euclaise/mathqa_programs huggingface dataset:
Problem: length of a rectangular plot is 50 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 50 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 50 ) + x ] = 200 2 x + 50 = 100 2 x = 50 x = 25 . hence , length = x + 50 = 75 m d"
Answer: d
Python program:
a = 5300 / 26
b = 2 * 50
c = a + b 
d = c / 4
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 110000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4400 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 110000 p = rs . [ ( 24 * 4 * 4 * 110000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 42240000 / 9600 ) = > p = rs . 4400 answer : d"
Answer: d
Python program:
a = 24 * 4
b = a * 4
c = b * 110000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
Problem: kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ?
Options: a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189
Rationale: p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c
Answer: c
Python program:
a = 5 * 5
b = const_60 * 3
c = 3 * 3
d = b + c 
e = a / d
Problem: a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e"
Answer: e
Python program:
a = 100 + 50 
b = 100 / 30
c = 50 / 60
d = b + c 
e = a / d
Problem: a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12
Rationale: "x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e"
Answer: e
Python program:
a = 3 * 2
b = a * 10
c = 3 * 2
d = 11 - c
e = b / d
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d"
Answer: d
Python program:
a = 3 * 5
b = 4 * 5
c = math.lcm(a, b)
Problem: if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c − a ?
Options: a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40"
Answer: a
Python program:
a = 70 * 2
b = 50 * 2
c = a - b
Problem: a invested $ 15000 in a business after 6 months b invested $ 18000 in the business . end of the year if they got $ 16000 as profit . find b shares ?
Options: a ) $ 10000 , b ) $ 12000 , c ) $ 5000 , d ) $ 6000 , e ) $ 7500
Rationale: "a : b = 15000 * 12 : 18000 * 6 a : b = 5 : 3 a ' s share = 16000 * 5 / 8 = 10000 b ' s share = 16000 * 3 / 8 = 6000 answer is d"
Answer: d
Python program:
a = 18000 / 2
b = 18000 / 2
c = 15000 + b 
d = a / c
e = 1 - d
f = 16000 * e
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a ."
Answer: a
Python program:
a = 85 + 70 
b = a + 5 
c = b - 100
Problem: a number when divided by 44 , gives 400 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 35
Options: a ) a ) 30 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 44 = 400 = > p = 400 * 44 = 17600 p / 35 = 17600 / 35 = 502 , remainder = 30 answer : option a"
Answer: a
Python program:
a = 44 * 400
b = a / 35
Problem: what is the area of a square field whose diagonal of length 22 m ?
Options: a ) 300 sq m , b ) 220 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m
Rationale: "d 2 / 2 = ( 22 * 22 ) / 2 = 220 answer : b"
Answer: b
Python program:
a = square_area / (
Problem: if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ?
Options: a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7
Rationale: p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) × p ( a ) p ( a n b ) = 0.2 × 0.18 p ( a n b ) = 0.36 b )
Answer: b
Python program:
a = 0 * 18
b = a * 10
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another surveyof 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "50 % of n people from eros prefer brand a . 50 % of n is 50 / 100 x n = n / 2 . 60 % of 100 people from angie prefer brand a . 60 % of 100 is 60 / 100 x 100 = 60 . of the total n + 100 people surveyed , n / 2 + 60 prefer brand a . given that this is 55 % , we have ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 solving the equation ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 ( n / 2 + 60 ) = 55 / 100 x ( n + 100 ) ( n / 2 + 60 ) = 11 / 20 n + 55 0 = 11 n / 20 – n / 2 + 55 - 60 now subtracting n / 2 and 60 from both sides 0 = n / 20 - 5 adding 5 on both sides 5 = n / 20 n = 100 hence , the total number of people surveyed is n + 100 = 100 + 100 = 200 . answer : d"
Answer: d
Python program:
a = 60 / 100
b = 100 * a
c = 55 / 100
d = 100 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: 325.124 x 12.98 ã · 3.001 + 21.21 = ?
