euclaise/mathqa_programs huggingface dataset:
Problem: find out the square of a number which when doubled exceeds its one nineth by 17 ?
Options: a ) 16 , b ) 25 , c ) 81 , d ) 26 , e ) 17
Rationale: "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 1 / a
c = 2 - b
d = 17 / c
e = d ** 2
Problem: the inner circumference of a circular race track , 25 m wide , is 880 m . find radius of the outer circle ?
Options: a ) 165 m , b ) 120 m , c ) 100 m , d ) 190 m , e ) 220 m
Rationale: "let inner radius be r metres . then , 2 π r = 880 ⇔ r = ( 880 x ( 7 / 44 ) ) = 140 m . radius of outer circle = ( 140 + 25 ) m = 165 m . hence a"
Answer: a
Python program:
a = 880 / math.pi
b = a / 2
c = 25 + b
Problem: find the compound interest on $ 800 for 1 year at 10 % p . a . if ci is component yearly ?
Options: a ) $ 40 , b ) $ 400 , c ) $ 840 , d ) $ 800 , e ) $ 80
Rationale: "a = p ( 1 + r / 100 ) ^ t = 800 ( 1 + 10 / 100 ) ^ 1 = 800 * 21 / 20 = $ 840 ci = a - p = 840 - 800 = $ 40 answer is a"
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 1
d = 800 * c
e = d - 800
Problem: how many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: e 90 1080 apples = 90 dozens the required number of boxes = 90 . answer : e
Answer: e
Python program:
a = 1080 / 12
Problem: a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 4 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 720 , d ) s . 740 , e ) s . 840
Rationale: s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 4 * 2 = rs . 100 . principal = ( 820 - 100 ) = rs . 720 . answer : c
Answer: c
Python program:
a = 1020 - 820
b = a / 4
c = b * 2
d = 820 - c
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84
b ) 1.75
c ) 3.36
d ) 2.72
e ) none of these
Rationale: here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 750 * 2 * ( 4 / 5 ) = 1200 2160 + 1200 = 3360 solving for units gives us 3.36 so the answer is c
Answer: c
Python program:
a = 3 * 900
b = 2 * 750
c = a + b 
d = 4 * c
e = 3 + 2 
f = d / e
g = f / 1000
Problem: a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 , b ) 660 , c ) 500 , d ) 267 , e ) 298
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 800 + x ) / 60 = 65 / 3 x = 500 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 800 / b
Problem: the sector of a circle has radius of 42 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 183 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 42 ) + 2 ( 42 ) = 99 + 84 = 183 cm answer : e"
Answer: e
Python program:
a = 42 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 42
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 7 miles each hour , so it takes 6 hours to catch car x . in 6 hours , car x travels 210 miles . the answer is d ."
Answer: d
Python program:
a = 72 / const_60
b = a * 35
c = 42 - 35
d = b / c
e = 35 * d
Problem: there are 4 more women than there are men on a local co - ed softball team . if there are a total of 18 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 7 / 11 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 18 m + 4 + m = 18 2 m = 14 m = 7 w = 11 ratio : 7 : 11 ans : c"
Answer: c
Python program:
a = 18 - 4
b = 1 + 1 
c = a / b
d = 18 - 4
e = 1 + 1 
f = d / e
g = f + 4 
h = c / g
Problem: a student gets 50 % in one subject , 60 % in the other . to get an overall of 60 % how much should get in third subject .
Options: a ) 75 % , b ) 70 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 60 + x = 3 * 60 110 + x = 180 x = 180 - 110 = 70 answer : b"
Answer: b
Python program:
a = 60 * 3
b = 50 + 60 
c = a - b
Problem: one pump drains one - half of a pond in 6 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 6 hours so 12 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 12 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 12 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 12 + 1 / a ) = 1 / 2 solving u get a = 12 / 11 = 1.1 hence answer is b"
Answer: b
Python program:
a = 6 * 2
b = 1 / a
c = 1 - b
d = 1 / c
Problem: an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of b ?
Options: a ) 360 , b ) 358 , c ) 356 , d ) 514 , e ) 504
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of b = 4 / 13 * 1638 = rs . 504 answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a + 4 
c = 1638 / b
d = c * 4
Problem: how much is 80 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88
Rationale: ( 80 / 100 ) * 40 – ( 4 / 5 ) * 25 32 - 20 = 12 answer : d
Answer: d
Python program:
a = 80 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: light glows for every 17 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 291 , b ) 292 , c ) 293 , d ) 384 , e ) 285
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 17 = 292 . so total 293 times light ll glow answer : c"
Answer: c
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 17
Problem: two trains of length 100 meters and 200 meters are 660 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 108 km / h . after how many seconds will the trains meet ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the speeds are 90000 / 3600 = 25 m / s and 108000 / 3600 = 30 m / s the relative speed is 55 m / s . time = 660 / 55 = 12 seconds the answer is a ."
Answer: a
Python program:
a = 90 + 108 
b = a * const_0_2778
c = 660 / b
Problem: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 35 % .
