euclaise/mathqa_programs huggingface dataset:
Problem: triangle atriangle b are similar triangles with areas 1792 units square and 2527 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 19 , c ) 23 : 27 , d ) 16 : 19 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1792 / 2527 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 7 ) / ( 19 * 19 * 7 ) ( x ^ 2 / y ^ 2 ) = 16 ^ 2 / 19 ^ 2 x / y = 16 / 19 ans = d"
Answer: d
Python program:
a = 1792 / 2527
b = math.sqrt(a)
Problem: a and b together have $ 1210 . if 4 / 15 of a ' s amount is equal to 2 / 5 of b ' s amount , how much amount does b have ?
Options: a ) $ 310 , b ) $ 395 , c ) $ 484 , d ) $ 512 , e ) $ 542
Rationale: 4 / 15 a = 2 / 5 b a = 2 / 5 * 15 / 4 b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 b ' s share = 1210 * 2 / 5 = $ 484 answer is c
Answer: c
Python program:
a = 2 / 5
b = 4 / 15
c = a / b
d = c + 1 
e = 1210 / d
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle . ?
Options: a ) 87 , b ) 98 , c ) 12 , d ) 27 , e ) 28
Rationale: "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c"
Answer: c
Python program:
a = square_edge_by_area / (
b = a / 2
c = 3 + 4 
d = c / 3
e = b + d
Problem: the speed of a boat in still water is 12 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 18 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 3.6 km , d ) 4.8 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 12 + 4 ) kmph = 16 kmph . distance travelled = ( 16 x 18 / 60 ) km = 4.8 km option d"
Answer: d
Python program:
a = 18 / const_60
b = 12 + 4 
c = a * b
Problem: a gambler bought $ 3000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b .
Answer: b
Python program:
a = 4 + 3 
b = a * 100
c = 10 - 1
d = c * 20
e = b + d 
f = e / 20
g = 2 + 2 
h = f - g
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 1 ½ hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) none
Rationale: sol . let the speed of the boat in still water be x kmph . then , speed downstream = ( x + 3 ) kmph , speed upstream = ( x - 3 ) kmph . ∴ ( x + 3 ) * 1 = ( x - 3 ) * 3 / 2 ⇔ 2 x + 6 = 3 x - 9 ⇔ x = 15 kmph . answer d
Answer: d
Python program:
a = 3 / 2
b = a * 3
c = b + 3 
d = 3 / 2
e = d - 1
f = c / e
Problem: simplify : 0.3 * 0.8 + 0.1 * 0.5
Options: a ) 0.52 , b ) 0.29 , c ) 0.48 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.3 * 0.8 + ( 0.1 * 0.5 ) = 0.24 + 0.05 = 0.29 answer is b ."
Answer: b
Python program:
a = 0 * 3
b = 0 * 1
c = a + b
Problem: working alone , pump a can empty a pool in 4 hours . working alone , pump b can empty the same pool in 2 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 65 , b ) 70 , c ) 75 , d ) 80 , e ) 85
Rationale: "pump a can empty ( 1 / 4 ) of the pool per hour . pump b can empty ( 1 / 2 ) of the pool per hour . together the pumps can empty 1 / 4 + 1 / 2 = 3 / 4 of the pool per hour . 1 pool / ( 3 / 4 ) pool per hour = 4 / 3 hours = 80 minutes . the answer is d ."
Answer: d
Python program:
a = 1 / 4
b = 1 / 2
c = a + b 
d = 1/(c)
e = d * const_60
Problem: a garrison of 2000 men has provisions for 62 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1893 , c ) 2700 , d ) 1900 , e ) 1278
Rationale: "2000 - - - - 62 2000 - - - - 47 x - - - - - 20 x * 20 = 2000 * 47 x = 4700 2000 - - - - - - - 2700 answer : c"
Answer: c
Python program:
a = 2000 * 62
b = 2000 * 15
c = a - b
d = c / 20
e = d - 2000
Problem: the diagonal of a square is the height in an equilateral triangle . if the side of the square is x , what is the side of the equilateral triangle in terms of x ?