Options: a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 325.124 x 12.98 ã · 3.001 + 21.21 = ? â ‰ ˆ ( 325.124 x 13 / 3 ) + 21.21 â ‰ ˆ 1408.87 + 21.21 â ‰ ˆ 1430.080 answer : option a"
Answer: a
Python program:
a = 12 ** 98
b = 325 * 124
Problem: gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ?
Options: a ) 2 : 3 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) none of these
Rationale: "? required ratio = 6 ? 4 = 3 : 2 answer b"
Answer: b
Python program:
a = 15 - 9
b = 19 - 15
c = a / b
Problem: in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 5.6 cm
b ) 2.4 cm
c ) 4.8 cm
d ) 2.16 cm
e ) 3.2 cm
Rationale: look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a .
Answer: a
Python program:
a = 7 * 8
b = a / 10
Problem: in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d"
Answer: d
Python program:
a = 15 + 11
Problem: two trains a and b are 125 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 11 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 125 + 150 = 275 m . time taken = 275 / 25 = 11 s . correct answer b ."
Answer: b
Python program:
a = 125 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the t job in 44 hours . answer : c ."
Answer: c
Python program:
a = 1 / 4
b = 1 / 11
c = a + b 
d = c / 15
e = 1 / d
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 320 m long platform ?
Options: a ) 44 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min
Rationale: "a 44 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 320 ) / 36 * 5 / 18 = 44 min ."
Answer: a
Python program:
a = const_0_2778 * 36
b = a * 12
c = 320 + b 
d = const_0_2778 * 36
e = c / d
Problem: the price of a book is increased from $ 300 to $ 450 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 450 â € “ rs 300 = rs 150 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 150 300 ) * 100 = 50 % d"
Answer: d
Python program:
a = 450 - 300
b = a / 300
c = b * 100
Problem: a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 24 , 2 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a"
Answer: a
Python program:
a = 26 + 22 
b = a / 2
c = b / 2
Problem: a train is walking at 6 / 7 of its usual speed , the train is 20 minutes too late . find its usual time to cover the journey .
Options: a ) 1 hour , b ) 30 min , c ) 3 hours 20 min , d ) 2 hours 30 min , e ) 2 hours
Rationale: new speed = 6 / 7 of the usual speed new time taken = 7 / 6 of the usual time taken so , ( 7 / 6 of the usual time ) - ( usual time ) = 20 min 1 / 6 of the usual time = 20 min usual time = 20 * 6 = 120 min = 2 hours correct option is e
Answer: e
Python program:
a = 6 / 7
b = a * 20
c = 6 / 7
d = 1 - c
e = b / d
f = e / const_60
Problem: by how much is 30 % of 80 greater than 4 / 5 th of 25 ?
Options: a ) 2 , b ) 4 , c ) 10 , d ) 15 , e ) 17
Rationale: "answer it is ( 30 x 80 ) / 100 - ( 4 x 25 ) / 5 = 24 - 20 = 4 correct option : b"
Answer: b
Python program:
a = 30 / 100
b = 80 * a
c = 4 / 100
d = c * 5
e = b - d
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . how tall is the fourth person ?
Options: a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c ."
Answer: c
Python program:
a = 77 * 4
b = 4 + 6 
c = 6 + b 
d = a - c
e = d / 4
f = 4 + 6 
g = e + f
Problem: t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Python program:
a = 5 + 6 
b = a + 9 
c = b / 100
Problem: a man whose speed is 7 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 6.7 , b ) 4 , c ) 6 , d ) 9 , e ) 3
Rationale: "m = 7.0 s = 1.5 ds = 8.5 us = 5.5 as = ( 2 * 8.5 * 5.5 ) / 14 = 6.7 answer : a"
Answer: a
Python program:
a = 7 - 1
b = 7 + a 
c = b / 2
Problem: a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum .
Options: a ) 3000 , b ) 6000 , c ) 2000 , d ) 4000 , e ) none of them
Rationale: "let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] – [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000  6 p = 36000  p = 6000 hence , sum = rs . 6000 . answer is b ."
