euclaise/mathqa_programs huggingface dataset:
Problem: a train traveling at 180 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 180 kmph * 12 seconds convert 180 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 180 kmph = 5 / 18 ∗ 180 = 50 m / sec therefore , length of the platform = 50 m / s * 12 sec = 600 meters . choice d"
Answer: d
Python program:
a = 180 * 1000
b = a / 3600
c = b * 30
d = 180 * 1000
e = d / 3600
f = e * 12
g = c - f
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 7 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 84 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: ans : c solution : simple multiplication s students , c classes , 7 books / month = 84 books a year total number of books = 84 cs
Answer: c
Python program:
a = 7 * 12
Problem: a man , a woman and a boy can complete a job in 3,4 and 12 days respectively . how many boys must assist 1 man and 1 woman to complete the job in ¼ of a day ?
Options: a ) 1 day , b ) 4 days , c ) 19 days , d ) 41 days , e ) 52 days
Rationale: ( 1 man + 1 woman ) ' s 1 days work = 1 / 3 + 1 / 4 = 7 / 12 work done by 1 man and 1 women n 1 / 4 day = ( ( 7 / 12 ) * ( 1 / 4 ) ) = 7 / 48 remaining work = 1 - 7 / 48 = 41 / 48 work done by 1 boy in ¼ day = ( ( 1 / 12 ) * ( 1 / 4 ) ) = 1 / 48 therefore , number of boys required = ( ( 41 / 48 ) * 48 ) = 41 days answer d 41 days
Answer: d
Python program:
a = 12 * 4
b = 3 + 4 
c = a - b
Problem: a train covers a distance of 12 km in 12 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 , b ) 168 , c ) 100 , d ) 120 , e ) 122
Rationale: "speed = ( 12 / 12 * 60 ) km / hr = ( 60 * 5 / 18 ) m / sec = 16.6 m / sec . length of the train = 16.6 * 6 = 100 m . answer : c"
Answer: c
Python program:
a = 12 / 12
b = a - 6
c = 12 / b
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 25 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 ) 7.0 , b ) 5.0 , c ) 6.0 , d ) 4.0 , e ) 8.0
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 25 kg joins the group , total weight of boys = 20 x + 25 so 20 x + 25 = 21 ( x + 1 ) = > x = 4 . answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 25 - a
c = b + 1
Problem: a dealer offers a cash discount of 10 % and still makes a profit of 35 % when he further allows 20 articles to be sold at the cost price of 15 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 80 % , b ) 100 % , c ) 120 % , d ) 60 % , e ) 90 %
Rationale: "given cash discount - 10 % profit - 35 % items sold - 20 price sold at = list price of 15 assume list price = $ 20 total invoice = $ 300 - 10 % cash discount = $ 270 let cost price of 20 items be x so total cost = 20 * x given the shopkeeper had a profit of 20 % 20 * x * 135 / 100 = 270 or x = $ 10 which means his products were listed at $ 20 which is a 100 % markup over $ 10 answer b"
Answer: b
Python program:
a = 100 + 35 
b = a / 100
c = 20 - 15
d = c / 20
e = 1 - d
f = b / e
g = 100 - 10
h = g / 100
i = f / h
j = i - 1
k = j * 100
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 20 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 18 %
Rationale: "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.22 - x ) + 2 * 20 x = 9 - - > x = 0.18 = 18 % answer : e ."
Answer: e
Python program:
a = 22 / 100
b = 22 / 100
c = 20 * 2
d = b * c
e = 9 - d
f = 15 * 3
g = 20 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: if ( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) = > 5 ^ 7 * 3 ^ 8 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 7 * 3 ^ 8 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 7 answer a"
Answer: a
Python program:
a = 5 ** 7
b = 9 ** 4
c = a * b
d = c / 3
e = math.log(d)
f = math.log(15)
g = e / f
Problem: henrikh lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work . if it takes him exactly 8 minutes more to walk to work than to ride his bicycle , then x equals
Options: a ) 4 , b ) 7 , c ) 12 , d ) 15 , e ) 20
Rationale: the best way would be . . . per km , he takes 40 secs extra if he walks so he will take 8 mins or 8 * 60 secs in 8 * 60 / 40 = 12 km answer : c
Answer: c
Python program:
a = 8 * const_60
b = 1 * const_60
c = b - 20
d = a / c
Problem: george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of christopher .
