 0.5 / ( 10 + x ) = 2 / 100 2 x = 30 x = 15 liters answer is b"
Answer: b
Python program:
a = 5 / 100
b = a * 10
c = 2 / 100
d = b / c
e = d - 10
Problem: the current in a river is 4 mph . a boat can travel 18 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 85.5 miles , c ) 96 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 18 - 4 = 14 mph downstream speed = 18 + 4 = 22 mph d / 14 + d / 22 = 10 hours solving for d we get d = 85.5 answer : b"
Answer: b
Python program:
a = 18 - 4
b = 18 + 4 
c = a * b
d = c * 10
e = 18 + 4 
f = 18 - 4
g = e + f 
h = d / g
Problem: a batsman scored 90 runs which included 2 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 57 % , d ) 60 % , e ) 80 %
Rationale: "explanation : number of runs made by running = 90 - ( 2 x 4 + 5 x 6 ) = 90 - ( 38 = 52 now , we need to calculate 38 is what percent of 90 . = > 52 / 90 * 100 = 57 % option c"
Answer: c
Python program:
a = 2 * 5
b = 5 * 2
c = a + b 
d = 90 - c
e = d / 90
f = e * 100
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 2835 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "2835 = 3 * 3 * 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 ( that is : 3 , 6 , and 9 = 3 * 3 ) . the answer is c ."
Answer: c
Python program:
a = 2835 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: in a class of 120 students , 25 did not opt for math . 10 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 63 , b ) 95 , c ) 77 , d ) 87 , e ) 48
Rationale: "120 students total 25 did not opt for math 10 did not opt for science 2 did not opt for either total of 95 students in math and 8 did not opt for sci but did for math 95 - 8 = 87 87 students of the class opted for both math and science answer : d . 87"
Answer: d
Python program:
a = 120 - 25
b = 120 - 10
c = b - 2
d = a - c
Problem: the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e"
Answer: e
Python program:
a = 4 ** 2
b = 1 ** 2
c = 2 ** 2
d = b + c 
e = a + d 
f = 1701 / e
g = math.sqrt(f)
Problem: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 4.25 = ( 20 * ( $ 4.25 ) ) / 100 - - > ( $ 85 ) / 100 - - > $ 0.85 therefore , chef wages per hour = $ 4.25 + $ 0.85 = = > $ 5.10 difference of wages between manager and chef = $ 8.50 - $ 5.10 = = > $ 3.40 answer : c"
Answer: c
Python program:
a = 100 + 20 
b = a / 100
c = 1 / 2
d = b * c
e = 1 - d
f = e * 8
Problem: 101 ã — 101 + 99 ã — 99 = ?
Options: a ) 10002 , b ) 20004 , c ) 20002 , d ) 20102 , e ) 20202
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1012 + 992 = ( 100 + 1 ) 2 + ( 100 â ˆ ’ 1 ) 2 = 2 ( 1002 + 12 ) = 2 ( 10000 + 1 ) = 20002 . answer : option c"
Answer: c
Python program:
a = 101 ** 2
b = a - 101
c = 99 ** 2
d = c - 99
e = b + d
Problem: in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a female or younger than 70 years old ?
Options: a ) 231 / 260 , b ) 117 / 130 , c ) 51 / 65 , d ) 23 / 32 , e ) 11 / 16
Rationale: "the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 the number of people who are either female or younger than 70 is 1800 + 510 = 2310 . p ( a person is younger than 70 or male ) = 2310 / 2600 = 231 / 260 the answer is a ."
Answer: a
Python program:
a = 5 * 5
b = a / const_0_25
c = const_26 * b
d = 5 * 5
e = d / const_0_25
f = 40 / e
g = 1 - f
h = 850 * g
i = c - h
j = 5 * 5
k = j / const_0_25
l = const_26 * k
m = i / l
Problem: jaclyn buys $ 40 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 950 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 40000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 950 answer : a"
Answer: a
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: 60 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 / 7 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "60 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 60 ) * 100 = 60 square feet answer : option d"
Answer: d
Python program:
a = 4 * 9
b = 60 / 100
c = a / b
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 500 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 500 bc , b ) 500 b / c , c ) 1000 bc , d ) 1000 b / c , e ) 1000 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 500 clips / box = 1000 bc paper clips the answer is c ."
