euclaise/mathqa_programs huggingface dataset:
Problem: a train starts full of passengers . at the first station , it drops one - third of the passengers and takes 280 more . at the second station , it drops one - half of the new total and takes 12 more . on arriving at the third station , it is found to have 248 passengers . find the number of passengers in the beginning .
Options: a ) 240 , b ) 248 , c ) 280 , d ) 288 , e ) 290
Rationale: let x be no . of passengers at beginning at , 1 st station is drops 1 / 3 rd so remaining 2 / 3 rd are in train only plus 280 i . e . , 2 x / 3 + 280 at 2 nd stop 1 / 2 of new total and 12 more i . e . , ( 2 x / 3 + 280 ) / 2 + 12 = 248 on solving above equation we get x as 288 answer : d
Answer: d
Python program:
a = 248 - 12
b = a * 2
c = b - 280
d = c * 3
e = d / 2
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 52.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 24.6 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 52 = 17 $ ( 17 / 69 ) * 100 = 24.6 % answer : b"
Answer: b
Python program:
a = 69 - 0
b = a / 69
c = b * 100
Problem: what will be the compound interest on rs . 35000 after 3 years at the rate of 12 % per annum
Options: a ) rs 13123.20 , b ) rs 14103.48 , c ) rs 12172.48 , d ) rs 14172.48 , e ) none of these
Rationale: "explanation : ( 35000 × ( 1 + 12 / 100 ) 3 ) = > 35000 × 28 / 25 × 28 / 25 × 28 / 25 = > 49172.48 so compound interest will be 49172.48 - 35000 = rs 14172.48 option d"
Answer: d
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: in what ratio must wheat at rs . 3.20 pe rkg be mixed with wheat at rs . 2.90 per kg so that the mixture be worth rs . 3.08 per kg
Options: a ) 3 : 4 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) 2 : 3
Rationale: if 2 ingredients are mixed , then the required ratio is given by , the rule of allegation c . p of a unit quantity of cheaper ( c ) c . p . of a unit quantity of dearer ( d ) mean price ( m ) d - m m - c  required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : given i . c . p of a unit quantity of i kind ( p ) = 3.20 ii . c . p of a unit quantity of ii kind ( p ) = 2.90 iii . mean price ( p ) = 3.08 iv . d – m = 3.08 – 2.90 = 0.18 v . m – c = 3.20 – 3.08 = 0.12  required ratio = 0.18 : 0.12 = 3 : 2 answer : b
Answer: b
Python program:
a = 3 - 8
b = 3 - 2
c = a / b
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 10 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12.5 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 10 days = 10 * ( 1 / 24 + 1 / 30 ) = 3 / 4 remaining work = 1 / 4 the number of days required for this initial work = 2.5 days . the total number of days required = 10 + 2.5 = 12.5 days . answer : a"
Answer: a
Python program:
a = 1 / 24
b = 1 / 30
c = a + b 
d = c * 10
e = 1 - d
f = 2 + 3 
g = 2 * 10
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k 
m = i + l 
n = e / m
o = n + 10
Problem: if a 2 + b 2 + c 2 = 213 and ab + bc + ca = 6 , then a + b + c is
Options: a ) 14 , b ) 20 , c ) 15 , d ) 32 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 213 and ab + bc + ca = 6 , ( a + b + c ) ^ 2 = 213 + 2 ( 6 ) = 225 = 15 ^ 2 therefore : a + b + c = 15 answer : c"
Answer: c
Python program:
a = 6 * 2
b = 213 + a 
c = math.sqrt(b)
Problem: if a - b = 6 and a 2 + b 2 = 48 , find the value of ab .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 6 , e ) 19
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 48 - 36 = 12 ab = 6 . answer : d"
Answer: d
Python program:
a = 6 ** 2
b = 48 - a
c = b / 2
Problem: a certain article of clothing was discounted during a special sale to 2 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 3 / 5 * $ 200 = $ 120 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 120 - 100 ) / 120 = 1 / 3 = 16.66 % . answer : d ."
Answer: d
Python program:
a = 2 / 5
b = 2 / 5
c = 1 / 2
d = b * c
e = a - d
f = e * 100
Problem: a committee is reviewing a total of 30 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 of the selected films are in color ?