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 answer : a
Answer: a
Python program:
a = 8 - 2
b = 60 - a
c = b / 3
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 74000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 74000 / 128000 = 74 / 128 = 37 / 65 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Python program:
a = 30 / 100
b = a * 56000
c = 40 / 100
d = c * 74000
e = b + d 
f = 74000 + 56000 
g = e / f
h = g * 100
Problem: 10 ^ ( 65 ) ã · 10 ^ ( 64 ) = ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) 10000
Rationale: "10 ^ ( 65 ) ã · 10 ^ ( 64 ) = 10 ^ ( 65 - 64 ) = 10 ^ 1 = 10 answer : b"
Answer: b
Python program:
a = 65 - 64
b = 10 ** a
Problem: the average of the marks of 11 students in a class is 36 . if the marks of each student are doubled , find the new average ?
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 75
Rationale: sum of the marks for the 11 students = 11 * 36 = 396 . the marks of each student are doubled , the sum also will be doubled . the new sum = 396 * 2 = 792 . so , the new average = 792 / 11 = 72 . answer : d
Answer: d
Python program:
a = 36 * 2
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 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: in a restaurant , the profit is 140 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 53 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 140 , s . p . = rs . 240 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 240 . profit = rs . ( 240 - 112 ) = rs . 128 . required percentage = ( 128 / 240 * 100 ) % = 53 % appox answer : b"
Answer: b
Python program:
a = 140 / 100
b = 100 * a
c = b + 100 
d = 12 / 100
e = 1 + d 
f = 100 * e
g = c - f
h = 140 / 100
i = 100 * h
j = i + 100 
k = g / j
l = 100 * k
Problem: a hemispherical bowl is made of 0.5 cm thick steel . inner radius of the bowl is 4 cm . the volume of steel used in making the bowl is
Options: a ) 55.83 cm 3
b ) 56.83 cm 3
c ) 113.67 cm 3
d ) 58.83 cm 3
e ) none of these
Rationale: inner r = 4 outer r = 4.5 formula = 2 / 3 * 22 / 7 ( r ^ 2 - r ^ 2 ) ( 2 / 3 ) * ( 22 / 7 ) * ( 4.5 * 4.5 * 4.5 - 4 * 4 * 4 ) = 56.83 answer : b
Answer: b
Python program:
a = 4 + 0 
b = volume_sphere - (
c = b / volume_sphere
Problem: a large box contains 18 small boxes and each small box contains 28 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 504
Rationale: "the only thing you have to do is a simple multiply we have : 18 * 28 = 504 correct answer is : e ) 504"
Answer: e
Python program:
a = 18 * 28
Problem: if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 5 , what is the value of k ?
Options: a ) 65 , b ) 79 , c ) 68 , d ) 87 , e ) 90
Rationale: "we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 5 ^ 2 + 3 * 5 - k = 0 k = 50 + 15 = 65 the answer is a"
Answer: a
Python program:
a = 5 ** 2
b = 2 * a
c = 3 * 5
d = b + c
Problem: from the salary of rahul , 20 % is deducted as house rent , 10 % of the rest he spends on children ’ s education and 10 % of the balance , he spends on clothes . after this expenditure he is left with rs 1377 . his salary is ?
