euclaise/mathqa_programs huggingface dataset:
Problem: convert 0.35 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 7 / 20 , d ) 19 / 50 , e ) none
Rationale: "answer 0.35 = 35 / 100 = 7 / 20 correct option : c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 0
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: how many multiples of 10 are there between 10 and 1000 , exclusive ?
Options: a ) 98 , b ) 99 , c ) 100 , d ) 101 , e ) 97
Rationale: "98 multiples of 5 between 1 and 36 exclusive . from 10 * 2 upto 10 * 99 , ( 2 , 3,4 , . . . , 99 ) . hence , 98 multiples ! correct option is a"
Answer: a
Python program:
a = 1000 - 10
b = a / 10
c = b + 1
Problem: find the average of all the numbers between 6 and 29 which are divisible by 5 ?
Options: a ) 17 , b ) 20 , c ) 25 , d ) 30 , e ) 15
Rationale: average = ( 10 + 15 + 20 + 25 ) 4 = 70 / 4 = 17 answer is a
Answer: a
Python program:
a = 6 + 4 
b = 29 - 4
c = a + b 
d = c / 2
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 36 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 320 , b ) 360 , c ) 400 , d ) 440 , e ) 480
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 6 miles per hour . the time to catch up is 60 / 6 = 10 hours . in 10 hours , train a travels another 30 * 10 = 300 miles for a total of 360 miles . the answer is b ."
Answer: b
Python program:
a = 30 * 2
b = 36 - 30
c = a / b
d = c * 36
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is ?
Options: a ) 1 hr , b ) 2 hr , c ) 6 hr , d ) 8 hr , e ) 7 hr
Rationale: let the duration of the flight be x hours . then , 600 / x - 600 / ( x + 1 / 2 ) = 200 x ( 2 x + 1 ) = 3 2 x 2 + x - 3 = 0 ( 2 x + 3 ) ( x - 1 ) = 0 x = 1 hr . answer : a
Answer: a
Python program:
a = 200 * 30
b = a / 10
c = 600 / b
Problem: solve the quickfire maths brain teaser √ 9 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
Rationale: "a 30 % √ 9 % = > √ 9 / √ 100 = > 3 / 10 = > 30 / 100 = > 30 %"
Answer: a
Python program:
a = 1 + 9 
b = 100 / a
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 789 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 1711 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 789 ) ( x - 8 ) ^ 2 = t + 789 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1711 + 789 = 2500 = 50 ^ 2 = ( x - 8 ) ^ 2 hence , x = 58 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 58 * 59 / 2 = 1711 hence , answer is a ."
Answer: a
Python program:
a = 4 * 100
b = 789 - a
c = 4 * 100
d = 789 - c
e = d * 2
f = e + 1 
g = b * f
Problem: the average of 20 numbers is calculated as 30 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 40 , b ) 26 , c ) 60 , d ) 97 , e ) 12
Rationale: "20 * 30 + 36 – 26 = 160 / 10 = 60 answer : 60 answer is c"
Answer: c
Python program:
a = 36 - 26
b = a / 20
c = 30 + b
Problem: when n is divided by 12 , the remainder is 2 . what is the remainder when 4 n is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let n = 2 ( leaves a remainder of 2 when divided by 15 ) 4 n = 4 ( 2 ) = 8 , which leaves a remainder of 3 when divided by 5 . answer c"
Answer: c
Python program:
a = 2 - reminder
Problem: s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is
Options: a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405
Rationale: last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c
Answer: c
Python program:
a = 64 - 1
b = a * 4
c = 68 + b
Problem: the “ s - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ s , where s is the s - number of the result of his die roll , and plots 3 ^ s on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
Rationale: if you calculate 3 ^ s for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: b
Python program:
a = 6 + 1 
b = a + 3 
c = b + 3 
d = 6 * 6
e = c / d
Problem: two numbers are respectively 20 % and 50 % more than a third number . what percentage is the first of the second ?
Options: a ) 25 % , b ) 60 % , c ) 80 % , d ) 55 % , e ) 74 %
Rationale: "required answer = ( 100 + x ) / ( 100 + y ) * 100 = 120 * 100 / 150 = 80 % answer is c"
Answer: c
Python program:
a = 20 + 100 
b = 50 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 3 / 4 of its own speed and got to its destination in 10 hours ?
