euclaise/mathqa_programs huggingface dataset:
Problem: rectangular tile each of size 25 cm by 16 cm must be laid horizontally on a rectangular floor of size 180 cm by 120 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 52 , b ) 54 , c ) 55 , d ) 65 , e ) 48
Rationale: "area of tile = 25 * 16 = 400 area of floor = 180 * 120 = 21600 no of tiles = 21600 / 400 = 54 so , the no of tile = 54 answer : b"
Answer: b
Python program:
a = 180 * 120
b = 25 * 16
c = a / b
Problem: a house wife saved $ 2.75 in buying an item on sale . if she spent $ 20 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 20 + 2.75 = $ 22.75 saving = 2.75 / 22.75 * 100 = 12 % approximately answer is e"
Answer: e
Python program:
a = 20 + 2 
b = 2 / 75
c = b * 100
Problem: the ratio of buses to cars on river road is 1 to 3 . if there are 40 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 60 , b ) 75 , c ) 85 , d ) 95 , e ) 105
Rationale: "b / c = 1 / 3 c - b = 40 . . . . . . . . . > b = c - 40 ( c - 40 ) / c = 1 / 3 testing answers . clearly eliminate bcde put c = 60 . . . . . . . . . > ( 60 - 40 ) / 60 = 20 / 60 = 1 / 3 answer : a"
Answer: a
Python program:
a = 3 - 1
b = 40 / a
c = b * 3
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 25 . the largest number is :
Options: a ) 28 , b ) 30 , c ) 36 , d ) 42 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 25 15 x = 75 x = 5 largest number = 6 x = 30 . answer b"
Answer: b
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: in a garden , 26 trees are planted at equal distances along a yard 600 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 24 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 600 / 25 = 24 i . e . , distance between two consecutive trees = 24 answer is d ."
Answer: d
Python program:
a = 26 - 1
b = 600 / a
Problem: on a wedding catering service , an experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours . if the catering service employs the same number of novice and experienced chefs , then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: experienced chefs work = 1 wedding / 6 hours novice chefs work = 1 wedding / 7 hours since we do n ' t know the number of experienced or novice chefs but know that there is an equal number each , let the number of chefs for each group equalx 1 hr and 36 mins = 8 / 5 an hour x / 6 + x / 7 = 1 wedding / ( 8 / 5 ) x / 6 + x / 7 = 5 / 8 x = 2 so there are 2 novice chefs and 2 experienced chefs . in total there are 4 . the answer is c .
Answer: c
Python program:
a = 1 / 6
b = 1 / 7
c = a + b 
d = 36 / const_60
e = 1 + d 
f = c * e
g = 2 / f
h = math.floor(g)
Problem: there is a 20 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 40 % , b ) 48 % , c ) 56 % , d ) 64 % , e ) 72 %
Rationale: "p ( china and not malaysia ) = 0.2 * 0.4 = 0.08 p ( malaysia and not china ) = 0.6 * 0.8 = 0.48 total probability = 0.08 + 0.48 = 0.56 = 56 % the answer is c ."
Answer: c
Python program:
a = 20 + 60 
b = 5 * 5
c = b * 4
d = a / c
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quality of alcohol in the given mixture .
Options: a ) 10 , b ) 8 , c ) 7.5 , d ) 6 , e ) 3.5
Rationale: "let the quantity of alcohol and water be 4 x and 3 x 4 x / ( 3 x + 5 ) = 4 / 5 20 x = 4 ( 3 x + 5 ) x = 2.5 quantity of alcohol = 4 * 2.5 = 10 liters . answer is a"
Answer: a
Python program:
a = 5 * 1
Problem: a 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 350 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 150 / 9 = 500 / 9 = > x + 150 = 500 = > x = 350 so the length of the train is 350 meters option d"
Answer: d
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 150
Problem: the average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?
Options: a ) 30.5 , b ) 26 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 18 + 22 + 7 * 3 = 61 / 2 = 30.5 answer : a"
Answer: a
Python program:
a = 18 + 22 
b = 7 * 3
c = a + b 
d = c / 2
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 100 and $ 105 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1000 , d ) 1200 , e ) 1440
Rationale: "$ 100 for 2 years = $ 50 per year . extra $ 5 yearned with the compound interest is the percent yearned on percent . so , $ 5 is yearned on $ 50 , which means that the interest = 10 % . this on the other hand means that half of the savings = 50 * 10 = $ 500 . twice of that = $ 1,000 . answer : c ."
