euclaise/mathqa_programs huggingface dataset:
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 15 x = 45 - - > 23 / 20 * x = 45 - - > x = 45 * 20 / 23 = 900 / 23 = ~ 39 . answer : b ."
Answer: b
Python program:
a = 100 + 15 
b = 100 / a
c = b * 45
Problem: salesperson a ' s compensation for any week is $ 360 plus 8 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 7,750 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 350 + 0.04 ( x - 1000 ) = 0.08 x x = 7,750 ans : d"
Answer: d
Python program:
a = 8 / 100
b = a * 1
c = 360 - b
d = 8 / 100
e = 8 / 100
f = d - e
g = c / f
h = 8 / 100
i = h * 1
j = 360 - i
k = 8 / 100
l = 8 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: a train 220 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 12 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 4 = 64 km / hr . = 64 * 5 / 18 = 160 / 9 m / sec . time taken to pass the men = 220 * 9 / 160 = 12 sec . answer : b"
Answer: b
Python program:
a = 60 + 4 
b = a * const_0_2778
c = 220 / b
Problem: what is the dividend . divisor 14 , the quotient is 12 and the remainder is 8
Options: a ) 175 , b ) 176 , c ) 177 , d ) 178 , e ) 179
Rationale: b = d * q + r b = 14 * 12 + 8 b = 168 + 8 b = 176
Answer: b
Python program:
a = 14 * 12
b = a + 8
Problem: jhon works for 60 days . for the day he is present he is paid 7.00 / - and for the day he is absent he is paid 3.00 / - per day . if he is paid 170 / - . how many days he is present .
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: let no . days be = x and no . days he is absent = 60 - x , so 7 x - 3 ( 60 - x ) = 170 x = 35 answer : a
Answer: a
Python program:
a = 3 * 60
b = a + 170 
c = 7 + 3 
d = b / c
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 140 kg . in the first week 60 percent is cut away . in the second week 40 percent of the remainder is cut away . in the third week the statue is completed when 30 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 24 kg , b ) 23 kg , c ) 28 kg , d ) 25 kg , e ) 27 kg
Rationale: a 24 kg 140 ã — 0.4 ã — 0.6 ã — 0.7 = 24 kg .
Answer: a
Python program:
a = 30 / 100
b = 1 - a
c = 40 / 100
d = 1 - c
e = 60 / 100
f = 1 - e
g = 140 * f
h = d * g
i = b * h
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . what is the number of participants ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 171 n * ( n - 1 ) = 342 = 19 * 18 ( trial and error ) the answer is e ."
Answer: e
Python program:
a = 171 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: a circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it . as a result the plate lost 1 / 6 th its original weight . the radius of the circular plate is
Options: a ) 16 sqrt 2
b ) 8 sqrt 2
c ) 32 sqrt 2
d ) sqrt 72
e ) sqrt 82
Rationale: area of 12 holes = 12 * pi * 1 ^ 2 = 12 * pi as 12 * pi = ( 1 / 6 ) th weight , so total area of plate = 12 * pi / ( 1 / 6 ) = 72 * pi if r = radius of the plate , then its area = pi * r ^ 2 = 72 * pi , so r = sqrt 72 answer : d
Answer: d
Python program:
a = circle_area * (
b = a * 12
c = b / 6
d = math.sqrt(c)
Problem: what is the ratio g of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?
Options: a ) 1 / 4
b ) 3 / 8
c ) 1 / 2
d ) 3 / 5
e ) 2
Rationale: one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area g = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )
Answer: d
Python program:
a = 2 * 3
b = 1 * 2
c = b * 2
d = 1 * 1
e = c + d 
f = e * 2
g = a / f
Problem: if the mean of numbers 28 , x , 50 , 78 and 104 is 62 , what is the mean of 48 , 62 , 98 , 124 and x ?
Options: a ) 76.5 , b ) 58 , c ) 39.8 , d ) 90.3 , e ) 66.67
Rationale: "mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 62 = ( x + 28 + 50 + 78 + 104 ) / ( 5 ) 62 x 5 = 260 + x x = 50 therefore mean of 2 nd series m 2 = ( x + 48 + 62 + 98 + 124 ) / 5 m 2 = 76.5 answer = a"
Answer: a
Python program:
a = 4 + 1 
b = 62 * a
c = 28 + 50 
d = c + 78 
e = d + 104 
f = b - e
g = f + 48 
h = g + 62 
i = h + 98 
j = i + 124 
k = 4 + 1 
l = j / k
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 68 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 13.33 %
Rationale: "increase = ( 8 / 60 ) * 100 = ( 2 / 15 ) * 100 = 13.33 % . e"
Answer: e
Python program:
a = 68 - 60
b = a / 60
c = b * 100
Problem: what will be the compound interest on a sum of rs . 24,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 9718.27 , b ) rs . 9750 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 24000 * ( 1 + 12 / 100 ) 3 ] = 24000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 33718.27 c . i . = ( 33718.27 - 24000 ) = rs . 9718.27 answer : a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a man can row 36 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?
