euclaise/mathqa_programs huggingface dataset:
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 2.5 . the factory holds a $ 62.50 worth stock of 22 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 31 , b ) 35 , c ) 21 , d ) 40 , e ) 45
Rationale: "so the number of $ 2.50 modules must be 21 so that the leftover 1 modules are of $ 10 which will give a total value $ 62.50 . 21 * 2.50 + 1 * 10 = 52.50 + 10 = 62.50 answer : c"
Answer: c
Python program:
a = 62 - 50
b = a / 2
Problem: mary goes into labor at her local grocery store and is rushed to a hospital in an ambulance traveling 60 mph . her husband don drives after the ambulance at an average speed of 30 mph . mary reaches the hospital fifteen minutes later . how long does it take don to get there from the store ?
Options: a ) 25 minutes , b ) 30 minutes , c ) 10 minutes , d ) 15 minutes , e ) 7 minutes
Rationale: distance covered by the ambulance in 15 minutes = 15 miles 60 mph is one mile per minute , therefore 30 mph will be 1 / 2 a mile per minute . so , he reaches the hospital half an hour after leaving the store . correct answer : b
Answer: b
Python program:
a = 3 + 12 
b = 3 + 12 
c = b / const_60
d = 30 * c
e = 60 - 30
f = d / e
g = f * const_60
h = a + g
Problem: what is the ratio between perimeters of two squares one having 7 times the diagonal then the other ?
Options: a ) 3 : 7 , b ) 3 : 5 , c ) 3 : 8 , d ) 7 : 1 , e ) 3 : 5
Rationale: "d = 7 d d = d a √ 2 = 7 d a √ 2 = d a = 7 d / √ 2 a = d / √ 2 = > 7 : 1 answer : d"
Answer: d
Python program:
a = 7 / 7
b = 7 / a
Problem: square a has an area of 65 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 0.1 , e ) 0.3
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 65 - 16 = 48 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 48 / 64 = 0.75 . answer : c"
Answer: c
Python program:
a = 16 / 4
b = a ** 2
c = 65 - b
d = c / 65
Problem: in an election , candidate a got 80 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 380800 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 c )"
Answer: c
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 80 / 100
e = c * d
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 560 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 76 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 560 breadth = 28 feet area to be fenced = 2 b + l = 2 ( 28 ) + 20 = 76 feet answer : d"
Answer: d
Python program:
a = 560 / 20
b = a * 2
c = b + 20
Problem: if a man earns rs 20 on first day and spends rs 15 on second day , and earns rs 20 on third day and spends rs 15 on fourth day and goes on on which day he will be having rs 60 .
Options: a ) 40 rs , b ) 45 rs , c ) 50 rs , d ) 55 rs , e ) 60 rs
Rationale: earns rs 20 on first day and spends rs 15 on second day means , end of day 2 , he have 5 rs . therefore , in 16 days he have 40 rs 2 * 8 = 16 days 5 rs * 8 = 40 rs and on the 17 th day again he earn rs . 20 , 40 + 20 = 60 rs . answer : e
Answer: e
Python program:
a = 3 + 2 
b = a / 2
c = 4 * 4
d = b * c
e = d + 20
Problem: 4 mat - weaves can weaves 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat - weaves in 8 days ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 17
Rationale: solution let the required number of mats be x . more weaves , more mats ( direct proportion ) more days , more mats ( direct proportion ) ∴ 4 × 4 × x = 8 × 8 × 4 ⇔ x = ( 8 x 8 x 4 ) / ( 4 x 4 ) = 16 . answer d
Answer: d
Python program:
a = 4 * 8
b = a * 8
c = 4 * 4
d = b / c
Problem: the average age of 36 students in a group is 14 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 31 , b ) 36 , c ) 41 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 37 × 15 – 36 × 14 ) years = 51 years . answer d"
Answer: d
Python program:
a = 36 + 1
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 18 seconds . what is the length of each train ( in meters ) ?
Options: a ) 20 , b ) 25 , c ) 35 , d ) 50 , e ) 65
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 18 seconds , the relative difference in distance traveled is 18 * 25 / 9 = 50 meters this distance is twice the length of each train . the length of each train is 50 / 2 = 25 meters the answer is b ."
Answer: b
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 18
e = d / 2
Problem: the numbers 272738 and 232342 , when divided by n , a 2 digit number leave a remainder 13 and 17 respectively . find the sum of digits of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "we have to find the h . c . f of both 1.272738 - 13 2.232325 - 17 h . c . f is 25 ans is 7 answer : d"
Answer: d
Python program:
a = 272738 - 2
b = 232342 - 13
c = math.gcd(a, b)
d = reminder + (
Problem: a train is 360 meter long is running at a speed of 90 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 11 seconds , e ) 20 seconds
Rationale: "speed = 90 km / hr = 90 * ( 5 / 18 ) m / sec = 25 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 25 ) = 20 seconds answer : e"
Answer: e
Python program:
a = 360 + 140 
b = 90 * 1000
c = b / 3600
d = a / c
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fourth of his earnings to charity . if the worker ' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 22 / 10 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 4 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 4 = 1 / 8 ( 11 + n ) = > 44 + 10 n / 40 = 11 + n / 8 352 + 80 n = 440 + 40 n = > 40 n = 88 n = 88 / 40 = 22 / 10 answer : d ."