Answer: c
Python program:
a = 105 - 100
b = 2 * a
c = b / 100
d = 100 / c
Problem: a walks at 4 kmph and 4 hours after his start , b cycles after him at 10 kmph . how far from the start does b catch up with a ?
Options: a ) 62.6 km , b ) 26.7 km , c ) 22.8 km , d ) 19.5 km , e ) none
Rationale: "sol . suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . ∴ x / 4 - x / 10 = 4 or x = 26.7 km . answer b"
Answer: b
Python program:
a = 4 * 10
Problem: barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 10 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 120 , b ) 600 , c ) 1000 , d ) 360 , e ) 240
Rationale: "let the additional invested amount for 10 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.10 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.10 x = 0.06 x + 0.06 * 2400 0.04 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.04 = 600 ans : b"
Answer: b
Python program:
a = 6 / 100
b = a * 2400
c = 5 / 100
d = 2400 * c
e = b - d
f = 10 / 100
g = 6 / 100
h = f - g
i = e / h
Problem: 100 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 100 + 50 % ( 100 ) = 100 + 50 = 150 . answer c"
Answer: c
Python program:
a = 50 / 100
b = 100 * a
c = 100 + b
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 5 kmph and the other is going towards south 5 kmph . what time will they take to be 50 km apart ?
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: "to be ( 5 + 5 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 10 * 50 = 5 hrs answer is d"
Answer: d
Python program:
a = 5 + 5 
b = 50 / a
Problem: what is the average ( arithmetic mean ) of the numbers 2 , 4 , 6 , 8 , 10 , 12 , 14 and 16 ?
Options: a ) 9 , b ) 10 , c ) 15 , d ) 12 , e ) 14
Rationale: "avg = sum of observations / number of observations avg = ( 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 ) / 8 = 9 answer is a"
Answer: a
Python program:
a = 2 + 6 
b = 6 - 2
c = b / 2
d = c + 1 
e = a * d
f = e / 2
g = 6 - 2
h = g / 2
i = h + 1 
j = f / i
Problem: a miniature roulette wheel is divided into 10 equal sectors , each bearing a distinct integer from 1 to 10 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun two times , approximately what is the probability that the product of the two winning sectors ’ integers will be even ?
Options: a ) 88 % , b ) 75 % , c ) 67 % , d ) 63 % , e ) 50 %
Rationale: the only way to have an odd product is if both integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 = 1 / 4 p ( even product ) = 1 - 1 / 4 = 3 / 4 = 75 % the answer is b .
Answer: b
Python program:
a = 10 / 2
b = a / 10
c = b ** 2
d = 1 - c
e = d * 100
Problem: when the number 2 y 31129 is exactly divisible by 11 , then what can be the smallest whole number in place of y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: "the given number = 2 y 31129 sum of the odd places = 9 + 1 + 3 + 2 = 15 sum of the even places = 2 + 1 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 15 - ( 3 + y ) = divisible by 11 12 � y = divisible by 11 . y must be 1 , to make given number divisible by 11 . a"
Answer: a
Python program:
a = 2 - 2
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 17 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 68 : 85
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 17 - - > x ( a - b ) = 17 . since 17 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 17 . the above implies that either x = 1 and ( a - b ) = 17 or x = 17 anda - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 17 . for the original question only option which fits is e , 4 : 5 . cats = 17 * 4 = 68 and dogs = 17 * 5 = 85 . answer : e ."
Answer: e
Python program:
a = 17 * 4
b = 17 * 4
c = b + 17 
d = a / c
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,15 = 15 / 100 x = 80 * 15 / 100 x = 12 12 / 10 = 1,2 = 120 % , answer c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 15 * b
d = c / 10
e = d * 100
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 3 dm by 5 dm . the number of stones required is :
Options: a ) 3600 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 30 * 50 ) therefore , number of stones = ( 3600 * 1500 / 30 * 50 ) = 3600 answer : a"
Answer: a
Python program:
a = 36 * 15
b = 3 * 5
c = b / 100
d = a / c
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6095 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 230 , d ) 276 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6095 [ 4 l - 40 ] = 6095 / 26.50 = 230 4 l = 270 l = 270 / 4 = 67.5 meters . answer : c"
Answer: c
Python program:
a = 6095 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: jill has 28 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 48 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 28 1 3 / 4 w = 28 w = 16 the total number of jars = 3 w = 48 answer : c
Answer: c
Python program:
a = 1 / 2
b = const_0_25 + a 
c = 1 + b 
d = 28 / c
e = d * 3
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 330 the other is
Options: a ) 330 , b ) 300 , c ) 210 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 330 = 210 answer is c ."
