euclaise/mathqa_programs huggingface dataset:
Problem: if 64 ( 2 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) - 6 , e ) 5
Rationale: "2 ^ x = 1 / 64 2 ^ x = 1 / 2 ^ 6 2 ^ x = 2 ^ - 6 x = - 6 d"
Answer: d
Python program:
a = 1 / 64
b = math.log(a)
c = math.log(2)
d = b / c
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c"
Answer: c
Python program:
a = 3 + 4 
b = 18 * 0
c = 3 + 4 
d = 23 - c
e = 13 * 0
f = b + e
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ?
Options: a ) 80 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , ( x + 100 ) / 36 = 5 = > x = 80 m . answer : a"
Answer: a
Python program:
a = 18 * const_0_2778
b = 20 * a
Problem: if the lcm and hcf of 12 and another number is 60 and 3 respectively . find the other number ?
Options: a ) 17 , b ) 12 , c ) 15 , d ) 13 , e ) 11
Rationale: "hcf x lcm = product of numbers 3 x 60 = 12 x the other number other number = ( 3 x 60 ) / 12 other number = 15 answer : c"
Answer: c
Python program:
a = 60 * 3
b = a / 12
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 280 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.2
Rationale: price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 280 / 45 = $ 6.2 answer : e .
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b * 280
d = 280 - c
e = 1 / 2
f = 5 - e
g = d / f
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 6 ) m = 120 m answer : option b"
Answer: b
Python program:
a = 100 / 0
b = a - 6
c = 100 / 0
Problem: if x / 2 = y / 4 = z / 6 , then find the value of ( x + y + z ) / z
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) none of these
Rationale: explanation : x / 2 = y / 4 = z / 6 = k , then x = 2 k , y = 4 k and z = 6 k . now , ( x + y + z ) / z = ( 2 k + 4 k + 6 k ) / 6 k = 12 k / 6 k = 2 answer : option e
Answer: e
Python program:
a = 2 / 6
b = 1 + a 
c = 2 / 3
d = b + c
Problem: country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Python program:
a = 15 / 100
b = a * 40000
c = 8000 - b
d = 20 / 100
e = c / d
f = e + 40000
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 1 / 49 , b ) 1 / 42 , c ) 1 / 09 , d ) 1 / 77 , e ) 1 / 12
Rationale: "2 / 3 * 6 / 7 * 1 / 3 * 1 / 8 = 1 / 42 answer : b"
Answer: b
Python program:
a = 2 * 7
b = 1/(a)
Problem: if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40
Rationale: "multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 38 = [ 99 / 6 ] - [ 38 / 6 ] = 16 - 6 = 10 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 30 + 20 - 10 = 40 answer option e"
Answer: e
Python program:
a = 99 - 39
b = a / 3
c = math.floor(b)
d = 99 - 39
e = d / 2
f = c + e 
g = 99 - 39
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: the number 500 can be written as the sum of the squares of 2 different positive integers . what is the difference of these 2 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 18 , e ) 13
Rationale: "22 ^ 2 + 4 ^ 2 = 500 - - > 22 - 4 = 18 . d"
Answer: d
Python program:
a = 4 + 2 
b = 2 + 2 
c = a + b 
d = c + 2
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 15 percent , what was the annual interest rate last year ?
Options: a ) 14.04 % , b ) 15.04 % , c ) 13.64 % , d ) 12.04 % , e ) 10.04 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.1 i ( last year ) = 1.1 i ( last year ) 15 = 1.1 x i ( last year ) i ( last year ) = 15 / 1.1 = 150 / 11 = 13.64 % answer : c"
Answer: c
Python program:
a = 15 * 100
b = 15 + 100 
c = a / b
Problem: a sum of money at simple interest amounts to rs . 845 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 728
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 845 - 117 ) = rs . 728 . answer : option e"
Answer: e
Python program:
a = 854 - 845
b = a * 3
c = b / 4
d = 845 - c
Problem: find number which is 70 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 24 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 80 is 24 . answer : c"
Answer: c
Python program:
a = 80 * 70
b = a / 100
Problem: the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10
Rationale: solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 ‹ = › 2 x = 14 ‹ = › x = 7 . therefore middle number = x + 2 = 9 . answer c
Answer: c
Python program:
a = 2 + 4 
b = 20 - a
c = 3 - 1
d = b / c
e = d + 2
Problem: the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e"
Answer: e
Python program:
a = 4 + 4 
b = 4 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 48 
g = f / 4
Problem: a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 700 / 7,500 * 100 = ~ 9.33 % of the remaining solution of 7,500 gallons . answer : c ."