Options: a ) 14 kmph , b ) 12 kmph , c ) 18 kmph , d ) 1 kmph , e ) none of these
Rationale: explanation : let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 36 x = 18 rate of upstream = 18 rate of downstream = 54 rate of stream 1 / 2 ( 54 - 18 ) = 18 kmph answer : option c
Answer: c
Python program:
a = 36 * 2
b = 3 + 1 
c = a / b
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 51 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 51 has the form 4 k + 3 , so the units digit of 93 ^ 51 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Python program:
a = reminder * (
b = reminder + (
Problem: how many multiples of 5 are there between 5 to 75 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) 13 , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 . answer : d"
Answer: d
Python program:
a = 75 - 5
b = a / 5
c = b + 1
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 765 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 192 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 765 . as per question we need to take 1 / 4 of 765 to be considered for top 10 movies = 191.25 approximate the value we 192 . answer : option b is the correct answer . ."
Answer: b
Python program:
a = 765 / 4
Problem: a box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) 37
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 24 , 40 and 16 . thus side of cube must be 8 , and total number of cubes = 24 / 8 * 40 / 8 * 16 / 8 = 30 ans b"
Answer: b
Python program:
a = 24 * 40
b = a * 16
c = 16 / 2
d = b / volume_cube
Problem: there are 11 baskets numbered from 1 to 11 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 180 , b ) 220 , c ) 260 , d ) 300 , e ) 340
Rationale: each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 11 * 12 / 2 = 66 apples . the total number of apples taken by 10 children is 10 * 66 = 660 the number of apples left in the end is 1000 - 660 = 340 apples . the answer is e .
Answer: e
Python program:
a = 1 + 11 
b = 10 / 2
c = a * b
d = 10 / 2
e = c + d 
f = e + 1 
g = f * 10
h = 1000 - g
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 3 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 26 : 11 , b ) 23 : 11 , c ) 21 : 11 , d ) 24 : 11 , e ) 25 : 11
Rationale: "vessel a = 300 gallons - - > milk = 225 , water = 75 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 525 , water 275 the ratio = 525 / 275 - - > 21 : 11 answer : c"
Answer: c
Python program:
a = 3 ** 3
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 508 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 656 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 8
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 508 . . . eq 1 8 x + 32 y = 656 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1016 8 x = 656 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 656 . . . then we get 32 y = 576 then y = 18 differenece between x and y is 8 answer : e"
Answer: e
Python program:
a = 508 * 2
b = a - 656
c = 22 * 2
d = c - 8
e = b / d
f = 22 * e
g = 508 - f
h = g / 16
Problem: a rectangular block 10 cm by 20 cm by 35 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 56 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 10 * 20 * 35 = 7000 cm ^ 3 side of the largest cube = h . c . f of 10 , 20,35 = 5 cm volume of the cube = 5 * 5 * 5 = 125 cm ^ 3 number of cubes = 7000 / 125 = 56 answer is b"
Answer: b
Python program:
a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d 
f = 3 * 1000
g = 35 * 10
h = f + g 
i = e / h
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 5 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
Answer: e
Python program:
a = 40 - 5
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
Problem: if a lends rs . 2000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 90 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 212.5
Rationale: "( 2000 * 1.5 * 3 ) / 100 = > 90 answer : a"
Answer: a
Python program:
a = 2000 * 11
b = a * 3
c = b / 100
d = 2000 * 10
e = d * 3
f = e / 100
g = c - f
Problem: a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is :
Options: a ) 260
b ) 262
c ) 270
d ) 272
e ) none of these
Rationale: explanation : volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 4 / 2 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 option c
Answer: c
Python program:
a = quadrilateral_area * (
Problem: the time taken by mr . dhoni to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 72 kmph , find the speed of the stream ?