Options: a ) 1.5 hrs , b ) 2.5 hrs , c ) 3.5 hrs , d ) 1.2 hrs , e ) 2.9 hrs
Rationale: "new speed = 3 / 4 of usual speed new time = 3 / 4 of usual time 3 / 4 of usual time = 10 hrs usual time = 10 * 3 / 4 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is b"
Answer: b
Python program:
a = 10 * const_60
b = 3 / 4
c = 10 * b
d = c * const_60
e = a - d
f = reminder / (
g = f + 100
Problem: angelina walked 1200 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 12 , b ) 23 , c ) 34 , d ) 48 , e ) 52
Rationale: "let the speed be x . . . so time taken from home to grocery = 1200 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 1200 / x - 240 / x = 40 . . 960 / x = 40 . . x = 24 m / secs . . so grocery to gym = 2 * 24 = 48 m / s . . . d"
Answer: d
Python program:
a = 480 / 2
b = 1200 - a
c = b / 40
d = c * 2
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 2 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 7 , e ) 6 / 9
Rationale: income = salary ( s ) + tips = s + s * 5 / 2 = s * 7 / 2 tips = s * 7 / 2 fraction of his income came from tips = ( s * 5 / 2 ) / ( s * 7 / 2 ) = 5 / 7 answer : d
Answer: d
Python program:
a = 5 / 2
b = 5 / 2
c = b + 1 
d = a / c
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 7 is divided by 41 ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 16 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . when k = 0 , 1,2 etc x + 7 = 82 k + 5 + 7 = 82 k + 12 or x + 7 = 12,94 , 176 etc . k = 0 , 1,2 when divided by 41 , we will get the remainder 12 . a"
Answer: a
Python program:
a = 5 + 7
Problem: a reduction of 50 % in the price of apples would enable a man to obtain 80 more for rs . 55 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 10
Rationale: c 55 * ( 50 / 100 ) = 28 - - - 64 ? - - - 12 = > rs . 4
Answer: c
Python program:
a = 50 * 55
b = a / 100
c = b / 80
d = c * 12
Problem: what is the next number : 3 , 18 , 258 , __
Options: a ) 2928 , b ) 3638 , c ) 4098 , d ) 4418 , e ) 5378
Rationale: "4 ^ 0 + 2 = 3 4 ^ 2 + 2 = 18 4 ^ 4 + 2 = 258 4 ^ 6 + 2 = 4098 the answer is c ."
Answer: c
Python program:
a = 258 * 10
b = a - 100
c = b - 3
d = c - 3
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 85 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.25
Rationale: "0.85 * { original price } = $ 85 - - > { original price } = $ 100 . { final price } = $ 85 * 1.25 = $ 106.25 . the difference = $ 106.25 - $ 100 = $ 6.25 . answer : e ."
Answer: e
Python program:
a = 100 + 25 
b = a / 100
c = 85 * b
d = 100 - 15
e = d / 100
f = 85 / e
g = c - f
Problem: how many books each of volume 200 meter cube can be packed into a crate of volume 4000 meter cube ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) can not be determined
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n ' t know , so we cant calculate answer : e"
Answer: e
Python program:
a = 4000 * 1
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose q = 60 / 62 = 30 / 31 of the selected films . answer : e .