Answer: d
Python program:
a = 12 - 1
b = 12 - 3
c = 1/(b)
d = 1/(10)
e = c - d
f = a * e
g = 1 + 4 
h = 1/(g)
i = 12 - 3
j = 1/(i)
k = h - j
l = f / k
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 360 , e ) $ 399
Rationale: "( 348 / 116 ) 120 = 360 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 120 = 360 ( 300 + 60 ) answer d"
Answer: d
Python program:
a = 16 / 100
b = 1 + a 
c = 348 / b
d = 20 / 100
e = 16 / 100
f = 1 + e 
g = 348 / f
h = d * g
i = c + h
Problem: if the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 11 / 15 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 11 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 11 : 15 answer b"
Answer: b
Python program:
a = 11 * 1
b = 3 * 5
c = a / b
Problem: what should be the least number to be added to the 2496 number to make it divisible by 5 ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 4 , e ) 26
Rationale: "answer : 4 option : d"
Answer: d
Python program:
a = 5 - reminder
Problem: 1 ⁄ 5 of a number is equal to 5 ⁄ 8 of the second number . if 35 is added to the first number then it becomes 4 times of second number . what is the value of the second number ?
Options: a ) 125 , b ) 70 , c ) 40 , d ) 25 , e ) none of these
Rationale: let x be the first number and y be the second number . 1 ⁄ 5 x = 5 ⁄ 8 y \ x ⁄ y = 25 ⁄ 8 . . . . . . ( i ) x + 35 = 4 y or , 25 ⁄ 8 y + 35 = 4 y \ y = 40 answee c
Answer: c
Python program:
a = 35 * 8
b = 8 * 4
c = 5 * 5
d = b - c
e = a / d
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 75 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 75 , remainder will be - 4 i . e . n will be 4 less than a multiple of 75 . so you must add 35 to n to make it a multiple of 75 e"
Answer: e
Python program:
a = 75 - reminder
Problem: in what time will a train 130 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 3.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 130 / 40 = 3.25 sec . answer : b"
Answer: b
Python program:
a = 144 * const_0_2778
b = 130 / a
Problem: donald duck can can swim his pool downstream ( with the pool current helping time ) in exact 40 seconds and upstream ( against the pool current ) in a pool in exact 60 seconds . the length of pool is 2 kilometers . how long donald duck can cover distance of one side at a still pool ( with no current ) .
Options: a ) 40 minutes , b ) 45 minutes , c ) 38 minutes , d ) 48 minutes , e ) 30 minutes
Rationale: d 48 minutes . donald duck ' s speed = x km / seconds pool current speed = y km / seconds 2 / ( x + y ) = 40 2 / ( x - y ) = 60 solving the simultaneous equations gives x = 1 / 24 therefore , to cover 2 km will take 2 / x = 48 seconds
Answer: d
Python program:
a = 2 * 1000
b = 2 * 1000
c = b / 40
d = 2 * 1000
e = d / 60
f = c + e 
g = f / 2
h = a / g
Problem: a number is increased by 11 % and then reduced by 10 % . after these operations , the number :
Options: a ) does not change , b ) decreases by 1 % , c ) increases by 1 % , d ) increases by 0.1 % , e ) none of these
Rationale: "let the original number be 100 . then , the new number = 100 × 1.1 × 0.9 = 99 i . e . the number decreases by 1 % . answer b"
Answer: b
Python program:
a = 11 + 100 
b = 100 - 11
c = a * b
d = c / 100
Problem: an plane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 5 / 3 hours , it must travel at a speed of ?