Options: a ) √ ( 2 / 3 ) × x
b ) 2 / √ 3 × x
c ) √ 3 x
d ) √ ( 8 / 3 ) × x
e ) 2 √ 3 × x
Rationale: the diagonal of the square x * sqrt ( 2 ) if that ' s the altitude of the equilateral triangle , the formula for which is side * sqrt ( 3 ) / 2 side is 2 sqrt ( 2 ) * x / sqrt ( 3 ) answer : ( option d )
Answer: d
Python program:
a = 1 + 1 
b = 1/(2)
c = a ** b
d = c * 2
e = 1/(2)
f = 3 ** e
g = d / f
Problem: if p ( a ) = 6 / 17 , p ( b ) = 5 / 17 , and p ( a ∪ b ) = 4 / 17 find p ( b | a ) ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 3 / 7 , e ) 4 / 9
Rationale: "p ( b | a ) = p ( a ∪ b ) / p ( a ) p ( b | a ) = ( 4 / 17 ) / ( 6 / 17 ) = 4 / 6 = 2 / 3 . a"
Answer: a
Python program:
a = 4 / 17
b = 6 / 17
c = a / b
Problem: last year elaine spent 20 % of her annual earnings on rent . this year she earned 15 % more than last year and she spent 25 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 152.5 , b ) 143.75 , c ) 155.5 , d ) 165.5 , e ) 117.5
Rationale: for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 15 % more , or $ 115 . she would ' ve spent 25 % of this on rent , or $ 28.75 do $ 34.5 / $ 20 this will give you 143.75 % b is the correct answer .
Answer: b
Python program:
a = 15 / 100
b = a + 1 
c = b * 25
d = c / 20
e = d * 100
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 20,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 1000 , e ) $ 900
Rationale: - > 250 / 5,000 = 5 % and 20,000 * 5 % = 1000 . thus , d is the answer .
Answer: d
Python program:
a = 2 * 100
b = a * 100
c = 250 * b
d = 2 * 100
e = d * 100
f = e / 4
g = c / f
Problem: a train running at the speed of 180 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 800 , b ) 900 , c ) 950 , d ) 1000 , e ) 1050
Rationale: "speed = ( 180 x ( 5 / 18 ) m / sec = ( 50 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 50 ) x 18 ) m = 900 m b"
Answer: b
Python program:
a = 180 * 1000
b = a / 3600
c = b * 18
Problem: a 18 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 225
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 18 , money invested = 100 × 18 / 8 = rs . 225 ie , market value of the stock = rs . 175 answer is e ."
Answer: e
Python program:
a = 100 / 8
b = a * 18
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 145 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 110.6 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 395 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 145 days - - > 145 / 250 work done = > 58 % 28 % work left . . . r alone will take 28 % * 395 = 110.6 days answer is ( b )
Answer: b
Python program:
a = 4 * 50
b = 145 / 100
c = b * 60
d = a - c
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 180 grams of water ?
Options: a ) 160 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is 180 18 x = 180 x = 10 since x is 10 , we know that there are 16 x 10 = 160 grams of oxygen in 180 grams of water . answer a ."
Answer: a
Python program:
a = 2 + 16 
b = 180 / a
c = 2 * b
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containing 19 % alcohol and now the percentage of alcohol was found to be 26 % . the quantity of whisky replaced is :
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "explanation : by the rule of alligation , we have : so , ratio of 1 st and 2 nd quantities = 7 : 14 = 1 : 2 required quantity replaced = 2 / 3 . answer is b"
Answer: b
Python program:
a = 40 - 26
b = 40 - 19
c = a / b
Problem: the speed of a train is 60 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 21 kmph , b ) 22 kmph , c ) 20 kmph , d ) 23 kmph , e ) 24 kmph
Rationale: "60 * 20 / 60 = 20 kmph answer : c"
Answer: c
Python program:
a = 20 / const_60
b = a * 60
Problem: find the average of all the numbers between 9 and 26 which are divisible by 5 .
