euclaise/mathqa_programs huggingface dataset:
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 40 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 88 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 40 / 5 = 8 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 8 = 88 secs . answer : b"
Answer: b
Python program:
a = 6 - 1
b = 40 / a
c = 12 - 1
d = b * c
Problem: the sum of two numbers is 12 and the product of the numbers is 35 . find sum of the squares of that numbers .
Options: a ) 84 , b ) 87 , c ) 96 , d ) 79 , e ) 74
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 12 ab = 35 so , 12 ^ 2 = a ^ 2 + b ^ 2 + 2 * 35 144 = a ^ 2 + b ^ 2 + 70 a ^ 2 + b ^ 2 = 74 ans e
Answer: e
Python program:
a = 12 ** 2
b = 35 - a
c = b / 2
Problem: the balance of a trader weighs 20 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 4 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 80 gms because it weighs 20 % less . say , the cost price is $ 80 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 80 + ( 30 / 100 ) * 80 = $ 104 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 104 , the mark up is simply 4 % . ans : a
Answer: a
Python program:
a = 4 * 20
b = 30 / 100
c = a * b
d = 4 * 20
e = c + d 
f = e - 100
Problem: it takes 2 workers a total of 12 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: 2 workers build 1 / 12 of a machine in one hour . 1 worker builds 1 / 24 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 24 ) * 3 = 9 / 24 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 24 . the total is 13 / 24 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 24 . the total is 18 / 24 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 24 . the total is 24 / 24 . the machine is complete at 5 : 00 . the answer is c .
Answer: c
Python program:
a = 2 * 12
b = a / 12
c = b - const_0_33
Problem: find the number , difference between number and its 3 / 5 is 50 .
Options: a ) 120 , b ) 123 , c ) 124 , d ) 125 , e ) 359
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 50 , = > ( 2 / 5 ) x = 50 = > 2 x = 50 * 5 , = > x = 125 option d"
Answer: d
Python program:
a = 50 / 2
b = a * 5
Problem: in a coconut grove , ( x + 3 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 3 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above
Rationale: "( x + 3 ) × 60 + x × 120 + ( x − 3 ) × 180 / ( x + 3 ) + x + ( x − 3 ) = 100 ⇒ 360 x − 360 / 3 x = 100 ⇒ 60 x = 360 ⇒ x = 6 answer d"
Answer: d
Python program:
a = 180 * 3
b = 60 * 3
c = a - b
d = 60 + 120 
e = d + 180 
f = 100 * 3
g = e - f
h = c / g
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much w does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) w = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: a 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 210 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 290 ) / 9 = 500 / 9 x + 290 = 500 x = 210 . b"
Answer: b
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 290
Problem: find the average of all prime numbers between 4 and 15 .
Options: a ) 30 , b ) 4 , c ) 9 , d ) 8 , e ) none
Rationale: sol . there are four prime numbers between 4 and 15 . they are 5 , 7 , 11 , 13 â ˆ ´ required average = [ 5 + 7 + 11 + 13 / 4 ] = 36 / 4 = 9 answer c
Answer: c
Python program:
a = 4 + 1 
b = 4 + 1 
c = b + 2 
d = a + c 
e = 15 - 4
f = 15 - 2
g = e + f 
h = d + g 
i = h / 4
Problem: 100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 21 , b ) 24 , c ) 28 , d ) 30 , e ) 32
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 40 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 40 + { editors } - x + 2 x - - > x = 60 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 60 - 39 = 21 . answer : a ."
Answer: a
Python program:
a = 38 + 1 
b = a + 40 
c = 100 - b
Problem: a milkman purchases the milk at rs . x per litre and sells it at rs . 2 x per litre still he mixes 2 litres water with every 6 litres of pure milk . what is the profit percentage ?