Answer: c
Python program:
a = 100 * 100
b = 7 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: the speed of a boat in still water is 18 kmph . what is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time ?
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "x = the speed of the stream ( 18 + x ) / ( 18 - x ) = 2 / 1 18 + x = 36 - 2 x 3 x = 18 x = 6 km / hour if the speed of the stream is 6 km / hour , then the ' downstream ' speed of the boat is 18 + 6 = 24 km / hour and the ' upstream ' speed of the boat is 18 - 6 = 12 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 24 = 48 km downstream and 2 x 12 = 24 km / hour upstream . answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 18 / a
Problem: a train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train ?
Options: a ) 322 , b ) 324 , c ) 326 , d ) 328 , e ) 330
Rationale: "length = speed * time speed = l / t s = 2000 / 25 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 324 kmph answer : b"
Answer: b
Python program:
a = 2000 / 1000
b = 25 / 3600
c = a / b
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32 % of the original number . what percent of the red candies remain ?
Options: a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 %
Rationale: "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.6 x red + yellow = 0.85 x red = 0.425 x , since red = yellow . the answer is d ."
Answer: d
Python program:
a = 2 + 3 
b = 100 / a
c = b / 2
d = 2 + 3 
e = 100 / d
f = e / 2
g = f / 2
h = c + g 
i = 32 - h
j = i / 2
k = 2 + 3 
l = 100 / k
m = j / l
n = m * 100
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b"
Answer: b
Python program:
a = 58 * 4
b = 61 - 56
c = a + b 
d = c / 20
Problem: n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n
Options: a ) 11
b ) 12
c ) 13
d ) 14
e ) 15
Rationale: each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 ( nc 2 - n ) = 28 on solving the above equation , we get n = 14 answer : d
Answer: d
Python program:
a = 28 / 2
Problem: in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ?
Options: a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68
Rationale: this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a
Answer: a
Python program:
a = 405 / 9
b = a + 9 
c = b - 1
Problem: each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e .
Options: a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27
Rationale: each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b
Answer: b
Python program:
a = 3 * 8
b = a - 8
c = b - 3
Problem: a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 %
Options: a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg
Rationale: exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a
Answer: a
Python program:
a = 25 / 100
b = a * 20
c = 20 / 10
d = b - c
e = 25 / 100
f = 1 - e
g = d / f
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is :
Options: a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) none
Rationale: "explanation : amount = rs . [ 7500 ( 1 + 4 / 100 ) 2 ] = rs . [ 7500 × 26 / 25 × 26 / 25 ] = rs . 8112 . correct option : d"
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: a and b invests rs . 10000 each , a investing for 4 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4000 , find their shares ?
Options: a ) 1000,3500 , b ) 1000,3000 , c ) 1000,2000 , d ) 1000,5000 , e ) 1000,2500
Rationale: the ratio of their profits a : b = 4 : 12 = 1 : 3 share of a in the total profit = 1 / 4 * 4000 = rs . 1000 share of b in the total profit = 3 / 4 * 4000 = rs . 3000 answer : b
Answer: b
Python program:
a = 10000 * 1
b = a / 3
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60
Rationale: "mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b"
Answer: b
Python program:
a = 18 + 2 
b = 18 - 2
c = b / 2
d = c + 1 
e = a * d
f = e / 2
g = 10 - 2
h = g / 2
i = h + 1 
j = 2 + 10 
k = i * j
l = k / 2
m = f / l
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720
Rationale: there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c .
