euclaise/mathqa_programs huggingface dataset:
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 2000 more than d , what is b ' s share ?
Options: a ) a ) 4000 , b ) b ) 2900 , c ) c ) 2000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 2000 = > x = 2000 . b ' s share = rs . 2 x = 2 * 2000 = rs . 4000 . answer : a"
Answer: a
Python program:
a = 4 - 3
b = a * 2000
c = b * 3
Problem: a and b together have rs . 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?
Options: a ) 484 , b ) 460 , c ) 550 , d ) 664 , e ) none of them
Rationale: 4 / 15 a = 2 / 5 b a = ( 2 / 5 x 15 / 4 ) b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 . therefore , b ' s share = rs . ( 1210 x 2 / 5 ) = rs . 484 . answer is a .
Answer: a
Python program:
a = 3 + 2 
b = 2 / a
c = b * 1210
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 10 weavers in 10 days ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "1 weaver can weave 1 mat in 4 days . 10 weavers can weave 10 mats in 4 days . 10 weavers can weave 25 mats in 10 days . the answer is d ."
Answer: d
Python program:
a = 4 * 4
b = 4 / a
c = 10 * b
d = 10 * c
Problem: if a trader sold two cars each at rs . 404415 and gains 15 % on the first and loses 15 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 2.02 % , c ) 1.04 % , d ) 2.25 % , e ) 3.40 %
Rationale: "explanation : sp of each car is rs . 404415 , he gains 15 % on first car and losses 15 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 15 ) ( 15 ) / 100 % = 2.25 % answer is d"
Answer: d
Python program:
a = 15 * 15
b = a / 100
Problem: robert ate 10 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 10 - 5 = 5 . answer is d
Answer: d
Python program:
a = 10 - 5
Problem: if a + b = − 9 , and a = 30 / b , what is the value of a ^ 2 + b ^ 2 ?
Options: a ) 31 , b ) 21 , c ) 41 , d ) 61 , e ) 51
Rationale: "a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 9 and a * b = 30 ( a + b ) ( a + b ) = ( - 9 ) ( - 9 ) = a ^ 2 + b ^ 2 + 2 * ( 30 ) a ^ 2 + b ^ 2 = 81 - 60 = 21 answer : b"
Answer: b
Python program:
a = 9 ** 2
b = 2 * 30
c = a - b
Problem: a basket contains 6 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "the total number of ways to choose 2 apples is 6 c 2 = 15 the number of ways that include the spoiled apple is 5 c 1 = 5 p ( the spoiled apple is included ) = 5 / 15 = 1 / 3 the answer is a ."
Answer: a
Python program:
a = 6 - 1
b = math.comb(a, 1)
c = math.comb(6, 2)
d = b / c
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 60 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 102
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 60 = > 2 * ( 2 ) ^ 2 + y = 60 = > 8 + y = 60 = > y = 52 f ( 5 ) = 2 * ( 5 ) ^ 2 + 52 = 102 answer e"
Answer: e
Python program:
a = 2 ** 2
b = a * 2
c = 60 - b
d = 5 ** 2
e = 2 * d
f = c + e
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 884 in 4 years . the sum is :
Options: a ) s . 608 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 884 - 815 ) = rs . 69 . s . i . for 3 years = rs . ( 69 x 3 ) = rs . 207 . principal = rs . ( 815 - 207 ) = rs . 608 . answer : option a"
Answer: a
Python program:
a = 884 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 2 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 2 n = > 14 q + 4 = > remainder = > 4 for some integer q alternatively = > n = 2 > 2 n = > 4 = > 4 divided by 7 will leave a remainder 4 hence d"
Answer: d
Python program:
a = 2 * 2
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6900 ?
Options: a ) 4966 , b ) 6477 , c ) 7391 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6900 x 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 answer : c"
Answer: c
Python program:
a = 6835 + 9927 
b = a + 6855 
c = b + 7230 
d = c + 6562 
e = d / 5
f = e - 6900
g = f * 5
Problem: if 60 percent of 600 is 50 percent of x , then x = ?