Answer: e
Python program:
a = 20 / 100
b = a + 6 
c = 6 / b
Problem: a train travels 125 km in 2.5 hours and 270 km in 3 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 72 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 125 + 270 = 395 km thus , total speed = 5.5 hrs or , average speed = 5 = 395 / 5.5 or , 72 kmph . answer : c"
Answer: c
Python program:
a = 125 + 270 
b = 2 + 5 
c = a / b
Problem: if 4 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 5 z / 12 , c ) z / 3 , d ) 3 z / 5 , e ) z / 9
Rationale: "4 x = 6 y = z x = z / 4 and y = z / 6 x + y = z / 4 + z / 6 = 5 z / 12 answer is b"
Answer: b
Python program:
a = 4 * 100
b = a / 2
c = b - 2
d = 4 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 7 ] * [ 8 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 75 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 7 ] * [ 8 ] = ( 7 * 2 + 1 ) ( 8 / 2 + 1 ) = [ 75 ] . ans - c"
Answer: c
Python program:
a = 7 / 2
b = a + 1 
c = 2 * 8
d = c + 1 
e = b * d
Problem: a dealer offers a cash discount of 10 % and still makes a profit of 20 % when he further allows 45 articles to be sold at the cost price of 40 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 40 % , b ) 50 % , c ) 55 % , d ) 80 % , e ) 90 %
Rationale: "given cash discount - 10 % profit - 20 % items sold - 45 price sold at = list price of 40 assume list price = $ 10 total invoice = $ 400 - 10 % cash discount = $ 360 let cost price of 45 items be x so total cost = 45 * x given the shopkeeper had a profit of 20 % 45 * x * 120 / 100 = 360 or x = $ 20 / 3 = $ 6 + ( 2 / 3 ) which means his products were listed at $ 10 which is a 50 % markup over $ 6 + ( 2 / 3 ) answer b"
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 45 - 40
d = c / 45
e = 1 - d
f = b / e
g = 100 - 10
h = g / 100
i = f / h
j = i - 1
k = j * 100
Problem: at the end of year x , automobile installment credit accounted for 20 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 171 , b ) 855 , c ) 870 , d ) 788 , e ) 684
Rationale: "system of equations a = ( 20 / 100 ) c ( 1 / 3 ) a = 57 - - > a = 171 substitution 171 = ( 20100 ) c c = ( 100 / 20 ) 171 - calculate 171 / 20 * 100 the correct answer b . the answer is 855 ."
Answer: b
Python program:
a = 57 * 3
b = 20 / 100
c = a / b
Problem: a man can row upstream at 32 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 27 , e ) 40
Rationale: "us = 32 ds = 48 m = ( 48 + 32 ) / 2 = 40 answer : e"
Answer: e
Python program:
a = 32 + 48 
b = a / 2
Problem: the radius of the two circular fields is in the ratio 3 : 10 the area of the first field is what percent less than the area of the second ?
Options: a ) 71 % , b ) 51 % , c ) 91 % , d ) 81 % , e ) 61 %
Rationale: "r = 3 ï € r 2 = 9 r = 10 ï € r 2 = 100 100 ï € â € “ 9 ï € = 91 100 - - - - ? = > 91 % . answer : c"
Answer: c
Python program:
a = 10 ** 2
b = 3 ** 2
c = a - b
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 24 / 80 oxen = 9 days the answer is b ."
Answer: b
Python program:
a = 24 / 4
b = a * 3
c = 15 + b 
d = 8 / 2
e = d * 3
f = c + e 
g = 24 * f
h = 15 + 30 
i = 24 + 60 
j = i / 4
k = j * 3
l = h + k 
m = 8 / 2
n = m * 3
o = l + n 
p = g / o
Problem: an woman swims downstream 64 km and upstream 24 km taking 8 hours each time ; what is the speed of the current ?
Options: a ) 1.6 , b ) 1.8 , c ) 3.5 , d ) 1.5 , e ) 2.5
Rationale: "64 - - - 8 ds = 8 ? - - - - 1 24 - - - - 8 us = 3 ? - - - - 1 s = ? s = ( 8 - 3 ) / 2 = 2.5 answer : e"
Answer: e
Python program:
a = 64 / 8
b = 24 / 8
c = a - b
d = c / 2
Problem: what is 30 % of 210 ?
Options: a ) 61 , b ) 63 , c ) 65 , d ) 67 , e ) 69
Rationale: "x / 210 = 30 / 100 100 x = 210 x 30 x = ( 210 x 30 ) / 100 x = 6300 / 100 = 63 answer = b = 63"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 30 * n
p = o / 100
Problem: company x provides bottled water to its employees in 1 liter bottles , $ 2 each . at least how many 1 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 10 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 27
Rationale: let the no . of 1 liter bottles be x , so the no . of 10 l bottles will be x / 10 ( to equate the vol . ) since the total cost will be equal , 2 x = 50 + x / 10 so x = 26.31 or 27 . answer is ( e ) .