Options: a ) 166.69 % , b ) 166.66 % , c ) 166.76 % , d ) 136.66 % , e ) 566.66 %
Rationale: let the cost price of 1 litre pure milk be re . 1 , then \ inline \ begin { bmatrix } 6 & litres ( milk ) & \ rightarrow & cp = rs . 6 \ \ 2 & litres ( water ) & \ rightarrow & cp = rs . 0 \ end { bmatrix } \ rightarrow cp = rs . 6 only and 8 litre mixture \ rightarrow sp \ rightarrow 8 x 2 = rs . 16 profit % = % answer : b
Answer: b
Python program:
a = 6 + 2 
b = a * 2
c = b / 6
d = c - 1
e = d * 100
Problem: a and b can do a work in 12 days , b and c in 15 days , c and a in 20 days . if a , b and c work together , they will complete the work in :
Options: a ) 5 days , b ) 7 5 / 6 days , c ) 10 days , d ) 15 2 / 3 days , e ) none of these
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 12 , ( b + c ) ' s 1 day ' s work = 1 / 15 ; ( a + c ) ' s 1 day ' s work = 1 / 20 adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ( 1 / 12 + 1 / 15 + 1 / 20 ) = 12 / 60 = 1 / 5 ( a + b + c ) ' s 1 day ' s work = 1 / 10 so , a , b and c together can complete the work in 10 days . correct option : c"
Answer: c
Python program:
a = 1/(12)
b = 1/(15)
c = a + b 
d = 1/(20)
e = c + d 
f = e / 2
g = 1 / f
Problem: a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 266666.7 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: 3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 10 % total = 45 + 30 + 10 = 85 % remaining = 100 - 85 = 15 % 15 % = 40000 100 % = 40000 * 100 / 15 = $ 266666.7 answer is a
Answer: a
Python program:
a = 15 * 3
b = a + 30 
c = b + 10 
d = 100 - c
e = 40000 / d
f = e * 100
Problem: how many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14 ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "250 / 15 = 16 ( plus remainder ) so there are 16 multiples of 15 250 / 14 = 17 ( plus remainder ) so there are 17 multiples of 14 we need to subtract 1 because 15 * 14 is a multiple of both so it was counted twice . the total is 16 + 17 - 1 = 32 the answer is c ."
Answer: c
Python program:
a = 4 + 15 
b = a - 1
c = math.factorial(b)
d = math.factorial(15)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 240 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 48 sec , e ) none of these
Rationale: speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 240 = 600 meter time taken to cross the platform = 600 / ( 25 / 2 ) = 600 ã — 2 / 25 = 48 seconds answer : d
Answer: d
Python program:
a = 240 / 1000
b = 360 / 1000
c = a + b 
d = c / 45
e = d * 3600
Problem: a train 300 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 48 , c ) 29 , d ) 27 , e ) 21
Rationale: "s = ( 300 + 300 ) / 45 = 600 / 45 * 18 / 5 = 48 answer : b"
Answer: b
Python program:
a = 300 + 300 
b = a / 1000
c = 45 / 3600
d = b / c
Problem: how long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length ?
Options: a ) 28 , b ) 41.25 , c ) 55 , d ) 18 , e ) 12
Rationale: "t = ( 660 + 165 ) / 72 * 18 / 5 t = 41.25 answer : b"
Answer: b
Python program:
a = 165 + 660 
b = 72 * const_0_2778
c = a / b
Problem: how many integers from 101 to 700 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 6 = 6 7 is not possible here because it would result in a number greater than 7 ( i . e 707 , 717 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 6 * 10 = 60 answer is b ."
Answer: b
Python program:
a = 700 / 10
Problem: what sum of money put at c . i amounts in 2 years to rs . 8800 and in 3 years to rs . 9261 ?
Options: a ) 7945 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8800 - - - - 461 100 - - - - ? = > 5.238 % x * 105.238 / 100 * 105.238 / 100 = 8800 x * 1.1075 = 8800 x = 8800 / 1.1075 = > 7945.70 answer : a"
Answer: a
Python program:
a = 9261 / 8800
b = a - 1
c = b + 1 
d = c ** 2
e = 8800 / d
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 63 = x ?
Options: a ) 1 , b ) 5 , c ) 3 , d ) 6 , e ) 7
Rationale: c ) 3
Answer: c
Python program:
a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 63 
g = reminder + ( 
h = math.floor(g, 1)
Problem: if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` gone ' ' would be
Options: a ) 3569 , b ) 1552 , c ) 4573 , d ) 4735 , e ) 5235
Rationale: g - 4 o - 7 n - 3 e - 5 so for mango the code is 4735 answer : d
Answer: d
Python program:
a = 1000 / 2
b = 12345 / 3
c = a + b
Problem: if henry were to add 4 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 32 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 4 galls 1 / 8 * x = 4 gallons x = 32 gallons answer a"
Answer: a
Python program:
a = 7 / 8
b = 3 / 4
c = a - b
d = 1 / c
e = 4 * d
Problem: a train 120 m long crosses a platform with a speed of 60 kmph in 15 sec ; find the length of the platform ?
Options: a ) 110 , b ) 130 , c ) 120 , d ) 125 , e ) 135
Rationale: d = 120 + x t = 15 s = 120 + x / 15 * 18 / 5 = 60 kmph . = > ( 120 + x ) * 18 = 4500 = > 120 + x = 250 = > x = 130 m answer : b
Answer: b
Python program:
a = 60 * const_0_2778
b = 15 * a
c = b - 120
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 5 % p . a . in 5 years . what is the sum ?