Answer: c
Python program:
a = 2 * 500
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 8 hours of the journey .
Options: a ) 296 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 8 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 = sum of 8 terms in ap whose first term is 30 and last term is 44 = 8 / 2 [ 30 + 44 ] = 296 km . answer : a"
Answer: a
Python program:
a = 2 * 8
b = 30 + a 
c = b + 30 
d = c / 2
Problem: a , b and c start a business with each investing rs 20000 . after 5 months a withdraws rs 5000 , b withdraws rs 4000 and c invests rs 6000 more . at the end of the year , a total profit of rs 69900 was recorded . find the share of a .
Options: a ) 20000 , b ) 21500 , c ) 20500 , d ) 22000 , e ) 21000
Rationale: a : b : c = ( 20000 × 5 + 15000 × 7 ) : ( 20000 × 5 + 16000 × 7 ) : ( 20000 × 5 + 26000 × 7 ) = ( 20 × 5 + 15 × 7 ) : ( 20 × 5 + 16 × 7 ) : ( 20 × 5 + 26 × 7 ) = 205 : 212 : 282 a ' s share = 69900 × 205 / ( 205 + 212 + 282 ) = 69900 × 205 / 699 = 20500 answer is c .
Answer: c
Python program:
a = 5000 / 10
b = 20000 + a
Problem: the c . p of 15 books is equal to the s . p of 20 books . find his gain % or loss % ?
Options: a ) 25 % loss , b ) 16 2 / 8 % loss , c ) 16 3 / 3 % loss , d ) 36 2 / 3 % loss , e ) 56 2 / 3 % loss
Rationale: "15 cp = 20 sp 20 - - - 5 cp loss 100 - - - ? = > 25 % loss answer : a"
Answer: a
Python program:
a = 15 / 20
b = 1 - a
c = b * 100
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6647 , how much amount did raghu invest ?
Options: a ) 2300 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6647 = x = 6647 / 2.89 = 2300 therefore , amount invested by raghu is rs . 2300 . answer : a"
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 - f
h = e + g 
i = h + 1 
j = 6647 / i
Problem: sonika bought a v . c . r . at the list price of 18,800 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,304 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,800 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,800 = 8 ⁄ 100 × 18800 = 1504 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,800 + 1504 = 20,304 . answer a"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = b + 8 
d = c * 100
e = 1 + 4 
f = e * 2
g = d * f
h = 1 + 4 
i = h * 100
j = g + i 
k = 100 + 8 
l = j * k
m = l / 100
n = 1 + 4 
o = n * 100
p = o * 2
q = m / p
r = math.floor(q)
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 42 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 48 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.42 m = = > revenue = price x quantity = 0.48 ( m + w ) = = > profit = 0.48 ( m + w ) - 0.42 m = 0.2 * ( 0.42 m ) [ 20 % of cost ] = = > 0.48 m + 0.48 w - 0.42 m = 0.084 m = = > 0.024 m = 0.48 w = = > m / w = 0.48 / 0.024 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Python program:
a = 20 / 2
b = 1 / a
Problem: 4524 - ? = 2456
Options: a ) 2058 , b ) 2069 , c ) 2072 , d ) 2089 , e ) none of these
Rationale: "explanation : none of these answer : option e"
Answer: e
Python program:
a = 4524 / 2456
b = a * 100
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 600 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 300 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 600 pounds . we sum the two variables to obtain : f + s = 600 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 600 3 f = 900 f = 300 answer is c"
Answer: c
Python program:
a = 600 + 300 
b = a / 3
Problem: in measuring the sides of a rectangle , one side is taken 8 % in excess , and the other 7 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.44 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c ."