Options: a ) 600 , b ) 720 , c ) 820 , d ) 800 , e ) 920
Rationale: "0.6 * 600 = 0.5 * x x = 6 / 5 * 600 = 720"
Answer: b
Python program:
a = 60 * 600
b = a / 50
Problem: a $ 89.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 33 %
Rationale: "listed selling price of chair = 89.95 $ discounted selling price of chair = 59.95 $ discount = 89.95 - 59.95 = 30 $ % decrease in price of chair = ( 30 / 89.95 ) * 100 % = 33 % approx answer e"
Answer: e
Python program:
a = 89 - 95
b = a / 89
c = b * 100
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 390 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 3.9 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 390 â † ’ t = 3.9 answer d
Answer: d
Python program:
a = 3 * 1000
b = a / 100
c = 1400 * 5
d = c / 100
e = b + d 
f = 390 / e
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 12.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 4,100 , d ) $ 3,250 , e ) $ 4,500
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 12 = $ 6000 profit : 6000 - 1900 = $ 4100 option c is correct"
Answer: c
Python program:
a = 500 * 12
b = 5 * 0
c = a - b
d = 500 - 100
e = d * 3
f = c - e
g = f / 1000
h = math.floor(g)
Problem: a car averages 50 mph for the first 4 hours of a trip and averages 80 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: let the time for which car averages 80 mph = t 65 * ( t + 4 ) = 50 * 4 + 80 t = > 15 t = 60 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a
Answer: a
Python program:
a = 65 * 4
b = 50 * 4
c = a - b
d = 80 - 65
e = c / d
f = e + 4
Problem: a sum of rs . 1000 at simple interest amounts to rs . 1192 in 4 years . the s . i . for 1 year is :
Options: a ) rs . 45 , b ) rs . 70 , c ) rs . 39 , d ) rs . 72 , e ) rs . 48
Rationale: s . i . for 4 years = rs . ( 1192 - 1000 ) = rs . 192 . s . i . for 1 year = rs . 192 / 4 = rs . 48 . answer : option e
Answer: e
Python program:
a = 1192 / 10
b = a - 100
c = b / 4
d = c * 10
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams . find the profit percent .
Options: a ) 12.11 , b ) 11.11 , c ) 13.11 , d ) 14.11 , e ) 15.11
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 900 100 + g / 100 + 0 = 1000 / 900 100 + g = 10 / 9 * 100 g = 11.11 answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 4 + 1 
c = a + b 
d = c * 100
e = d - 900
f = e / 900
g = f * 100
Problem: if 0.5 % of a = 75 paise , then the value of a is ?
Options: a ) rs . 150 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 75 / 100 ∴ a = rs . ( 75 / 0.5 ) = rs . 150 correct option : a"
Answer: a
Python program:
a = 75 / 0
Problem: if | 4 x + 6 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 46 or 4 x + 6 = - 46 = > x = 10 or x = - 12 sum of both the values will be - 12 + 10 = - 2 answer is b"
Answer: b
Python program:
a = 46 - 6
b = a / 4
Problem: ( √ 27 + √ 192 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 11 / ( 3 * √ 2 ) , e ) √ 2
Rationale: "( √ 27 + √ 192 ) / √ 54 = ( 3 √ 3 + 8 √ 3 ) / 3 √ 3 * 2 = 11 √ 3 / 3 √ 3 * 2 = 11 / ( 3 * √ 2 ) = 11 / ( 3 * √ 2 ) . hence , the correct answer is d ."
Answer: d
Python program:
a = math.sqrt(27)
b = math.sqrt(192)
c = a + b 
d = math.sqrt(54)
e = c / d
Problem: 60 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100.5 , b ) 200.5 , c ) 300.5 , d ) 350.5 , e ) 412.5
Rationale: "6 x / 10 - x / 3 = 110 4 x / 15 = 110 x = 412.5 answer : e"
Answer: e
Python program:
a = 60 / 100
b = 1 / 3
c = a - b
d = 110 / c
Problem: a train traveling at 72 kmph crosses a platform in 32 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 280 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 32 = 640 m . so , length of platform = 640 - 360 = 280 m imo , answer a"
Answer: a
Python program:
a = 72 * 1000
b = a / 3600
c = b * 32
d = 72 * 1000
e = d / 3600
f = e * 18
g = c - f
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 5 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1330
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 5 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1330 . answer : e"
Answer: e
Python program:
a = 100 - 5
b = a * 1400
c = b / 100
Problem: the population of a bacteria colony doubles every day . if it was started 5 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 64 , d ) 2048 , e ) 4096
Rationale: "2 ^ 5 ( 2 ) = 2 ^ 6 = 64 the answer is c"
Answer: c
Python program:
a = 5 + 1 
b = 2 ** a
c = b - 1
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 36 seconds . what is the length of the goods train ?
Options: a ) 470 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 36 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 36 ] = 20 = > x + 250 = 720 = > x = 470 . answer : a"
Answer: a
Python program:
a = const_0_2778 * 72
b = 250 / a
c = 36 - b
d = const_0_2778 * 72
e = c * d
Problem: if an integer n is to be selected at random from 1 to 900 , inclusive , what is probability n ( n + 1 ) will be divisible by 9 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 2 / 3
Rationale: for n ( n + 1 ) to be a multiple of 9 , either n or n + 1 has to be a multiple of 9 . thus n must be of the form 9 k or 9 k - 1 . the probability is 2 / 9 . the answer is d .