Options: a ) rs 2125 , b ) rs 2040 , c ) rs 2100 , d ) rs 2200 , e ) rs 2,300
Rationale: suppose that his salary = rs 100 house rent = rs 20 , balance = rs 80 expenditure on education = rs ( 10 x 80 ) / 100 = rs 8 balance = rs 72 expenditure on clothes rs ( 10 x 72 ) / 100 = rs 7.2 balance now = rs 64.8 if balance is rs 64.8 , salary = rs 100 if balance is rs 1,377 , salary = rs ( 100 x 1377 ) / 64.8 rs 2,125 answer : a
Answer: a
Python program:
a = 1377 * 100
b = 100 - 20
c = 100 - 20
d = 10 * c
e = d / 100
f = b - e
g = 100 - 20
h = 100 - 20
i = 10 * h
j = i / 100
k = g - j
l = k * 10
m = l / 100
n = f - m
o = a / n
Problem: the closest approximation of q = ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "q = ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c"
Answer: c
Python program:
a = 0 / 4
b = a * 69
Problem: in an office , totally there are 800 employees and 25 % of the total employees are males . 40 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 120 , b ) 160 , c ) 132 , d ) 130 , e ) none of these
Rationale: "number of male employees = 800 * 25 / 100 = 200 required number of male employees who are less than 50 years old = 200 * ( 100 - 40 ) % = 200 * 60 / 100 = 120 . answer : a"
Answer: a
Python program:
a = 800 * 25
b = a / 100
c = 100 - 40
d = c / 100
e = b * d
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 13 is divided by 41 ?
Options: a ) 3 , b ) 18 , c ) 6 , d ) 16 , e ) 5
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 13 = 82 k + 5 + 13 = 82 k + 18 or x + 13 = 18,100 , 182 etc . when divided by 41 , we will get the remainder 18 . b"
Answer: b
Python program:
a = 5 + 13
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 341 in 2 years ?
Options: a ) 221 , b ) 309 , c ) 400 , d ) 288 , e ) 171
Rationale: "explanation : 341 = p ( 21 / 20 ) 2 p = 309.29 answer : b"
Answer: b
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 341 / c
Problem: a sum fetched total simple interest of 4016.25 at the rate of 10 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 8925 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: let the sums be p . now , 50 % of p = 4016.25 or , p = 8032.5 answer b
Answer: b
Python program:
a = 100 * 4016
b = 10 * 5
c = a / b
Problem: in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 45 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 45 - 25 x 50 = 100 ∴ average for last 5 days = 100 / 5 = 20 a"
Answer: a
Python program:
a = 25 + 5 
b = a * 45
c = 25 * 50
d = b - c
e = d / 5
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 42 ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "21 # 42 = 21 * 24 * 27 * 30 * 33 * 36 * 39 * 42 = 3 ^ 11 * 7 ^ 2 * 2 ^ 7 * 5 ^ 1 * 11 ^ 1 * 13 ^ 1 so total is = 11 + 2 + 7 + 1 + 1 + 1 = 23 answer a"
Answer: a
Python program:
a = 2 + 2 
b = 3 + a 
c = 2 + 2 
d = b + c 
e = 2 + 2 
f = 3 + e 
g = d + f
Problem: ( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + 1.08 + ( 0.9 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.6 , c ) 0.8 , d ) 0.3 , e ) none of them
Rationale: "given expression = ( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + ( 1.2 x 0.9 ) + ( 0.9 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 1.2 - 0.9 ) = 0.3 answer is d"
Answer: d
Python program:
a = 1 ** 2
b = 0 ** 9
c = a - b
d = 1 ** 2
e = d + 1 
f = 0 ** 9
g = e + f 
h = c / g
Problem: a volume of 10996 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 2749
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10996 l can be kept in ( 10996 / 4 ) hemispheres ans . 2749 answer : e"
Answer: e
Python program:
a = 10996 / 4
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 200 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 200 . so 1 / 4 of her savings is $ 200 . so her original savings are 4 times $ 200 = $ 800 correct answer d"
Answer: d
Python program:
a = 3 / 4
b = 1 - a
c = 200 / b
Problem: a lent rs . 4000 to b for 2 years and rs . 2000 to c for 4 years on simple interest at the same rate of interest and received rs . 2200 in all from both of them as interest . the rate of interest per annum is :
Options: a ) 14 % , b ) 15 % , c ) 12 % , d ) 13.75 % , e ) 14.56 %
Rationale: explanation : let the rate of interest per annum be r % simple interest for rs . 4000 for 2 years at r % + simple interest for rs . 2000 for 4 years at r % = 2200 ( 4000 × r × 2 ) / 100 + ( 2000 × r × 4 ) / 100 = 2200 80 r + 80 r = 2200 160 r = 2200 16 r = 220 4 r = 55 r = 55 / 4 = 13.75 % answer : option d
Answer: d
Python program:
a = 4000 * 2
b = 2000 * 4
c = a + b 
d = 2200 / c
e = d * 100
Problem: what is the 23 th digit to the right of the decimal point in the decimal form of 36 / 66 ?