Answer: c
Python program:
a = 8 - 7
b = 8 * 7
c = b / 100
d = a - c
Problem: what is the 9 th digit to the right of the decimal point in the decimal equivalent of 48 / 11 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 2
Rationale: "48 / 11 = 4.3636 . . . . 36 is non - terminating repeating decimal . the 9 th digit to the right of decimal point will be 3 . answer a"
Answer: a
Python program:
a = 48 / 11
Problem: a is two years older than b who is twice as old as c . the total of the ages of a , b and c is 27 . how old is b ?
Options: a ) 25 , b ) 20 , c ) 15 , d ) 10 , e ) 5
Rationale: "let age of c = x . then , age of b = 2 x age of a = 2 + 2 x total age of a , b and c = 27 ⇒ ( 2 + 2 x ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 255 = 5 b ' s age = 2 x = 2 × 5 = 10 answer is d ."
Answer: d
Python program:
a = 27 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: find the value of x : x ² + 6 x + 9 .
Options: a ) 9 , b ) - 1 , c ) - 3 , d ) 3 , e ) - 9
Rationale: that quadratic is factored as follows : x ² + 6 x + 9 = ( x + 3 ) ( x + 3 ) . lesson 17 . now , it is easy to see that that both factors will be 0 when x = - 3 . the solution is : x = - 3 c
Answer: c
Python program:
a = 6 * 3
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 6 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 120 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 6 ) * 360 = 60 gallons . remaning paint = 300 gallons paint used in the second week = ( 1 / 5 ) * 300 = 60 gallons total paint used = 120 gallons . option b"
Answer: b
Python program:
a = 360 / 6
b = a * 1
c = 360 / 6
d = c * 1
e = 360 - d
f = e / 5
g = b + f
Problem: the e train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the e train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says e it took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Python program:
a = 7 + 5 
b = 7 - 5
c = a / b
Problem: dana borrows 5000 pounds annually for her college education . if dana gives her parents 4 % of that amount back each month , how much will she still owe her parents after 4 years of college ?
Options: a ) 9800 , b ) 10000 , c ) 10200 , d ) 10400 , e ) 10600
Rationale: dana borrows 5000 and returns 4 % per month . so returns 200 per month . and 2400 per year . so dana owes 5000 - 2400 = 2600 per year . after 4 years she will owe 10400 . ans ( c )
Answer: c
Python program:
a = 5000 * 4
b = 3 * 4
c = 5000 * 4
d = c / 100
e = b * d
f = e * 4
g = a - f
Problem: a student scored an average of 75 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 95 , e ) 26
Rationale: "given m + p + c = 75 * 3 = 225 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 225 = 95 answer : d"
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 75 * 3
e = c - d
Problem: a positive number x is multiplied by 8 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 8 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "sq rt ( 8 x / 3 ) = x = > 8 x / 3 = x ^ 2 = > x = 8 / 3 ans - c"
Answer: c
Python program:
a = 8 / 3
Problem: a and b working together could mow a field in 28 days and with the help of c they could have mowed it in 21 days . how long would c take by himself ?
Options: a ) 68 days , b ) 84 days , c ) 90 days , d ) 72 days , e ) 50 days
Rationale: required answer = 28 * 21 / 28 - 21 = 84 days answer is b
Answer: b
Python program:
a = 1 / 21
b = 1 / 28
c = a - b
d = 1/(c)
Problem: two employees x and y are paid a total of rs . 590 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 268 , b ) s . 288 , c ) s . 298 , d ) s . 300 , e ) s . 388
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 590 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 590 ⇒ y [ 12 / 10 + 1 ] = 590 ⇒ 22 y / 10 = 590 ⇒ 22 y = 5900 ⇒ y = 5900 / 22 = 500 / 2 = rs . 268 a )"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = 590 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g