Answer: d
Python program:
a = 2 / 9
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ?
Options: a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000
Rationale: "p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e"
Answer: e
Python program:
a = 10 * 2
b = 100 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 45 meters deep by working for 6 hours ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 45 x = 90 total workers 90 - 45 = 45 new workers the answer is c ."
Answer: c
Python program:
a = 8 / 6
b = 45 * a
c = 45 / 30
d = b * c
e = d - 45
Problem: if p / q = 4 / 5 , then the value of 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 4 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 4 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 4 / 7 + 6 / 14 = 4 / 7 + 3 / 7 = 7 / 7 = 1 . correct option : c"
Answer: c
Python program:
a = 4 / 7
b = 4 / 5
c = 2 - b
d = 4 / 5
e = 2 + d 
f = c / e
g = a + f
Problem: patrick purchased 70 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 70 pencils is how many times the selling price of 70 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.28 , e ) 1.35
Rationale: "say the cost price of 70 pencils was $ 70 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 70 - 70 p = 20 p - - > p = 7 / 9 . ( cost price ) / ( selling price ) = 1 / ( 7 / 9 ) = 9 / 7 = 1.28 . answer : d ."
Answer: d
Python program:
a = 70 + 20 
b = 70 / a
c = 1/(b)
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 4 men and 5 women will do that task .
Options: a ) 13 / 14 , b ) 13 / 10 , c ) 13 / 18 , d ) 13 / 16 , e ) 13 / 11
Rationale: 3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 4 m + 5 w = 13 w answer is 13 / 14 answer : a
Answer: a
Python program:
a = 8 - 2
b = 6 - 3
c = a / b
d = c * 4
e = d + 5 
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2 
k = e / j
Problem: 40 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 1100 , b ) 2100 , c ) 1300 , d ) 1650 , e ) 1400
Rationale: "4 x / 10 - x / 3 = 110 1 x / 15 = 110 x = 1650 answer : d"
Answer: d
Python program:
a = 40 / 100
b = 1 / 3
c = a - b
d = 110 / c
Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 330 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 48 , b ) 66 , c ) 72 , d ) 80 , e ) 84
Rationale: let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 330 / ( 330 + x ) = 5 / 6 x = 66 the answer is b .
Answer: b
Python program:
a = 330 / 5
b = a * 12
c = b / 2
d = c - 330
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 70 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 70 x = 28 the answer is c ."
Answer: c
Python program:
a = 18 / 45
b = 70 * a
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 33 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 33 kg joins the group , total weight of boys = 20 x + 33 so 20 x + 33 = 21 ( x + 1 ) = > x = 12 . answer : a"
Answer: a
Python program:
a = 20 + 1 
b = 33 - a
c = b + 1
Problem: presently the ratio between the ages of dan and james is 6 : 5 . after 4 years dan will be 28 . what is the present age of james ?
Options: a ) 20 , b ) 19 , c ) 21 , d ) 18 , e ) 22
Rationale: let the present ages dan and james be 6 x years and 5 x years respectively 6 x + 4 = 28 6 x = 24 x = 4 kim ' s age = 5 x = 20 years answer is a
Answer: a
Python program:
a = 4 * 2
b = 28 - a
Problem: the sum of two numbers is 62 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 25 - 37
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 62 : word problem = 62 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 62 â ˆ ’ 12 = 50 . x = 50 / 2 = 25 . this is the first number . therefore the other number is x + 12 = 25 + 12 = 37 . the sum of 25 + 37 is 62 . e"
Answer: e
Python program:
a = 62 - 12
b = a / 2
Problem: a tank is filled by 3 pipes a , b , c in 5 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 5 7 / x = 1 / 5 x = 35 hours answer is b"
Answer: b
Python program:
a = 2 * 2
b = a + 2 
c = b + 1 
d = c * 5
Problem: if 12 men and 16 boys can do a piece of work in 5 days ; 13 men and 24 boys can do it in 4 days , then the ratio of the daily work done by a man to that of a boy is ?