Options: a ) 22 / 21 , b ) 20 / 21 , c ) 23 / 21 , d ) 25 / 21 , e ) 28 / 21
Rationale: "say x = y = 10 . in this case we would have : 30 x = 300 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 3 black - and - white films and all 60 color films , thus total of 63 films were selected . color films thus compose 60 / 63 = 20 / 21 of the selected films . answer : b"
Answer: b
Python program:
a = 30 / 100
b = a + 6 
c = 6 / b
Problem: after paying a 10 percent tax on all income over $ 3000 , a person had a net income of $ 12000 . what was the income before taxes ?
Options: a ) $ 13300 , b ) $ 13000 , c ) $ 12900 , d ) $ 10000 , e ) $ 9000
Rationale: let x be the income over 3000 then ( x - x / 10 ) + 3000 = 12000 = > x = 10000 therefore income before taxes = 10000 + 3000 = 13000 option ( b )
Answer: b
Python program:
a = 10 / 100
b = a * 3000
c = 12000 - b
d = 10 / 100
e = 1 - d
f = c / e
Problem: sam invested rs . 8000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 3200.0 , b ) 11520.0 , c ) 8820.0 , d ) 7354.0 , e ) 16537.11
Rationale: "p = rs . 8000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = ( 8000 * 21 / 20 * 21 / 20 ) = rs . 8820.00 answer : c"
Answer: c
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 8000
Problem: half a number plus 5 is 11 . what is the number ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "solution let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 11 ( 1 / 2 ) x + 5 - 5 = 11 - 5 ( 1 / 2 ) x = 6 2 × ( 1 / 2 ) x = 6 × 2 x = 12 answer c"
Answer: c
Python program:
a = 11 - 5
b = a * 2
Problem: a can complete a certain job in 19 days . b is 90 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: "let , total work unit = 190 units a can finish in 19 days = 190 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 90 / 100 ) * 10 = 19 unit work days in which b will complete the work alone = 190 / 19 = 10 days answer : option e"
Answer: e
Python program:
a = 19 * 90
b = a / 100
Problem: if 20 men can build a water fountain 56 metres long in 7 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 42 m , c ) 47 m , d ) 49 m , e ) 50 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 7 : 3 : : 56 : x therefore ( 20 x 7 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 140 = 42 hence , the required length is 42 m . answer : b"
Answer: b
Python program:
a = 20 * 7
b = 56 / a
c = 35 * 3
d = b * c
Problem: jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 10 , c ) 22 , d ) 25 , e ) 30
Rationale: "let ' s test answer c : 22 seashells . . . with 22 seashells , jamie would have 22 ( 20 ) = 440 cents . this would allow him to buy 8 books for 440 cents total , so this is the correct answer . c"
Answer: c
Python program:
a = math.lcm(20, 55)
b = a / 20
c = b + 10
Problem: how many positive integers less than 248 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: "244 / 4 = 61 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 61 - 20 = 41 answer : b"
Answer: b
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 41 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 210 sq . ft . so , b = 10.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 21 ) ft = 41 ft . answer b"
Answer: b
Python program:
a = 210 / 20
b = a * 2
c = b + 20
Problem: in the coordinate plane a slope of the line k is 4 times the x - intercept of the line k . what is the y - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2
Rationale: as 4 y = mx + c , from 4 y = 0 m + m we get y = 1 / 4 . hence , the correct answer choice is d .
Answer: d
Python program:
a = 1 / 4
Problem: find the smallest four - digit number which is a multiple of 112 .