Answer: e
Python program:
a = 1 / 1
b = 1 - a
c = 50 / b
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.3 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 5 : 6
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e"
Answer: e
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . what is the speed of the car ?
Options: a ) 22 , b ) 28 , c ) 120 , d ) 287 , e ) 278
Rationale: let speed of the car = x kmphthen speed of the train = ( 100 + 50 ) 100 x = 150100 x = 32 x kmphtime taken by the car to travel from a to b = 75 x hourstime taken by the train to travel from a to b = 75 ( 32 x ) + 12.560 hourssince both start from a at the same time and reach point b at the same time 75 x = 75 ( 32 x ) + 12.56025 x = 12.560 x = 25 × 6012.5 = 2 × 60 = 120 answer : c
Answer: c
Python program:
a = 12 * 5
b = a - 1
c = 12 * 5
d = b * c
e = 4 + 1 
f = d / e
Problem: if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 160 , e ) 2848
Rationale: "the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d"
Answer: d
Python program:
a = 32 * 10
b = a / 2
Problem: the remainder when q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 .
Options: a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3
Rationale: q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as ' 3 ' and number of terms as ' 201 ' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c
Answer: c
Python program:
a = 200 + 1 
b = 3 ** a
Problem: p and q invested in a shop . the profits were divided in the ratio of 5 : 2 respectively . if p invested rs . 5600 , the amount invested by q is :
Options: a ) 3500 , b ) 5600 , c ) 2200 , d ) 2400 , e ) none
Rationale: suppose q invested rs . y . then , 5600 / y = 5 / 2 or y = [ 5600 x 2 / 5 ] = 2240 answer e
Answer: e
Python program:
a = 5600 / 5
b = a * 2
Problem: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?
Options: a ) 8.5 gallons , b ) 5 gallons , c ) 7 gallons , d ) 5.5 gallons , e ) 6 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 120 kilometers ? 120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer e"
Answer: e
Python program:
a = 120 / 20
Problem: a cuboidal block 6 cm x 9 cm x 12 cm is cut up into an exact number of equal cubes . the least possible number of equal cubes will be
Options: a ) 6 , b ) 9 , c ) 24 , d ) 30 , e ) 35
Rationale: explanation : volume of block = ( 6 x 9 x 12 ) cm 3 = 648 cm 3 side of largest cube = h . c . f of 6 , 912 = 3 cm volume of the cube = ( 3 x 3 x 3 ) = 27 cm 3 number of cubes = ( 648 / 27 ) = 24 answer : c
Answer: c
Python program:
a = 6 * 9
b = a * 12
c = 6 / 2
d = 6 / 2
e = c * d
f = 6 / 2
g = e * f
h = b / g
Problem: in a class of 25 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e ."
Answer: e
Python program:
a = 25 * 2
b = 12 * 1
c = b + 4 
d = c + 2 
e = 25 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 4 * 2
j = h + i 
k = g + j 
l = a - k
Problem: the sector of a circle has radius of 21 cm and central angle 180 o . find its perimeter ?
Options: a ) 91.5 , b ) 92 , c ) 108 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 108 cm answer : option c"
Answer: c
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: beginning in town a , biker bob rides his bike 30 miles west , 6 miles north , 15 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 27 miles , b ) 25 miles , c ) 24 miles , d ) 28.3 miles , e ) 23 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 30 - 15 = 15 m now this third side or the distance between town a and town b = 24 ^ 2 + 15 ^ 2 = sq root 801 = 28.3 m answer : d"
Answer: d
Python program:
a = 6 + 18 
b = a ** 2
c = 15 ** 2
d = b + c 
e = math.sqrt(d)
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 68 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 28 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 68 - x ounces of q is present in the mixture ( as the total = 68 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 68 - x ) = 15 = > x = 40 = > 68 - 40 = 28 ounces of q is present in the mixture . answer is b ."
Answer: b
Python program:
a = 20 / 100
b = a * 68
c = 15 - b
d = 25 / 100
e = 20 / 100
f = d - e
g = c / f