Options: a ) 2 : 1 , b ) 2 : 8 , c ) 2 : 9 , d ) 2 : 5 , e ) 2 : 2
Rationale: "let 1 man ' s 1 day work = x and 1 boy ' s 1 day work = y . then , 12 x + 16 y = 1 / 5 and 13 x + 24 y = 1 / 4 solving these two equations , we get : x = 1 / 100 and y = 1 / 200 required ratio = x : y = 1 / 100 : 1 / 200 = 2 : 1 . answer : a"
Answer: a
Python program:
a = 4 * 24
b = 5 * 16
c = a - b
d = 5 * 12
e = 4 * 13
f = d - e
g = c / f
Problem: a certain company ’ s profit in 1996 was 20 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 44 % , e ) 38 %
Rationale: "profit in 1995 - 100 profit in 1996 - 120 % increae profit in 1997 in comparison to 1995 = 20 + 120 * 20 % = 44 correct option : d"
Answer: d
Python program:
a = 20 / 100
b = a + 1 
c = 20 / 100
d = 1 + c 
e = b * d
f = e - 1
g = f * 100
Problem: a cycle is bought for rs . 670 and sold for rs . 880 , find the gain percent ?
Options: a ) 31 % , b ) 35 % , c ) 54 % , d ) 38 % , e ) 80 %
Rationale: "explanation : 670 - - - - 210 100 - - - - ? = > 31 % answer : a"
Answer: a
Python program:
a = 880 - 670
b = a / 670
c = b * 100
Problem: a certain no . when divided by 20 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 20 + 25 = 45 / 15 = 3 ( remainder ) a"
Answer: a
Python program:
a = 20 - 25
b = a - 4
c = b - 2
Problem: the s . i . on a certain sum of money for 6 years at 14 % per annum is half the c . i . on rs . 7000 for 2 years at 7 % per annum . the sum placed on s . i . is ?
Options: a ) 603.75 , b ) 555.75 , c ) 569.55 , d ) 256.25 , e ) 563.23
Rationale: c . i . = [ 7000 * ( 1 + 7 / 100 ) 2 - 7000 ] = ( 7000 * 11 / 10 * 11 / 10 - 7000 ) = rs . 1014.3 . sum = ( 507.15 * 100 ) / ( 6 * 14 ) = rs . 603.75 answer : a
Answer: a
Python program:
a = 7 / 100
b = 1 + a 
c = b ** 2
d = 7000 * c
e = d - 7000
f = e / 2
g = 14 / 100
h = 6 * g
i = f / h
Problem: selling an kite for rs . 30 , a shop keeper gains 20 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 20 %
Rationale: explanation : marked price = rs . 30 c . p . = 100 / 120 * 30 = rs . 25 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.2 / 25 * 100 = 8 % . answer : a
Answer: a
Python program:
a = 30 / 100
b = 100 - 10
c = a * b
d = 30 * 100
e = 20 + 100 
f = d / e
g = c - f
h = 30 * 100
i = 20 + 100 
j = h / i
k = g / j
l = k * 100
Problem: a fruit seller sells mangoes at the rate of rs . 10 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.35 , c ) rs 10.35 , d ) rs 12.35 , e ) none of these
Rationale: "explanation : 85 : 10 = 105 : x x = ( 10 × 105 / 85 ) = rs 12.35 option d"
Answer: d
Python program:
a = 100 + 5 
b = 10 * a
c = 100 - 15
d = b / c
Problem: a certain galaxy is known to comprise approximately 3 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 6,000 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 3 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 3 * 10 ^ 11 / 50 * 10 ^ 6 = 30 * 10 ^ 3 / 5 = 6000 therefore answer is b"
Answer: b
Python program:
a = 3 * 10
b = a / 50
c = 10 ** 4
d = b * c
e = d / 1000
f = e * 3
Problem: a hostel had provisions for 250 men for 32 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 32 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 32 250 × 32 = 200 x 5 × 32 = 4 x x = 5 × 8 = 40 answer b"
Answer: b
Python program:
a = 250 * 32
b = 250 - 50
c = a / b
Problem: how many different values of positive integer x , for which | x + 5 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer e i opted to put the random value option . i used 0 , 5 , - 5 and the the extreme of 40 and - 40 . . i was able to solve it in 1 : 09 e"
Answer: e
Python program:
a = 5 + 5
Problem: if a speaks the truth 80 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: explanation : probability that a speaks truth is 80 / 100 = 0.8 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.8 × 0.6 = 0.48 answer : b
Answer: b
Python program:
a = 4 * 5
b = a * 5
c = 80 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
Problem: tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 ] p ( e ) = n ( e ) / n ( s ) = 9 / 27 = 1 / 3 the answer is a ."
Answer: a
Python program:
a = 27 / 3
b = a / 27
Problem: a man can row downstream at the rate of 12 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 6 ) = 9 km / hr rate of current = 1 / 2 ( 12 - 6 ) = 3 km / hr answer : option c"
Answer: c
Python program:
a = 12 - 6
b = a / 2