euclaise/mathqa_programs huggingface dataset:
Problem: how many 3 - digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number ?
Options: a ) 16 , b ) 120 , c ) 160 , d ) 180 , e ) 240
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 3 ways total = 4 * 10 * 3 = 120 ans : b"
Answer: b
Python program:
a = 100 * 3
b = a + 100
Problem: an automobile parts supplier charges $ 20 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1005 , b ) 1045 , c ) 1075 , d ) 1015 , e ) 1096
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 20 * 4 / 5 = 16 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 12 gaskets = 20 * 10 + 16 * 2 = 200 + 32 = 232 2 . he sold 15 % of the gaskets to y = 9 gaskets = 20 * 9 = 180 3 . he sold remaining 65 % to z = 39 gaskets = 20 * 10 = 200 + 16 * 29 = 684 thus , total money earned 232 + 180 + 684 = 1096 answer is e"
Answer: e
Python program:
a = 4 / 5
b = 20 * a
c = 20 / 100
d = 60 * c
e = 60 - d
f = 20 / 100
g = 60 * f
h = e - g
i = h - 10
j = b * i
k = 20 * 10
l = j + k 
m = 20 / 100
n = 60 * m
o = 20 * n
p = 20 / 100
q = 60 * p
r = 20 * q
s = o + r 
t = l + s
Problem: the length of a rectangle is increased by 25 % and its breadth is decreased by 15 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 10625 , d ) 10000 , e ) 2887
Rationale: "100 * 100 = 10000 125 * 85 = 10625 answer : c"
Answer: c
Python program:
a = 25 + 100 
b = 100 - 15
c = a * b
Problem: suraj has a certain average of runs for 8 innings . in the 9 th innings he scores 90 runs thereby increasing his average by 6 runs . what is his average after the 9 th innings ?
Options: a ) 42 , b ) 64 , c ) 36 , d ) 72 , e ) 27
Rationale: "to improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings . thus , the average after the 9 th innings = 90 - 48 = 42 . answer : a"
Answer: a
Python program:
a = 8 * 6
b = 90 - a
c = 9 - 8
d = b / c
Problem: 20 men or 25 women can finish a work in 25 days . how many days 38 men and 15 women will take to finish this job ?
Options: a ) 12 days , b ) 10 days , c ) 5 days , d ) 6 days , e ) 15 days
Rationale: 20 men = 25 women therefore , 1 women = 20 / 25 men = 4 / 5 men 15 women = 4 / 5 * 15 men = 12 men i . e . 38 men + 15 women = 38 men + 12 men = 50 men 1 work done by men = 20 * 25 20 * 25 = 50 * ? number of days = 20 * 25 / 50 = 10 days . b
Answer: b
Python program:
a = 25 * 25
b = 25 / 20
c = b * 38
d = c + 15 
e = a / d
Problem: two heavily loaded sixteen - wheeler transport trucks are 940 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 150 , d ) 140 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 940 - 90 = 850 k ratio of speeds 9 : 8 - > 850 / 17 = 50 truck a = 90 + 50 * 9 = 540 truck b = 50 * 8 = 400 delta = 140 km answer d"
Answer: d
Python program:
a = 940 - 90
b = 90 + 80 
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
Problem: in an examination , 32 % of total students failed in hindi , 56 % failed in english and 12 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 24 , b ) 37 , c ) 28 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 32 + 56 â € “ 12 = 76 therefore students who passed = 100 â € “ 76 = 24 . answer : a"
Answer: a
Python program:
a = 32 + 56 
b = a - 12
c = 100 - b
Problem: of the 250 employees at company x , 80 are full - time , and 175 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "250 employees 80 are full - time 175 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 250 - 80 = 170 employees not full time 170 - 20 = 150 employees not full time who worked over a year 175 employees have worked at company x for at least a year - 150 employees not full time who worked over a year = 25 full - time employees of company x have worked at the company for at least a year ans a"
Answer: a
Python program:
a = 250 - 80
b = a - 20
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 221 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 33 , c ) 55 , d ) 77 , e ) 39
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 221 = > . 1 x + 3 / 4 x = 221 = > x = 260 260 - 221 = pure gala = 39 . e"
Answer: e
Python program:
a = 10 / 100
b = 3 / 4
c = a + b 
d = 221 / c
e = d - 221
Problem: the ratio between the perimeter and the breadth of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the length of the rectangle ?