Options: a ) 15 , b ) 19 , c ) 18 , d ) 22 , e ) none
Rationale: "sol . average = ( 10 + 15 + 20 + 25 / 4 ) = 70 / 4 = 17.5 answer c"
Answer: c
Python program:
a = 9 + 4 
b = 26 - 4
c = a + b 
d = c / 2
Problem: what is the least common multiple of 12,15 , 18,27
Options: a ) 640 , b ) 540 , c ) 691 , d ) 385 , e ) 789
Rationale: "factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 15 = 3 * 5 factors of 18 = 2 * 3 * 3 thus the l . c . m is 2 * 3 * 2 * 3 * * 1 * 5 * 3 = 540 the answer is b"
Answer: b
Python program:
a = 12 + 15 
b = a * 2
Problem: given a spinner with 4 sections of equal size labeled e , b , c , and d , what is the probability of not getting an e after spinning the spinner two times ?
Options: a ) 15 / 16 , b ) 9 / 16 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 8
Rationale: the probability of not getting an e after spinning the spinner two times is 3 / 4 * 3 / 4 = 9 / 16 ( so getting any of the remaining 3 letters out of 4 ) . answer : b .
Answer: b
Python program:
a = 3 / 4
b = a ** 2
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 3 carpenters build in 4 hours ?
Options: a ) 2.4 . , b ) 4.8 . , c ) 4.2 . , d ) 5.5 . , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 3 carpenters in 4 hrs = 3 × rate of each carpenter x time = 3 × 2 / 5 × 4 = 4.8 desks b is the correct answer ."
Answer: b
Python program:
a = 4 / 2
b = 2 / a
c = b / 2
d = c * 3
e = d * 4
Problem: p and q started a business investing rs . 45,000 and rs . 10,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 9 : 2 , b ) 4 : 5 , c ) 9 : 3 , d ) 17 : 9 , e ) 17 : 4
Rationale: "p : q = 45000 : 10000 = 9 : 2 answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 240 cm 2 , d ) 177 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 30 ( 10 + 6 ) = 240 cm 2 answer : c"
Answer: c
Python program:
a = 1 / 2
b = 6 + 10 
c = a * b
d = c * 30
Problem: a certain junior class has 1,200 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 16,000
Rationale: "total number of ways of choosing one student from each group is = 800 * 1200 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 800 * 1200 ) = 1 / 16,000 e"
Answer: e
Python program:
a = 1 / 3
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.65 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 42 , b ) 77 , c ) 48 , d ) 99 , e ) 11
Rationale: relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.65 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a
Answer: a
Python program:
a = 1 * 1
b = 60 * 1000
c = b / 3600
d = a / c
e = 0 * 65
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 10 terms of the arithmetic progression ?
Options: a ) 300 , b ) 100 , c ) 150 , d ) 170 , e ) 270
Rationale: n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 10 . . . we get 10 / 2 [ 2 a + 14 d ] = 10 [ a + 7 d ] = 10 * 10 = 100 . . . answer is b . . .
Answer: b
Python program:
a = 20 * 10
b = a / 2
Problem: a salt manufacturing company produced a total of 3000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 119 , b ) 185 , c ) 190 , d ) 116 , e ) 200
Rationale: "total production of salt by the company in that year = 3000 + 3100 + 3200 + . . . . + 4100 = 42600 . average monthly production of salt for that year = 42600 / 365 â ‰ ˆ 116 answer : d"
Answer: d
Python program:
a = 3000 * 2
b = 12 - 1
c = b * 100
d = a + c 
e = d * 12
f = e / 2
g = 3 * 100
h = 2 * 3
i = h * 10
j = g + i 
k = 2 + 3 
l = j + k 
m = f / l
Problem: set x consists of the integers from 10 to 15 , inclusive , while set y consists of the integers from 5 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 1 , e ) 9
Rationale: "x = { 10 , 11 , 12,13 , 14,15 } y = { 5,6 , 7 , 8 , 9 , 10 } common elements = { 10 } = 1 element answer : option d ."
Answer: d
Python program:
a = 15 - 10
b = a + 10
Problem: in a class of boys and girls vikas ' s rank is 9 th and tanvi ' s rank is 17 th . vikas ' s rank among the boys in that class is 4 th from the top and 18 th from the bottom and tanvi ' s rank among the girls is 8 th from top and 21 st from bottom . in the order of rank , how many girls are there between tanvi and vikas ?