Answer: c
Python program:
a = 30 * 2310
b = a / 330
Problem: 11 friends went to a hotel and decided to pay the bill amount equally . but 10 of them could pay rs . 60 each as a result 11 th has to pay rs . 50 extra than his share . find the amount paid by him .
Options: a ) 110 , b ) 111 , c ) 115 , d ) 123 , e ) none
Rationale: explanation : average amount paid by 10 persons = rs . 60 increase in average due to rs . 50 paid extra by the 11 th men = rs . 50 / 10 = rs . 5 therefore , average expenditure of 11 friends = rs . 60 + rs . 5 = rs . 65 therefore , amount paid by the 11 th men = rs . 65 + rs . 50 = rs . 115 correct option : c
Answer: c
Python program:
a = 60 * 10
b = a + 50 
c = b / 10
d = 50 + c
Problem: at a certain zoo , the ratio of sea horse to penguins is 5 to 11 . if there are 85 more penguins than sea horses at the zoo , how many sea horses are there ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 70 , e ) 132
Rationale: 5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70
Answer: d
Python program:
a = 5 + 1 
b = 85 / a
c = b * 5
d = math.floor(c)
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 105 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 24 hours . answer b"
Answer: b
Python program:
a = 9 + 1 
b = 105 / a
c = 9 - 1
d = 105 / c
e = b + d
Problem: what is the remainder when 7 ^ 700 is divided by 100 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 7 ^ 700 ) mod 100 = [ 7 ^ ( 2 * 350 ) ] mod 100 = [ 49 ^ 350 ] mod 100 = [ ( 50 - 1 ) ^ 350 ] mod 100 = [ { 350 c 349 } * 50 * ( - 1 ) ^ 349 + 350 c 350 * ( - 1 ) ^ 350 ] mod 100 = [ - 350 * 50 + 1 ] mod 100 = 1 mod 100 so , evidently , the remainder will be 1 . answer : a"
Answer: a
Python program:
a = 100 / 2
b = 7 * 7
c = a - b
Problem: a person bought 110 glass bowls at a rate of rs . 10 per bowl . he sold 100 of them at rs . 14 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 279 / 8
Rationale: "cp = 110 * 10 = 1100 and sp = 100 * 14 = 1400 gain % = 100 * ( 1400 - 1100 ) / 1100 = 300 / 11 answer : b"
Answer: b
Python program:
a = 100 * 14
b = 110 * 10
c = a - b
d = 110 * 10
e = c / d
f = e * 100
Problem: the difference between a number and its two - fifth is 45 . what is the number ?
Options: a ) 76 , b ) 56 , c ) 88 , d ) 66 , e ) 75
Rationale: "explanation : let the number be x . x – ( 2 / 5 ) x = 45 ( 3 / 5 ) x = 45 x = 75 answer : e"
Answer: e
Python program:
a = 45 + 4 
b = a ** 4
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d"
Answer: d
Python program:
a = 3 * 4
b = 4 * 4
c = math.lcm(a, b)
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 3 : 1 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 8 , b ) 9 : 2 , c ) 1 : 2 , d ) 5 : 4 , e ) 3 : 2
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 3 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 3 / 9 + 2 / 9 = 5 / 9 losses = 1 - 5 / 9 = 4 / 9 the ratio of wins to losses is 5 : 4 . the answer is d ."
Answer: d
Python program:
a = 3 + 2 
b = 3 + 0 
c = a / b
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 124 billion gallons to 138 billion gallons . if the storm increased the amount of water in the reservoirs to 82 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 9 , b ) 14 , c ) 25 , d ) 30 , e ) 44
Rationale: "since we need to find only an approximate value and the answer choices are quite widespread , then use : 80 % instead of 82 % ( notice that this approximation gives the bigger tank capacity ) ; 140 billion gallons instead of 138 billion gallons ( notice that this approximation also gives the bigger tank capacity ) ; 130 billion gallons instead of 124 billion gallons ; . notice that the third approximation balances the first two a little bit . so , we ' ll have that : capacity ∗ 0.8 = 140 - - > capacity = 140 / 0.8 = 175 hence , the amount of water the reservoirs were short of total capacity prior to the storm was approximately 175 − 130 = 45 billion gallons . answer : e ."