Options: a ) 896 , b ) 1008 , c ) 1120 , d ) 1024 , e ) none of these
Rationale: "the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b"
Answer: b
Python program:
a = 112 / 1000
b = a / 3
c = b / 3
d = c / 3
e = 112 / 1000
f = e / 3
g = f / 3
h = g / 3
i = d * h
Problem: the difference between the place values of two sevens in the numerical 69758472 is
Options: a ) 0 , b ) 6993 , c ) 699930 , d ) 996330 , e ) none of them
Rationale: "required difference = ( 700000 - 70 ) = 699930 . answer is c"
Answer: c
Python program:
a = 69758472 + 1 
b = a / 2
Problem: a set s = { x , - 8 , - 5 , - 3 , 3 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 2 , b ) 0 , c ) - 1 , d ) can not be determined , e ) 1
Rationale: "median of the set = ( - 3 + 3 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 18 - 16 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer a"
Answer: a
Python program:
a = 9 + 8 
b = a + 3 
c = b - 3
d = c - 5
e = d - 8
Problem: the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 10,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 4,000 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800
Rationale: "b . market value in 1982 = $ 10000 market value in 1983 = $ 10000 - ( $ 10000 x 30 / 100 ) = 10000 - 3000 = $ 7000 market value in 1984 = market value in 1983 - ( 30 % of $ 10000 ) = 7000 - 3000 = $ 4000"
Answer: b
Python program:
a = 100 * 30
b = 2 * 4
c = a * b
d = 100 * 30
e = 2 * 4
f = d * e
g = 30 / 100
h = g * 2
i = f * h
j = c - i
Problem: the value of log 2 16 is
Options: a ) 1 / 8 , b ) 4 , c ) 8 , d ) 16 , e ) 17
Rationale: "solution let log 216 = n . then , 2 n = 16 = 24 ‹ = › n = 4 . answer b"
Answer: b
Python program:
a = 4 + 1 
b = a * 1000
c = 16 - b
d = math.log(c)
e = 4 + 1 
f = math.log(e)
g = d / f
h = math.log(g)
Problem: dividing by 3 ⁄ 7 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 35 ⁄ 18 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 7 * 5 / 6 = x * 7 / 3 * 5 / 6 = x * 35 / 18 a"
Answer: a
Python program:
a = 7 / 3
b = 5 / 6
c = a * b
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 13 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 13 x = 13 answer : c"
Answer: c
Python program:
a = 7 / 5
b = 13 / 7
c = a * b
d = c * 5
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 5 km less . time taken to cover 5 km = ( 5 / 50 ) x 60 = 6 min answer : b"
Answer: b
Python program:
a = 50 - 45
b = a / 50
c = const_60 * b
Problem: by selling 16 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 25 , c ) 24 , d ) 23 , e ) 21
Rationale: "80 % - - - 16 120 % - - - ? 80 / 120 * 16 = 24 answer : c"
Answer: c
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 16
Problem: the ratio of spinsters to cats is 2 to 9 . if there are 42 more cats than spinsters , how many spinsters are there ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 42 x = 6 and the number of spinsters is 2 ( 6 ) = 12 . the answer is d ."
Answer: d
Python program:
a = 9 - 2
b = 42 / a
c = b * 2
Problem: find the smallest number in a gp whose sum is 38 and product 1728
Options: a ) 12 , b ) 20 , c ) 8 , d ) all of these , e ) none of these
Rationale: "in gp : - a / r + a + ar . . . . = 38 a ( 1 + r + r ^ 2 ) = 38 r . . . . . . eq 1 product a ^ 3 = 1728 a = 12 now put this value in eq 1 12 ( 1 + r + r ^ 2 ) = 38 r r = 2 / 3 and 3 / 2 . . so sallest number is 8 answer : c"
Answer: c
Python program:
a = 38 / 1000
b = a / 3
c = b / 3
d = c / 3
e = 38 / 1000
f = e / 3
g = f / 3
h = g / 3
i = d * h
Problem: 76 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 76 = 33.25 answer : c"
Answer: c
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 76
f = e / 2
Problem: in a division sum , the quotient is 40 , the divisor 72 and the remainder 64 , find the dividend ?