Rationale: "25 % of 2 litres = 0.5 litres 50 % of 6 litres = 3.0 litres therefore , total quantity of alcohol is 3.5 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 35 % answer : e"
Answer: e
Python program:
a = 25 / 100
b = a * 2
c = 50 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18300 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 6100
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18300 = 6100 answer : e"
Answer: e
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 18300 / h
j = a * i
Problem: how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18
Rationale: so , the numbers should be from 10 , 000,000 to 100 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 10 , 000,001 10 , 000,010 10 , 000,100 10 , 001,000 10 , 010,000 10 , 100,000 11 , 000,000 7 numbers . 2 . one 2 and the rest are 0 ' s : 20 , 000,000 1 number . total = 8 numbers . answer : d
Answer: d
Python program:
a = 4 + 3 
b = a + 1
Problem: the workforce of company x is 60 % female . the company hired 26 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 312 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 26 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 26 ) 0.05 x = 14.3 x = 286 - this is quantity of employees before adding 26 men so after adding it will be 312 answer is c"
Answer: c
Python program:
a = 55 / 100
b = a * 26
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 26
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 33.3 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) 74
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 33.3 kg zinc , mixture , melted = [ 20 / 9 x 33.3 ] kg = 74 kg . answer e"
Answer: e
Python program:
a = 11 / 9
b = a * 33
c = b + 33
Problem: a good train 800 metres long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 minute , then the length of the tunnel ( in meters ) is :
Options: a ) 600 , b ) 300 , c ) 400 , d ) 500 , e ) 200
Rationale: speed = 78 * 5 / 18 m / sec = = > 65 / 3 length of the tunnel be x then 800 + x / 60 = 65 / 3 3 ( 800 + x ) = 3900 x = 500 answer d
Answer: d
Python program:
a = 4 + 1 
b = const_60 + a 
c = const_60 / 3
d = b * c
e = d - 800
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 25 % profit ?
Options: a ) 15.75 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 125 % of rs . 630 = 125 / 100 * 630 = rs . 787.5 s . p . per kg = 787.5 / 50 = 15.75 . answer : a"
Answer: a
Python program:
a = 30 * 11
b = 20 * 14
c = a + b 
d = 30 * 11
e = 20 * 14
f = d + e 
g = f / 100
h = g * 25
i = c + h 
j = 30 + 20 
k = i / j
Problem: find the c . i . on a sum of rs . 2000 for 6 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 205 , b ) 305 , c ) 3025 , d ) 5540 , e ) 315
Rationale: "c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 205 answer : a"
Answer: a
Python program:
a = const_0_25 / 4
b = 1 + a 
c = const_0_25 / 4
d = 1 + c 
e = b * d
f = 2000 * e
g = f - 2000
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio q of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio q of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Python program:
a = 1 / 3
b = 1 + a 
c = 2 / b
Problem: of 30 applicants for a job , 12 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "d . 7 30 - 3 = 27 27 - 12 - 18 = - 7 then 7 are in the intersection between 4 years experience and degree . answer d"
Answer: d
Python program:
a = 12 + 18 
b = 30 - 3
c = a - b
d = 18 - 12
e = c + d
Problem: how many multiples of 5 are there between 10 and 100 , exclusive ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14
Rationale: "5 * 2 = 10 5 * 20 = 100 total multiples = ( 20 - 2 ) + 1 = 19 exclude 10 and 100 = 19 - 2 = 17 answer is b"
Answer: b
Python program:
a = 100 - 10
b = a / 5
c = b + 1
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 25 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 25 = 10 hours answer d"
Answer: d
Python program:
a = 9 / 15
b = 1 - a
c = b * 25
Problem: find the sum of first 35 natural numbers
Options: a ) 470 , b ) 468 , c ) 630 , d ) 463 , e ) 520
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 35 ( 35 + 1 ) / 2 = 35 ( 36 ) / 2 = 630 answer : option c"
Answer: c
Python program:
a = 35 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 35 / e
g = f / 2
h = 35 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 35 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: a line that passes through ( – 1 , – 4 ) and ( 5 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2
Rationale: slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 5 + 1 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !
Answer: c
Python program:
a = 4 / 5
Problem: total dinning bill for 8 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 30.33
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 8 = 30.33 answer : e"
Answer: e
Python program:
a = 15 * 211
b = a / 100
c = 211 + 0 
d = c / 8
Problem: how much 50 % of 56 is greater than 30 % of 50 ?
Options: a ) 18 , b ) 99 , c ) 13 , d ) 55 , e ) 71
Rationale: "( 50 / 100 ) * 56 – ( 30 / 100 ) * 50 28 - 15 = 13 answer : c"
Answer: c
Python program:
a = 50 * 56
b = a / 100
c = 30 * 50
d = c / 100
e = b - d
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 865 in 4 years . the sum is :
Options: a ) s . 665 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 720
Rationale: "s . i . for 1 year = rs . ( 865 - 815 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 815 - 150 ) = rs . 665 . answer : option a"
Answer: a
Python program:
a = 865 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: a shopkeeper fixes the marked price of an item 32 % above its cost price . the percentage of discount allowed to gain 7 % is
Options: a ) 18.94 % , b ) 18.93 % , c ) 18.92 % , d ) 18.91 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 132 required gain = 7 % , so selling price = rs 107 discount = 132 - 107 = 25 discount % = ( 25 / 132 ) * 100 = 18.93 % option b"
Answer: b
Python program:
a = 7 + 100 
b = 32 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: the diagonals of the two squares are in the ratio of 2 : 5 find the ratio of their area .