Options: a ) 29 , b ) 8 , c ) 2 , d ) 4 , e ) 6
Rationale: explanation : vikas ' s rank in the class is 9 . so there are 8 people before him . his rank among boys is 4 . so 3 boys are before him . so there are 8 – 3 = 5 girls before him . tanvi ' s rank among the girls is 8 . so there are 7 girls before her . so number of girls between vikas and tanvi is 7 – 5 = 2 answer : c
Answer: c
Python program:
a = 8 - 1
b = 9 - 1
c = 4 - 1
d = b - c
e = a - d
Problem: arjun started a business with rs . 5,000 and is joined afterwards by anoop with rs . 10 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 5000 * 12 = 10000 * ( 12 – x ) = > x = 6 . answer : d"
Answer: d
Python program:
a = 4 * 100
b = a * 100
c = b * 12
d = 2 * 100
e = d * 100
f = e * 12
g = c - f
h = 10 * 100
i = h * 10
j = g / i
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 910 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1110 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 10 kg of mangoes = 55 × 10 = 550 . total cost he has to pay = 560 + 550 = 1110 . a )"
Answer: a
Python program:
a = 8 * 70
b = 910 * 55
c = a + b
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio q of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Python program:
a = 100 + 7 
b = 100 + 1 
c = a - b
d = 100 + 1 
e = 100 - 11
f = d - e
g = c / f
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 50 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 2.4 , b ) 3.2 , c ) 4.0 , d ) 4.8 , e ) 5.6
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 4.8 hours to travel 240 km , so c leaves 3.2 hours after a . the answer is b ."
Answer: b
Python program:
a = 40 - 30
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint r , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b
Answer: b
Python program:
a = const_0_25 * 2
b = 2 * 5
c = a + b
Problem: what least number must be subtracted from 652543 so that remaining no . is divisible by 12
Options: a ) 3 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 652543 by 12 we get the remainder 7 , so 7 should be subtracted option c"
Answer: c
Python program:
a = 652543 / 12
b = math.floor(a)
c = b * 12
d = 652543 - c
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 25 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: "20 men is 6 days can build 112 metres 25 men in 3 days can build = 112 * ( 25 / 20 ) x ( 3 / 6 ) = 70 meters answer : c ."
Answer: c
Python program:
a = 25 * 3
b = 20 * 6
c = a / b
d = 112 * c
Problem: if the sides of a triangle are 26 cm , 24 cm and 12 cm , what is its area ?
Options: a ) 144 , b ) 772 , c ) 288 , d ) 266 , e ) 2848
Rationale: "the triangle with sides 26 cm , 24 cm and 12 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 12 = 144 cm 2 answer : a"
Answer: a
Python program:
a = 24 * 12
b = a / 2
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 10 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24.4 % , d ) 25 % , e ) 34 %
Rationale: "since 10 % of the customers who sample the candyare notcaught , then 90 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.90 = 0.22 ; { % of customers who sample candy } = 0.25 . answer : c ."
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 22 / b
Problem: carl can wash all the windows of his house in 7 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 11 6 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: work hrs = ab / ( a + b ) = 28 / 11 = 11 6 / 2 answer is c
Answer: c
Python program:
a = 1 / 7
b = 1 / 4
c = a + b 
d = const_60 / c
e = 1 / 7
f = 1 / 4
g = e + f 
h = d * g
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 108 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 6000 , d ) $ 3600 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 108 x = 3600 answer d"
Answer: d
Python program:
a = 3 + 2 
b = 100 * a
c = 30 + 20 
d = c + 35 
e = 100 - d
f = 108 / e
g = b * f
Problem: if a certain toy store ' s revenue in november was 2 / 3 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 3
Rationale: "let dec rev = 100 then nov rev is 2 / 3 ( 100 ) = > 67 therefore jan rev = 1 / 3 ( nov rev ) = 1 / 3 ( 67 ) = > 23 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 67 + 23 ) / 2 x = 100 / 45 = > 2.22 = 3 ans ) e"
Answer: e
Python program:
a = 2 / 3
b = 2 / 3
c = 1 / 3
d = b * c
e = a + d 
f = e / 2
g = 1 / f
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2475 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 825 , d ) s . 900 , e ) s . 920
Rationale: "2475 * 1 / 3 = 825 option c"
Answer: c
Python program:
a = 1 / 3
b = 2475 * a