Answer: e
Python program:
a = 138 * 100
b = a / 82
c = b / 2
Problem: for what value of x between − 6 and 6 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 6 , b ) − 2 , c ) 0 , d ) 2 , e ) 6
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 6 will give the greatest value . . ans a"
Answer: a
Python program:
a = negate ** (
b = a + 2 
c = b - 16
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is :
Options: a ) 22 , b ) 88 , c ) 12 , d ) 73 , e ) 29
Rationale: "explanation : s . i . for 3 years = rs . ( 12005 - 9800 ) = rs . 2205 . s . i . for 5 years = rs . = rs . 3675 principle = rs . ( 9800 - 3675 ) = rs . 6125 hence , rate = = 12 % answer : c ) 12 %"
Answer: c
Python program:
a = 12005 - 9800
b = 9800 * 8
c = 5 * 12005
d = b - c
e = a / d
f = e * 100
Problem: how many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 110 + 150 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec e"
Answer: e
Python program:
a = 150 + 110 
b = 36 * const_0_2778
c = a / b
Problem: a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?
Options: a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 79
Rationale: ratio is 4 : 6 : 5 , numbers are 4 x , 6 x , 5 x total scores of each class is ( 65 * 4 x + 6 x * 90 + 77 * 5 x ) = 260 x + 540 x + 385 x = 1185 x total number of students = 15 x average = 1185 x / 15 x = 79 e is the answer
Answer: e
Python program:
a = 65 * 4
b = 90 * 6
c = a + b 
d = 77 * 5
e = c + d 
f = 4 + 6 
g = f + 5 
h = e / g
Problem: a merchant purchased a jacket for $ 54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 18
Rationale: "actual cost = $ 54 sp = actual cost + mark up = actual cost + 40 % sp = 54 * 100 / 60 on sale sp = 80 / 100 ( 54 * 100 / 60 ) = 72 gross profit = $ 18 answer is e"
Answer: e
Python program:
a = 40 / 100
b = 1 - a
c = 54 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 54
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 19 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 27.50 , b ) $ 28.50 , c ) $ 29.50 , d ) $ 30.50 , e ) $ 31.50
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 19 ) = 0.8 x x = 1.2 ( 19 ) / 0.8 = 1.5 ( 19 ) = $ 28.50 the answer is b ."
Answer: b
Python program:
a = 20 / 100
b = a * 19
c = b + 19 
d = 100 - 20
e = d / 100
f = c / e
Problem: three pipes of same capacity can fill a tank in 12 hours . if there are only two pipes of same capacity , the tank can be filled in ?
Options: a ) 18 , b ) 8 , c ) 12 , d ) 6 , e ) 4
Rationale: "the part of the tank filled by three pipes in one hour = 1 / 12 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 12 = 1 / 18 . the tank can be filled in 18 hours . answer : a"
Answer: a
Python program:
a = 2 / 3
b = 1 / 12
c = a * b
d = 1/(c)
Problem: what is the least number to be subtracted from 800 to make it a perfect square ?
Options: a ) 1 , b ) 16 , c ) 20 , d ) 71 , e ) 60
Rationale: "the numbers less than 800 and are squares of certain number is 784 . the least number that should be subtracted from 800 to make it perfect square = 800 - 784 = 16 . answer : b"
Answer: b
Python program:
a = 3 * 2
b = 10 + a 
c = 100 * b
d = c - 800
Problem: a train crosses a platform of 110 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 88 , c ) 77 , d ) 310 , e ) 52
Rationale: "length of the train be â € ˜ x â € ™ x + 110 / 15 = x + 250 / 20 4 x + 440 = 3 x + 750 x = 310 m answer : d"
Answer: d
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 110 * e
g = c - f
Problem: bucket p has thrice the capacity as bucket q . it takes 80 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 80 , e ) 100
Rationale: "explanation : let capacity of q = 1 litre . then , capacity of p = 3 litre . given that it takes 80 turns for bucket p to fill the empty drum . = > capacity of the drum = 80 × 3 = 240 litre . number of turns required if both p and q are used having each turn together 240 / 3 + 1 = 60 litre . answer : option c"
Answer: c
Python program:
a = 1 / 80
b = 80 * 3
c = 1 / b
d = a + c 
e = 1 / d
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance ( in km ) is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "sol . let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 ⇔ 47 x / 60 = 47 / 60 ⇔ x = 1 . ∴ total distance = ( 3 * 1 ) km = 3 km . answer c"
Answer: c
Python program:
a = 47 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000