Options: a ) 12021 , b ) 14520 , c ) 16065 , d ) 18925 , e ) 12887
Rationale: "principal = ( 100 * 4016.25 ) / ( 5 * 5 ) = rs . 16065 . answer : c"
Answer: c
Python program:
a = 4016 * 25
b = a / 5
c = b / 5
Problem: a man rows his boat 84 km downstream and 48 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 84 / ( 2 ) = 42 kmph speed upstream = d / t = 48 / ( 2 ) = 24 kmph the speed of the stream = ( 42 - 24 ) / 2 = 9 kmph answer : c"
Answer: c
Python program:
a = 84 / 2
b = 48 / 2
c = a - b
d = c / 2
Problem: what number has a 20 : 1 ratio to the number 10 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120
Rationale: "20 : 1 = x : 10 x = 10 * 20 x = 150 answer : c"
Answer: c
Python program:
a = 10 * 20
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 146 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 146 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Python program:
a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 5 * 5
f = d + e 
g = 146 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 5 * 5
n = l + m 
o = 146 / n
p = i * o
q = h - p
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.3 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.12 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 30 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 30 - cent increment ) and the the difference in sequential prices of the pots is 30 cents , the largest pot probably has a price that is a 30 - cent increment . from the answer choices , i would then test answer d if . . . . the largest pot = $ 2.125 the other 5 pots are . . . . 0.625 0.925 1.225 1.525 1.825 2.125 total = $ 8.25 so this must be the answer . d"
Answer: d
Python program:
a = 6 - 1
b = a * 6
c = b / 2
d = c * 0
e = 8 - 25
f = e / 6
g = 6 - 1
h = g * 0
i = f + h
Problem: what quantity of water should taken out to concentrate 15 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: required answer is = 15 ( 60 - 40 ) / 60 = 5 liters answer is a
Answer: a
Python program:
a = 15 * 40
b = a / 60
c = 15 - b
Problem: what is the remainder when 9 ^ 19 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "9 ^ 0 = 1 9 ^ 1 = 9 9 ^ 2 = 81 9 ^ 3 = 729 9 ^ 4 = . . . 1 9 ^ 5 = . . . . . 9 and so on in a distinct last - digit pattern of 9,1 , 9,1 . . . after ignoring the first last - digit of 1 19 / 2 = 9 ( with a remainder of 1 ) so the last number is a 9 . alternatively , 19 is an odd number and hence the last digit is a 9 when 9 ^ 19 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Python program:
a = 5 / 2
b = 9 * 9
c = a - b
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 5 hours ?
Options: a ) 675 , b ) 750 , c ) 1,125 , d ) 5,900 , e ) 7,500
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 5 hours ) = 1125 cans . the answer is c ."
Answer: c
Python program:
a = 5 * 360
b = 5 * 360
c = 4 + 4 
d = b / c
e = 5 * d
f = a - e
Problem: a trained covered x km at 65 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22 , b ) 99 , c ) 26 , d ) 66 , e ) 887
Rationale: "total time taken = x / 65 + 2 x / 20 hours = 3 x / 26 hours average speed = 3 x / ( 3 x / 26 ) = 26 kmph answer : c"
Answer: c
Python program:
a = 65 * 3
b = 65 / 65
c = 2 * 65
d = c / 20
e = b + d 
f = a / e
Problem: ms . lopez deposits $ 140 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 169.40 , d ) $ 122.00 , e ) $ 140.00
Rationale: using formula - a = p ( 1 + r / n ) ^ nt given p = 140 n = 2 t = 1 r = 0.2 substituting value in formula a = 140 ( 1 + 0.2 / 2 ) ^ 2 a = 169.40 $ = c
Answer: c
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 2
e = 140 * d
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 286 , b ) 278 , c ) 255 , d ) 180 , e ) 287
Rationale: "speed = ( 72 * 5 / 18 ) m / sec = ( 20 ) m / sec length of the train = ( speed x time ) = ( 20 * 9 ) m = 180 m . answer : d"
Answer: d
Python program:
a = 72 * 1000
b = a / 3600
c = b * 9
Problem: the speed at which a man can row a boat in still water is 20 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 9.4 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 20 + 3 = 23 kmph = 23 * 5 / 18 = 115 / 18 m / s hence time taken to cover 60 m = 60 * 18 / 115 = 9.4 seconds . answer : d"
Answer: d
Python program:
a = 20 + 3 
b = a * const_0_2778
c = 60 / b