Options: a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 6
Rationale: "we first have to use some long division . this long division allows us to get 36 / 66 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then about the 10 digit to the right of the decimal point and we see that 10 is even , we know that the 10 th digit is a 4 . answer b ."
Answer: b
Python program:
a = 36 / 66
Problem: a man can row his boat with the stream at 6 km / h and against the stream in 2 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 5 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "ds = 6 us = 2 s = ? s = ( 6 - 2 ) / 2 = 2 kmph answer : b"
Answer: b
Python program:
a = 6 - 2
b = a / 2
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "explanation : let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 5 ) = 4 / 5 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a"
Answer: a
Python program:
a = 5 * 1
Problem: if the l . c . m of two numbers is 600 and their product is 18000 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18000 / 600 = 30 . answer : b"
Answer: b
Python program:
a = 18000 / 600
Problem: working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 18 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "each hour they complete 1 / 3 + 1 / 18 = 7 / 18 of the job . in 2 hours , they complete 2 ( 7 / 18 ) = 7 / 9 of the job . the time for p to finish is ( 2 / 9 ) / ( 1 / 3 ) = ( 2 / 3 ) hour = 40 minutes the answer is c ."
Answer: c
Python program:
a = 1/(3)
b = 1/(18)
c = a + b 
d = c * 2
e = 1 - d
f = 1/(3)
g = e / f
h = g * const_60
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses q at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) q = 256 , d ) q = 384 , e ) q = 480
Rationale: "most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Python program:
a = 16 * 2
b = a * 15
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 7 meters , and the interior of tank b has a height of 7 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 70 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "the radius of tank a is 7 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 49 / ( 4 * pi ^ 2 ) = 245 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 7 * pi * 100 / ( 4 * pi ^ 2 ) = 350 / ( 2 * pi ) tank a / tank b = 245 / 350 = 7 / 10 = 70 % the answer is a ."
Answer: a
Python program:
a = 7 / 10
b = a ** 2
c = 10 / 7
d = b * c
e = d * 100
Problem: car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 10 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 70 × 4 = 280 km the ratio is 400 : 280 = 40 : 28 = 10 : 7 the answer is c ."
Answer: c
Python program:
a = 50 * 8
b = 70 * 4
c = a / b
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12700 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 8828 , d ) 2387 , e ) 3810
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12700 = 3810 answer : e"
Answer: e
Python program:
a = 6300 + 4200 
b = a + 10500 
c = 6300 / b
d = c * 12700
Problem: sum of two numbers is 25 and their difference is 13 . find their product .
Options: a ) 104 , b ) 108 , c ) 114 , d ) 124 , e ) 142
Rationale: "explanation : friends , this sort of question is quite important in competitive exams , whenever any question come which have relation between sum , product and difference , this formula do the magic : = > ( x + y ) 2 = ( x − y ) 2 + 4 xy < = > ( 25 ) 2 = ( 13 ) 2 + 4 xy < = > 4 xy = ( 25 ) 2 − ( 13 ) 2 < = > xy = 456 / 4 = 114 option c"
Answer: c
Python program:
a = 13 / 2
b = 25 - a
c = b / 2
d = 25 - c
Problem: if 13 = 13 w / ( 1 - w ) , then ( 3 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 3 w = 3 / 2 3 w * 2 = 3 / 2 * 2 = 3 answer : e"
Answer: e
Python program:
a = 13 + 13 
b = 13 / a
c = b * 3
Problem: john ' s bank ' s saving amount is decreased 12 % due to loan payment and current balance is rs . 44000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 50000 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: 12 % decreased 88 % balance = 44000 100 % = 44000 / 88 * 100 = 50000 answer : b
Answer: b
Python program:
a = 44000 * 12
b = a / 100
c = b + 44000