Answer: b
Python program:
a = 2 / 100
b = a * 3
c = 360 / b
Problem: 30 ^ 10 / 210 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 30 / 7 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 210 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 30 / 7 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 210 ^ 5 = ( 30 ^ 10 ) / ( 7 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 7 ^ 5 ) = ( 30 / 7 ) ^ 5 . thus , c is the answer ."
Answer: c
Python program:
a = 30 ** 10
b = 30 ** 5
c = a / b
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 420 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d"
Answer: d
Python program:
a = 15 * 420
b = 15 * 120
c = a - b
d = 120 - 110
e = c / d
Problem: if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a"
Answer: a
Python program:
a = 13 + 9 
b = a / 2
c = 9 - b
d = c ** 2
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans ( which is ( 60 * 0.7 ) = 42 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 52 ( 42 + 10 ) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 ( 52 - 48 ) votes . therefore candidate x is expected to win the election by ( 4 / 100 ) votes which is equivalent to 4 % . i think the answer is b .
Answer: b
Python program:
a = 25 / 100
b = a * 2
c = 70 / 100
d = c * 3
e = b + d 
f = 70 / 100
g = f * 3
h = 3 - g
i = 25 / 100
j = i * 2
k = 2 - j
l = h + k 
m = e - l
n = 3 + 2 
o = m / n
p = o * 100
Problem: a family pays $ 800 per year for an insurance plan that pays 85 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,100 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 15 % of first 1000 $ in expense = 150 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1100 $ ( since insurance plan will pay 100 % of amount that exceeds 950 $ ) answer a"
Answer: a
Python program:
a = 1 - 0
Problem: a vendor bought toffees at 6 for a dollar . how many for a dollar must he sell to gain 20 % ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 8
Rationale: "c 5 c . p . of 6 toffees = $ 1 s . p . of 6 toffees = 120 % of $ 1 = $ 6 / 5 for $ 6 / 5 , toffees sold = 6 . for $ 1 . toffees sold = 6 * 5 / 6 = 5"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 6 * b
Problem: if each year the population of the country grows by 100 % , how many years will elapse before the population of the country doubles ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2010 , population is 100 . year 2001 : population becomes 200 . . . . . . . . . . . . . 1 year elapsed answer : a"
Answer: a
Python program:
a = 4 + 4
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 50 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 140 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 50 y / 100 * 4 y = 50 y = 35 and x = 140 answer - d"
Answer: d
Python program:
a = 50 / 50
b = 50 / 50
c = a * b
d = c * 1000
Problem: the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a"
Answer: a
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ?
Options: a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000
Rationale: "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c"
Answer: c
Python program:
a = 8 ** 2
b = a ** 3
c = 8 ** 3
d = b / c
Problem: in a group of 28 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 4 , e ) 3
Rationale: "a 7 seven students are not taking a language . add 7 + 10 + 4 to get 21 . then subtract 21 from the total students : 28 - 21 = 7 ."
Answer: a
Python program:
a = 7 + 10 
b = 28 - a
Problem: on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e"
Answer: e
Python program:
a = 17 - 5
b = 720 / a
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ."
Answer: e
Python program:
a = 384 / 10
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.0 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,500 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5 $ then total value is 300 * 5.0 = 1500 . imo option b is correct answer . ."
Answer: b
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 5
j = i / 1000
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 12880 , b ) 12789 , c ) 27108 , d ) 17600 , e ) 18291
Rationale: "explanation : price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 110 / 100 = rs . 17600"
Answer: d
Python program:
a = 100 + 10 
b = 12500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: 9873 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9873 = 3327 option : a"
Answer: a
Python program:
a = 13200 - 9873
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 5 days starting with sunday is
Options: a ) 1215 , b ) 1314 , c ) 2900 , d ) 1710 , e ) 2750
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 5 ) = 1710 answer : option d"
Answer: d
Python program:
a = 3 + 4 
b = 5 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 5 / f
h = math.floor(g)
i = h + 1 
j = 5 - i
k = j * 240
l = e + k 
m = l / 5