Options: a ) 18 cm
b ) 20 cm
c ) 22 cm
d ) 24 cm
e ) 25 cm
Rationale: 2 ( l + b ) = 5 b 1 2 l + 2 b = 5 b 3 b = 2 l b = 2 l 3 then , area = 216 cm 2 l x b = 216 l x 2 l = 216 3 l 2 = 324 l = 18 cm . a
Answer: a
Python program:
a = 3 / 2
b = 216 * a
c = math.sqrt(b)
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 44 ( 44 - 12 ) must be those with four screens or more e is the answer"
Answer: e
Python program:
a = 20 / 100
b = 20 / 300
c = b * 300
d = a * c
Problem: on a two - dimensional coordinate plane , the line q = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s q = x ^ 2 - x ^ 3 instead of q = x ^ 2 - q ^ 3 . in this case : the x - intercept is the value ( s ) of x for q = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Python program:
a = max(3)
b = a - 1
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 60 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 24
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 60 / 100 = 50.40 so x = 18.75 answer : e"
Answer: e
Python program:
a = 100 / 60
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 10 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 13 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 10 which means that in effect , all numbers are equal to 10 . if the largest number is 20 , it is 10 more than 20 . we need r to be maximum so k and m should be as small as possible to get the average of 10 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average . 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s . since s must be greater than r , r can be 10 + 3 = 13 and s can be 10 + 4 = 14 . so r is 13 . answer ( c )"
Answer: c
Python program:
a = 10 * 5
b = a - 20
c = b / 2
d = c - 2
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ?
Options: a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a"
Answer: a
Python program:
a = 15 - 10
b = 15 / a
c = 10 * b
Problem: the population of a bacteria culture doubles every 1 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 1 minutes so answer is 9 * 1 = 9 minutes answer ( a )"
Answer: a
Python program:
a = 4 + 1 
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 1
Problem: a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b"
Answer: b
Python program:
a = negate + ( 
b = 4 ** 2
c = 48 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 48 / g
Problem: what is the units digit of 28 ! + 50 ! + 3 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 4 = 10 the units digit is 0 . the answer is a ."
Answer: a
Python program:
a = 4 + 3 
b = a + 2
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 119 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 177 , b ) s . 168 , c ) s . 144 , d ) s . 129 , e ) s . 112
Rationale: "given that sp = rs . 119 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 119 ) / 85 = rs . 140 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 140 * 120 ) / 100 = rs . 168 answer : b"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 119 / b
d = 15 / 100
e = 1 - d
f = 119 / e
g = 20 / 100
h = f * g
i = c + h
Problem: eight women can do a work in 10 days . ten men can complete the same work in 6 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) none of these
Rationale: "explanation : ( 8 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 80 ( 10 ã — 6 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 60 so , required ratio = 1 / 80 : 1 / 60 = 4 : 3 answer : d"
Answer: d
Python program:
a = 10 * 6
b = 1 / a
c = 6 * 10
d = 1 / c
e = b / d
Problem: x , y and z , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2350 , what will be z ' s share of the earnings ?
Options: a ) $ 525 , b ) $ 550.50 , c ) $ 1080.02 , d ) $ 522.3 , e ) $ 1020.2
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2350 = $ 522.3 hence : d"
Answer: d
Python program:
a = 1/(6)
b = 1/(8)
c = a + b 
d = 1/(12)
e = c + d 
f = 2350 / e
g = 1/(6)
h = f * g
Problem: the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .
Options: a ) 9
b ) 7
c ) 4
d ) 8
e ) 6
Rationale: first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 6.5 cm each . the surface area of 1 side of the cube is 42.25 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes surface area is 253.5 cm . now we know that the surface area of the ball is 253.5 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 4 . then divide by pi . then determine the square root of the answer . the radius is 4.460 . rounding to the nearest whole number the radius is 4 . the correct answer is ( c ) .