Answer: c
Python program:
a = 2 ** 5
b = a - 2
c = 4 * 4
d = b * c
Problem: the difference between simple and compound interest on rs . 1600 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8 , b ) 3 , c ) 9 , d ) 4 , e ) 2
Rationale: "s . i . = ( 1600 * 10 * 1 ) / 100 = rs . 160 c . i . = [ 1600 * ( 1 + 5 / 100 ) 2 - 1600 ] = rs . 164 difference = ( 164 - 160 ) = rs . 4 . answer : d"
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = 10 / 100
f = e + 1 
g = d - f
h = g * 1600
Problem: a person travels equal distances with speeds of 4 km / hr , 5 km / hr and 6 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 2 km , b ) 4 km , c ) 7 km , d ) 9 km , e ) 5 km
Rationale: "let the total distance be 3 x km . then , x / 4 + x / 5 + x / 6 = 47 / 60 37 x / 60 = 47 / 60 = > x = 1.27 total distance = 3 * 1.27 = 3.81 km . answer : b"
Answer: b
Python program:
a = 47 / const_60
b = 1 / 4
c = 1 / 5
d = b + c 
e = 1 / 6
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: one hour after yolanda started walking from x to y , a distance of 10 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 4
Rationale: "when b started walking y already has covered 3 miles out of 10 , hence the distance at that time between them was 10 - 3 = 7 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 7 / 7 = 1 hours . in 6 hours b walked 1 * 4 = 4 miles . answer : e ."
Answer: e
Python program:
a = 10 - 3
b = 3 + 4 
c = a / b
d = c * 4
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 7 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 7 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 7 × 2 / 100 = 700 his overall gain in 2 years = rs . 700 - rs . 400 = rs . 300 his overall gain in 1 year = 300 / 2 = rs . 150 answer : option b"
Answer: b
Python program:
a = 5000 * 7
b = a * 2
c = b / 100
d = 5000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: one fourth of one third of two fifth of a number is 14 . what will be 40 % of that number
Options: a ) 168 , b ) 150 , c ) 180 , d ) 200 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 14 then x = 14 * 30 = 420 40 % of 420 = 168 answer : option a"
Answer: a
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 14 / f
h = g * 40
i = h / 100
Problem: a vantakes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 kmph , b ) 61 kmph , c ) 62 kmph , d ) 64 kmph , e ) 66 kmph
Rationale: time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph a )
Answer: a
Python program:
a = 3 / 2
b = a * 6
c = 540 / b
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.30 until we get a multiple of $ 0.70 . $ 7.30 , $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 3 apples . the answer is b ."
Answer: b
Python program:
a = 0 * 80
b = 7 - 30
c = b / 0
d = c + 2
Problem: a can do a piece of work in 4 days . b can do it in 9 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 36 / 5 days , c ) 67 days , d ) 17 / 7 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 9 = 5 / 36 = > 36 / 5 days answer : b"
Answer: b
Python program:
a = 4 * 9
b = 4 * 9
c = 4 * 9
d = c / 4
e = 4 * 9
f = e / 9
g = d + f 
h = g * 2
i = b - h
j = i / 2
k = a / j
Problem: a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460
Rationale: easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c
Answer: c
Python program:
a = 255 * 2
b = a - 112
Problem: if 30 % of a number is 12.6 , find the number ?
Options: a ) 42 , b ) 40 , c ) 26 , d ) 36 , e ) 66
Rationale: "a 40"
Answer: a
Python program:
a = 12 / 6
b = 30 / 100
c = a / b
Problem: 5 + 3
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: a
Answer: a
Python program:
a = 5 / 3
b = a * 100
Problem: find the number , difference between number and its 3 / 5 is 60 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a"
Answer: a
Python program:
a = 60 / 2
b = a * 5
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 16 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 16 days whole work will be done by y in 16 * 5 / 4 = 20 days answer is e"
Answer: e
Python program:
a = 8 / 40
b = 1 - a
c = 1/(b)
d = 16 * c
Problem: a positive number x is multiplied by 3 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 4 / 3 because x is positive , x = 4 / 3 . the answer is c ."
Answer: c
Python program:
a = 3 / 3
Problem: 10 men do a work in 10 days . how many men are needed to finish the work in 4 days ?
Options: a ) 25 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 4 days = 10 * 10 / 4 = 25 answer is a"
Answer: a
Python program:
a = 10 * 10
b = a / 4
Problem: a trader sells 80 meters of cloth for rs . 6900 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 90 , d ) 78 , e ) 66
Rationale: "sp of 1 m of cloth = 6900 / 80 = rs . 86 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 86 - rs . 20 = rs . 66 . answer : e"
Answer: e
Python program:
a = 6900 / 80
b = a - 20