Options: a ) 5 : 89 , b ) 7 : 96 , c ) 4 : 25 , d ) 5 : 84 , e ) 8 : 96
Rationale: "let the diagonals of the square be 2 x and 5 x respectively . ratio of their areas = 1 / 2 ( 2 x ) ^ 2 : 1 / 2 ( 5 x ) = 4 x ^ 2 : 25 x ^ 2 = 4 : 25 answer ( c )"
Answer: c
Python program:
a = 2 ** 2
b = a / 2
c = 5 ** 2
d = c / 2
e = b / d
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 6 : 5 , b ) 6 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 9 = 6 : 3 answer : b"
Answer: b
Python program:
a = math.sqrt(36)
b = math.sqrt(9)
c = a / b
Problem: carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 7 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 ) 42 3 / 3 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 42 / 13 = 42 3 / 3 answer is c"
Answer: c
Python program:
a = 1 / 6
b = 1 / 7
c = a + b 
d = const_60 / c
e = 1 / 6
f = 1 / 7
g = e + f 
h = d * g
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 2 days , then the fraction of the work that is left is :
Options: a ) 23 / 20 , b ) 5 , c ) 23 / 30 , d ) 23 / 12 , e ) 2
Rationale: "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 2 day ' s work = ( 7 / 60 * 2 ) = 7 / 30 therefore , remaining work = ( 1 - 7 / 30 ) = 23 / 30 . ans : c"
Answer: c
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 2
e = 1 - d
Problem: find the common factors of 15 and 18 .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 70 , e ) 90
Rationale: first of all we need to find the prime factors of 15 and 18 15 = 5 x 3 18 = 3 x 3 x 2 lcm is the product of highest exponent of all the factors . lcm ( 15,18 ) = 5 x 3 ^ 2 x 2 = 90 answer : 90
Answer: e
Python program:
a = math.lcm(15, 18)
Problem: half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 42 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 3 , b ) 12 , c ) 9 , d ) 8 , e ) 7
Rationale: there are total 42 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 21 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 42 = 7 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 21 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 42 = 21 + 7 - b + ( 21 - b - 1 ) b = 3 answer ( a )
Answer: a
Python program:
a = 42 / 2
b = a - 1
c = 42 / 2
d = 42 / 6
e = c + d 
f = 42 - e
g = b - f
h = g / 2
Problem: find the length of the wire required to go 13 times round a square field containing 24336 m 2 .
Options: a ) 15840 , b ) 3388 , c ) 2667 , d ) 8112 , e ) 66711
Rationale: "a 2 = 24336 = > a = 156 4 a = 624 624 * 13 = 8112 answer : d"
Answer: d
Python program:
a = square_perimeter * (
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 4 | + 3 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: "x ^ 2 - 8 x + 18 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 14 = 0 x = 11 , 7,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 7 + 2 = 20 ans ( c )"
Answer: c
Python program:
a = 3 * 4
Problem: rs . 1430 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 540 , e ) s . 660
Rationale: "a + b + c = 1430 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1430 = rs . 660 answer : e"
Answer: e
Python program:
a = 4 + 2 
b = a + 3 
c = 1430 / b
d = 4 * c
Problem: last year a worker saved 5 % of her annual salary . this year , she made 20 % more money than last year and she saved 6 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 136 % , b ) 140 % , c ) 144 % , d ) 148 % , e ) 152 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.05 x . this year , she saved 0.06 ( 1.2 x ) = 0.072 x 0.072 x / 0.05 x = 144 % the answer is c ."
Answer: c
Python program:
a = 20 + 100 
b = 6 / 100
c = a * b
d = 5 / c
e = 100 * d
Problem: two trains 125 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.15 , e ) 7.2
Rationale: "t = ( 125 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.2 answer : e"
Answer: e
Python program:
a = 125 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: a circular path of 20 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 49 , b ) rs . 40 , c ) rs . 44 , d ) rs . 42 , e ) rs . 66
Rationale: "explanation : π ( 22 ^ 2 - 20 ^ 2 ) = 22 / 7 * ( 484 - 400 ) = 264 264 * 1 / 4 = rs . 66 answer : option e"
Answer: e
Python program:
a = 20 + 2 
b = circle_area - (
c = 25 * b
Problem: stacy has a 81 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 27 , c ) 10 , d ) 8.5 , e ) 6
Rationale: "81 / 3 = 27 answer : b"
Answer: b
Python program:
a = 81 / 3
Problem: the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 23 × b ∴ l = 23 m and l – b = 10 ∴ b = 23 – 10 = 13 m answer a"
Answer: a
Python program:
a = 23 - 10
Problem: in a group of ducks and cows , the total number of legs are 12 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 4 , e ) 12
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 12 = > 2 x = 12 = > x = 6 a"
Answer: a
Python program:
a = 12 / 2