Answer: c
Python program:
a = surface_cube / (
b = a / 4
c = math.sqrt(b)
d = math.floor(c)
Problem: ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 )
Options: a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7
Rationale: "let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a"
Answer: a
Python program:
a = 100 + 20 
b = a / 100
c = b * 3
d = 7 / 5
e = c - d
f = 2 / e
g = 7 / 5
h = f * g
i = 3 * h
j = 100 + 20 
k = j / 100
l = k * 3
m = 7 / 5
n = l - m
o = 2 / n
p = o + 6 
q = i / p
Problem: if a = { 9 , 17 , 25 , 28 , 29 , 30 } , how much less is the mean of the numbers in a than the median of the numbers in s ?
Options: a ) 1.0 , b ) 9.6 , c ) 3.5 , d ) 3.2 , e ) 5.1
Rationale: "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 9 + 17 + 25 + 28 + 29 + 30 ) / 6 = 23 median = ( 25 + 28 ) / 2 = 26.5 difference = 3.5 option c"
Answer: c
Python program:
a = 9 + 17 
b = a + 25 
c = b + 28 
d = c + 29 
e = 4 + 1 
f = d / e
g = f + 25
Problem: a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c"
Answer: c
Python program:
a = 700 + 600 
b = a - 1000
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 10 more than 1 / 4 of the fine and peter paid $ 10 less than 1 / 3 of the fine , leaving pay $ 25 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 10 ] + [ ( 1 / 3 ) f – 10 ] + [ ( 1 / 2 ) f – 25 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 25 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 300 12 f = 13 f – 300 – f = – 300 f = 300 well , if the fine cost $ 300 , then sam paid the part not covered by joe or peter . half the fine is $ 150 , and sam paid $ 25 less than this : $ 125 answer = b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 4
c = 1 / 3
d = b + c 
e = a + d 
f = e * 25
g = f + 25 
h = g * 2
i = h + 10
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ?
Options: a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52
Rationale: "the total number of cards is 52 . the number of kings is 4 . p ( king ) = 4 / 52 = 1 / 13 the answer is c ."
Answer: c
Python program:
a = 4 * 3
b = a / 52
Problem: if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k =
Options: a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear"
Answer: a
Python program:
a = 18 * 2
b = a / 4
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d"
Answer: d
Python program:
a = 300 / 5
b = a * 8
c = 300 + b
Problem: the sale price sarees listed for rs . 390 after successive discount is 15 % and 25 % is ?
Options: a ) 298 , b ) 237 , c ) 248 , d ) 876 , e ) 291
Rationale: "390 * ( 85 / 100 ) * ( 75 / 100 ) = 248 answer : c"
Answer: c
Python program:
a = 390 * 15
b = a / 100
c = 390 - b
d = 390 * 15
e = d / 100
f = 390 - e
g = f * 25
h = g / 100
i = c - h
Problem: a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ?
Options: a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2
Rationale: explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c
Answer: c
Python program:
a = 1 / 9
b = a * 9
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b"
Answer: b
Python program:
a = 25 / 5
b = 10 - a
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e"
Answer: e
Python program:
a = 5 + 1 
b = a * 7000
c = 6435 + 6927 
d = c + 6855 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches
Rationale: "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e"
Answer: e
Python program:
a = 1 + 1 
b = 1 / 5
c = 30 * b
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42
Rationale: "the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ."
Answer: c
Python program:
a = 45 / 2
b = 1 + 4 
c = a / b
d = 2 * c
e = 45 - d
Problem: what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 6 + 1 = 7 x = 5 - - > result = 1 + 7 + 0 = 8 x = 2 - - > result = 2 + 4 + 3 = 9 so minimum value of the expression occurs at x = 4 and the resultant value = 7 answer : d"
Answer: d
Python program:
a = 2 + 5
Problem: the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg
Rationale: "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d"
Answer: d
Python program:
a = 8 * 4
b = 65 + a
Problem: a train 120 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 27 kmph
Rationale: "s = 120 / 16 * 18 / 5 = 27 kmph answer : e"
Answer: e
Python program:
a = 120 / 16
b = const_3_6 * a