Problem: a 16 % stock yielding 14 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 114 , d ) s . 120 , e ) s . 140
Rationale: "income of rs 14 on investment of rs 100 income of rs 16 on investment of ? = ( 16 * 100 ) / 14 = 114 answer : c"
Answer: c
Python program:
a = 100 / 14
b = a * 16
Problem: the value of ( ( x – y ) ³ + ( y - z ) ³ + ( z – x ) ³ ) / ( 15 ( x – y ) ( y – z ) ( z – x ) ) is equal to :
Options: a ) 0 , b ) 1 / 12 , c ) 1 , d ) 1 / 5 , e ) 1 / 3
Rationale: since ( x – y ) + ( y – z ) + ( z – x ) = 0 , so ( x – y ) ³ + ( y – z ) ³ + ( z – x ) ³ = 3 ( x – y ) ( y – z ) ( z – x ) . ( 3 ( x – y ) ( y – z ) ( z – x ) ) / ( 15 ( x – y ) ( y – z ) ( z – x ) ) = 1 / 5 . answer : d
Answer: d
Python program:
a = 3 / 15
Problem: a is the product of each integer from 1 to 50 , inclusive and b = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of a ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k → k = 12 / 2 = 6 a
Answer: a
Python program:
a = 10 / 2
b = 50 / a
c = b + 2 
d = c / 2
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 432 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 432 12 r 2 = 432 r 2 = 36 r = 6 . answer : b"
Answer: b
Python program:
a = 432 * 100
b = a / 1200
c = math.sqrt(b)
Problem: if n is the greatest positive integer for which 4 ^ n is a factor of 10 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 10 ! = 3628800 e . 4 ^ 10 = 1048576 ( 3628800 / 1048576 ) - this is not a factor of 10 ! d . 4 ^ 8 = 65536 ( 3628800 / 65536 ) - this is not a factor of 10 ! c . 4 ^ 6 = 4096 ( 3628800 / 4096 ) - this is not a factor of 10 ! b . 4 ^ 4 = 256 ( 3628800 / 256 ) - this is a factor of 10 ! b is answer
Answer: b
Python program:
a = 10 / 2
b = a - 1
Problem: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1400 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 3150 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1400 - - > { not on display } = 2100 . according to ( i ) 2 / 3 * { total } = 2100 - - > { total } = 3150 . answer : b ."
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1400 / b
d = 1 / 3
e = 1 - d
f = c / e
Problem: the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ?
Options: a ) 55 , b ) 56 , c ) 64 , d ) 65 , e ) 66
Rationale: "let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c"
Answer: c
Python program:
a = 66 / 3
b = a * 2
c = 60 / 3
d = b + c
Problem: if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ?
Options: a ) 0.33 , b ) 33 , c ) 0.033 , d ) 0.0033 , e ) 3.3 e - 05
Rationale: 99 * 0.33 = 32.67 approx . 33 answer : b
Answer: b
Python program:
a = 10 * 10
b = 10 * 10
c = b - 1
d = a * c
e = 10 * 10
f = e - 1
g = 33 / f
h = d * g
i = h / 1000
j = i * 10
Problem: sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ?
Options: a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )
Answer: a
Python program:
a = 10 * 3
b = a + 5 
c = 2 + 3 
d = b / c
Problem: two whole numbers whose sum is 72 can not be in the ratio
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 5 : 7 , e ) none
Rationale: "sol . the sum of the ratio terms must divide 72 . so , the ratio can not be 3 : 4 . answer a"
Answer: a
Python program:
a = 72 / 2
b = a - 10
c = b / 2
d = 72 / 2
e = d + 10 
f = c / e
Problem: a group of men decided to do a work in 20 days , but 2 of them became absent . if the rest of the group did the work in 22 days , find the original number of men ?
Options: a ) 15 , b ) 22 , c ) 27 , d ) 29 , e ) 18
Rationale: "original number of men = 2 * 22 / ( 22 - 20 ) = 22 answer is b"
Answer: b
Python program:
a = 2 * 22
b = 22 - 20
c = a / b
Problem: a train 280 m long is running at 70 kmph . in how much time will it pass a platform 210 m long ?
Options: a ) 1.5 seconds , b ) 9.56 seconds , c ) 28.56 seconds , d ) 30.56 seconds , e ) 3.5 seconds
Rationale: distance travelled = 280 + 210 m = 490 m speed = 70 * 5 / 8 = 205 / 4 m time = 490 * 4 / 205 = 9.56 seconds answer : b .
Answer: b
Python program:
a = 280 + 210 
b = const_60 * 0
c = a / b
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 25 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 25 ? - - - 1 = > rs . 0.8 100 - - - 80 ? - - - 0.8 = > rs . 1 answer : b"
Answer: b
Python program:
a = 20 / 100
b = a * 100
c = b / 25
d = 20 / 100
e = d * 100
f = c / e
g = f * 100