Options: a ) 2674 , b ) 2944 , c ) 2464 , d ) 2924 , e ) 2994
Rationale: explanation : 40 * 72 + 64 = 2944 answer : b
Answer: b
Python program:
a = 40 * 72
b = a + 64
Problem: a store sells chairs and tables . if the price of 3 chairs and 1 table is 60 % of the price of 1 chair and 3 tables , and the price of 1 table and 1 chair is $ 80 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 68 , b ) 84 , c ) 72 , d ) 60 , e ) 64
Rationale: "let c = chair ; t = table 3 c + 1 t = 0.6 ( 1 c + 3 t ) or c ( 3 - 0.6 ) = 1.8 t - 1 t or 2.4 c = 0.8 t therefore c = 0.8 / 2.4 t = 1 / 3 t ic + 1 t = 80 or 1 / 3 t + 1 t = 80 therefore t = 80 * 3 / 4 = 60 d"
Answer: d
Python program:
a = 80 * 3
b = 60 / 100
c = 80 * b
d = a - c
e = 60 / 100
f = e + 1 
g = d / f
Problem: the probability that a man will be alive for 10 more yrs is 1 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 3 / 5 , e ) 3 / 8
Rationale: sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 2 ans . ( a )
Answer: a
Python program:
a = 1 / 4
b = 1 - a
c = 1 / 3
d = 1 - c
e = b * d
Problem: how many positive even integers less than 100 contain digits 4 or 7 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "one digit numbers : 4 two digit numbers : 4 at tens place : 40 , 42,44 , 46,48 7 at tens place : 70 , 72,74 , 76,78 4 at units place : 14 , 24,34 , 54,64 , 84,94 ( duplicates removed ) if 7 is at units place , the number cant be even total : 1 + 5 + 5 + 7 = 18 answer c"
Answer: c
Python program:
a = 4 * 2
Problem: a car traveled from san diego to san francisco at an average speed of 48 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 48 x total distance traveled = 2 * 48 x = 96 x total time taken = x + 2 x = 3 x average speed = 96 x / 3 x = 32 answer : b"
Answer: b
Python program:
a = 1/(48)
b = 1/(48)
c = b / 2
d = a + c 
e = 1/(d)
Problem: amount of bacteria present time amount 1 : 00 p . m . 8.0 grams 4 : 00 p . m . x grams 7 : 00 p . m . 12.4 grams data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same fraction during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 : 00 p . m . ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 10.0 , e ) 10.4
Rationale: the question says that bacteria increased by same fraction , not by same amount in 2 intervals of 3 hours . let x represent the amount of bacteria present at 4 : 00 pm . since the fractional increase must remain constant from 1 to 4 pm as it is from 4 pm to 7 pm : fractional increase from 1 pm to 4 pm = x / 8.0 fractional increase from 4 pm to 7 pm = 12.4 / x x \ 8 = 12.4 \ x x ^ 2 = 12.4 * 8 x = 10 answer : d
Answer: d
Python program:
a = 8 * 12
b = math.sqrt(a)
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.60 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 7 : 9 , e ) none of these
Rationale: "solution required ratio = 70 : 90 = 7 : 9 answer d"
Answer: d
Python program:
a = 6 - 30
b = 7 - 20
c = a / b
Problem: i bought two books ; for rs . 300 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 175 , b ) 280 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 300 - x ) 119 / 100 x = 175 answer : a"
Answer: a
Python program:
a = 100 + 19 
b = 300 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 130 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 83.6 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 380 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 130 days - - > 130 / 250 work done = > 52 % 22 % work left . . . r alone will take 22 % * 380 = 83.6 days answer is ( b )"
Answer: b
Python program:
a = 4 * 50
b = 130 / 100
c = b * 60
d = a - c
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 15 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 459 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 15 customers equally . so , total number of pastry must be a multiple of 15 only option a satisfies the condition , and hence is the answer"
Answer: a
Python program:
a = 49 * 6
b = 49 - 15
c = a / b
d = c * 15
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 8 + 3 and * 8 + 8 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 8 would be divisible by all numbers from 1 to 8 . = > * 8 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 8 is divisible by 3 ) in fact adding anyprimenumber between 1 to 8 to * 8 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 8 + 3 and * 8 + 11 then the answer would be 1 . for * 8 + 3 and * 8 + 13 , it is 2 and so on . . . a"
Answer: a
Python program:
a = 8 * 3
b = a * 2
c = b * 4
d = c + 8 
e = 8 * 3
f = e * 2
g = f * 4
h = g + 3 
i = d - h
j = i - 1
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is :
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 9 cm
Rationale: "explanation : curved surface area of sphere = 4 / π r 2 surface area of cylinder = 2 π rh = > 4 / π r 2 = 2 π rh = > r 2 = 6 ∗ 12 / 2 = > r 2 = 36 = > r = 6 note : diameter of cylinder is 12 so radius is taken as 6 . option b"
Answer: b
Python program:
a = 12 / 2
b = 12 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
Problem: during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets e sold was 25200 , how many of them were sold at full price ?
Options: a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700
Rationale: given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c
Answer: c
Python program:
a = 25200 - 5400
b = a * 5
c = 2 + 4 
d = b / c
Problem: a cricket bat is sold for $ 900 , making a profit of $ 100 . the profit percentage would be
Options: a ) 24 % , b ) 12.5 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "100 / ( 900 - 100 ) = 100 / 800 = 0.125 = 12.5 % . answer : b"
Answer: b
Python program:
a = 900 - 100
b = 100 / a
c = b * 100