Options: a ) 24 kmph , b ) 25 kmph , c ) 26 kmph , d ) 30 kmph , e ) 28 kmph
Rationale: the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 72 / 3 = 24 kmph . answer : a
Answer: a
Python program:
a = 72 * 2
b = a / 3
c = b / 2
Problem: a math teacher has 24 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 7 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 24 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 24 - 17 = 7 answer ( a )"
Answer: a
Python program:
a = 24 * 8
b = a / 10
c = b / 2
d = c - const_0_25
e = d - const_0_25
Problem: increasing the original price of a certain item by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 30.0 , d ) 32.75 , e ) 32.25
Rationale: "we ' re told that the original price of an item is increased by 15 % and then that price is increased by 15 % . . . . if . . . . starting value = $ 100 + 15 % = 100 + . 15 ( 100 ) = 115 + 15 % = 115 + . 15 ( 115 ) = 115 + 17.25 = 132.25 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 32.25 / 100 = 32.25 % final answer : e"
Answer: e
Python program:
a = 15 / 100
b = a + 1 
c = 15 / 100
d = c + 1 
e = b * d
f = e - 1
g = f * 100
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability t that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Python program:
a = 3 + 2 
b = 4 * 4
c = a / b
Problem: raj invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) 3000 , b ) 4000 , c ) 5000 , d ) 5500 , e ) 6000
Rationale: investment in 12 % stock be x then investment 15 % stock = ( 12000 - x ) 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x = 4000 answer b
Answer: b
Python program:
a = 15 / 125
b = a * 12000
c = b - 1360
d = 15 / 125
e = 12 / 120
f = d - e
g = c / f
Problem: if 42.24 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 42.24 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.24 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.24 = km / 50 . . . . . . 24 / 100 = 3 m / 50 . . . . . . m = 4 k + m = 3 + 4 = 7 answer : b
Answer: b
Python program:
a = 1 / 100
b = const_0_25 - a
c = b * 50
d = 1 / 100
e = const_0_25 - d
f = 42 - 24
g = f / 14
h = c / g
i = 1 / 100
j = const_0_25 - i
k = 42 - 24
l = k / 14
m = h + l
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 14 - meter platform and caught it after it had traveled 41.7 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 14 + 14 + 7 + 3.5 + 1.75 + 0.9 + 0.5 ans b"
Answer: b
Python program:
a = 14 / 2
b = a / 2
Problem: a and b are two partially filled buckets of water . if 2 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 2 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 21 , e ) 22 / 5
Rationale: "let a contains a , b contains b liters so , ( a - 2 ) / ( b + 2 ) = 1 / 3 . . . . . . . ( 1 ) or 3 a - 6 = b + 2 or 3 a - b = 8 again , ( b - 2 ) / ( a + 2 ) = 1 / 2 . . ( 2 ) or 2 b - 4 = a + 2 or 2 b - a = 6 from ( 1 ) ( 2 ) we find a = 22 / 5 ans : e"
Answer: e
Python program:
a = 2 + 3 
b = a + 2 
c = 2 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: the reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 182
Rationale: "reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 so , hcf = 14 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 14 * 312 / 24 = 182 answer : e"
Answer: e
Python program:
a = 14 * 312
b = a / 24
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 30 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 30 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 30 ) = 90 ( x - 5 ) 300 = 10 x = > x = 30 answer : b"
Answer: b
Python program:
a = 90 * 5
b = 5 * 30
c = a - b
d = 90 - 80
e = c / d
Problem: a , b and c have rs . 450 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 100 , b ) b ) 110 , c ) c ) 120 , d ) d ) 130 , e ) e ) 140
Rationale: "a + b + c = 450 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 450 - - - - - - - - - - - - - - - - c = 100 answer : a"
Answer: a
Python program:
a = 200 + 350 
b = a - 450
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 21 liters of forest green to change it to verdant green ?
Options: a ) 1 / 3 , b ) 7 , c ) 1 / 2 , d ) 1 / 7 , e ) 1 / 8
Rationale: "21 liter of forset green have 12 liter of blue and 9 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 12 / ( 9 + x ) = ¾ 27 + 3 x = 48 = > x = 7 answer : b"
Answer: b
Python program:
a = 4 / 3
b = a * 4
c = b - 3
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 4 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "20 / 6 = 3.33 answer : d"
Answer: d
Python program:
a = 100 / 3
b = a / 6
c = b / 100
d = c * 100
Problem: a and b invests rs . 4000 and rs . 6000 in a business . after 4 months , a withdraws three - fourth of his capital and 4 months later , b withdraws half of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 7
Rationale: "a : b ( 4000 * 4 ) + ( 1000 * 8 ) : ( 6000 * 8 ) + ( 3000 * 4 ) 24000 : 60000 2 : 5 answer : a"
Answer: a
Python program:
a = 4000 * 4
b = 6000 / 3
c = 4 * 4
d = b * c
e = a + d 
f = 4 * 3
g = 6000 * f
h = 6000 / 3
i = 6000 - h
j = 4 * 3
k = i * j
l = g + k 
m = e / l
Problem: a trader marked the selling price of an article at 10 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 110 * 100 ] % = 10 % answer a"
Answer: a
Python program:
a = 2 + 3 
b = a * 2
c = b + 1 
d = 100 + 10 
e = c / d
f = 100 * e
Problem: a goods train runs at the speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 240 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 280 / 26 = 20 x + 280 = 520 x = 240 . answer : c"
Answer: c
Python program:
a = const_0_2778 * 72
b = 280 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: two cars start at the same time from opposite ends of a highway that is 500 miles long . one car is riding at 40 mph and the second car is riding at 60 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: as cars are moving in opposite directions their speeds will be added . so their relative speeds : 60 + 40 = 100 mph total distance to be covered = 500 miles . time taken would be : 500 miles / 100 mph = 5 hours e is the answer .
Answer: e
Python program:
a = 40 + 60 
b = 500 / a
Problem: the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 12 . what is the radius of circle o ?
Options: a ) – 2 / pi
b ) 2
c ) 3
d ) 4
e ) 6
Rationale: pi * r ^ 2 + 2 r - 2 * pi * r = 12 simplifying the equation : pi * r ( r - 2 ) + 2 r = 12 without much algebraic : we can test the answers quickly , then 6 is the only possible answer that will eliminate pi from equation . answer is e
Answer: e
Python program:
a = 12 / 2