Options: a ) 100 , b ) 720 , c ) 1100 , d ) 940 , e ) 860
Rationale: we know distance = speed * time = 240 * 5 = 1200 km now to cover 1200 km in 5 / 3 hrs , speed = distance / time = 1200 / ( 5 / 3 ) = 720 kmph ans - b
Answer: b
Python program:
a = 5 / 3
b = 5 / a
c = 240 * b
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 132 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 33
Rationale: ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 132 x = 3 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 3 = 33 answer e
Answer: e
Python program:
a = 4 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 4 * 5
f = d + e 
g = 132 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 4 * 5
n = l + m 
o = 132 / n
p = i * o
q = h - p
Problem: two vessels contains equal number of mixtures milk and water in the ratio 5 : 2 and 6 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 5 / 7 + 6 / 7 ) : ( 2 / 7 + 1 / 7 ) = 11 / 7 : 3 / 7 = 11 : 3 answer is d"
Answer: d
Python program:
a = 6 + 1 
b = 5 + 2 
c = a / b
d = 5 * c
e = d + 6 
f = 6 + 1 
g = 5 + 2 
h = f / g
i = 2 * h
j = i + 1 
k = e / j
Problem: ashok secured average of 80 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 99 , d ) 110 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 80 therefore total marks in 6 subjects = 80 * 6 = 480 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 480 – 370 = 110 answer : d"
Answer: d
Python program:
a = 80 * 6
b = 74 * 5
c = a - b
Problem: out of 410 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 140 , e ) 220
Rationale: n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 410 - 50 = 360 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 360 = 140 . answer is d
Answer: d
Python program:
a = 175 + 325 
b = 410 - 50
c = a - b
Problem: a number consists of 3 digit whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :
Options: a ) 145 , b ) 253 , c ) 370 , d ) 352 , e ) 300
Rationale: explanation : let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the unit ' s digit . hence , required number = 253 . answer is b
Answer: b
Python program:
a = 10 + 2 
b = a / 4
c = b - 1
d = c * 100
e = 10 + 2 
f = e / 4
g = 10 + 2 
h = g / 4
i = h - 1
j = f + i 
k = j * 10
l = d + k 
m = 10 + 2 
n = m / 4
o = l + n
Problem: what amount does an investor receive if the investor invests $ 5000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 5850 , b ) $ 5950 , c ) $ 6050 , d ) $ 6150 , e ) $ 6250
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 6050 the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 5000 * c
Problem: of the 3,600 employees of company x , 1 / 4 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 4 are clerical out of 3600 so 900 are clerical 900 reduced by 1 / 4 is 900 * 1 / 4 so it reduced 225 people , so there is 675 clerical people left but since 225 people left , it also reduced from the total of 3600 so there are 3375 people total since 675 clerical left / 3375 people total you get ( c ) 20 %"
Answer: c
Python program:
a = 1 / 4
b = 1 / 4
c = 1 - b
d = a * c
e = 1 / 4
f = 1 / 4
g = 1 - f
h = e * g
i = 1 / 4
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: there are 12 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 55 , b ) 66 , c ) 77 , d ) 88 , e ) 99
Rationale: "12 c 2 = 66 the answer is b ."
Answer: b
Python program:
a = 12 - 1
b = 12 * a
c = b / 2
Problem: tough and tricky questions : statistics . set x consists of prime numbers { 3 , 11 , 7 , a , 17 , 19 } . if integer y represents the product of all elements in set x and if 11 y is an even number , what is the range of set x ?
Options: a ) 14 , b ) 16 , c ) 17 , d ) 20 , e ) 26
Rationale: since 11 y = even therefore y has to beevensince 11 is a odd integer ( even * odd = even ) similarly , y is the product of all integers in set x but all integers in set x are odd except the unknown a and since x contains only prime numbers , a has to equal to 2 . . . ( 2 is the only even prime number and the product of all prime numbers in set x has to be even , even * odd = even ) since you know value of a you can calculate the range = largest integer in the set minus smallest integer in the set = 19 - 2 = 17 answer is c
Answer: c
Python program:
a = 19 - 2
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 4
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 3
Rationale: "total number of cases = 3 * 3 = 9 favourable cases = [ ( 2,3 ) , ( 3,2 ) , ( 3,3 ) ] = 3 so probability = 3 / 9 = 1 / 3 answer is e"
Answer: e
Python program:
a = 2 * 3
b = 4 - a
c = b / 4
Problem: what is the total number of integers between 100 and 250 that are divisible by 5 ?
Options: a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 25
Rationale: "105 , 110 , 115 , . . . , 240,245 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 245 - 105 ) / ( 5 ) + 1 = 140 / 5 + 1 = 28 + 1 = 29 answer is c"
Answer: c
Python program:
a = 250 - 100
b = a / 5
c = b + 1
Problem: what profit percent is made by selling an article at a certain price , if by selling at 4 / 5 rd of that price , there would be a loss of 20 % ?
Options: a ) 0 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 4 / 5 sp 1 cp = 100 sp 2 = 80 4 / 5 sp 1 = 80 sp 1 = 100 100 - - - 100 = > 0 % answer : a"
Answer: a
Python program:
a = 100 - 20
b = 4 / 5
c = a / b
d = c - 100
Problem: on a sum of money , the simple interest for 2 years is rs . 320 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 12.5 % , d ) 10.5 % , e ) 11.5 %
Rationale: explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - simple interest for 2 years is rs . 320 = > simple interest for first year = 320 / 2 = 160 = > similarly , simple interest for second year is also 160 compound interest for first year = 160 compound interest for second year = 340 - 160 = 180 we can see that compound interest for second year is more than simple interest for second year by 180 - 160 = 20 i . e . , rs . 20 is the simple interest on rs . 160 for 1 year r = 100 × si / pt = ( 100 × 20 ) / ( 160 × 1 ) = 12.5 % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r × si ) / ( 2 × 100 ) difference between the compound interest and simple interest = 340 - 320 = 20 ( r × si ) / ( 2 × 100 ) = 20 ( r × 320 ) / ( 2 × 100 ) = 20 r = 20 × 100 × 2320 = 12.5 % answer : option c
Answer: c
Python program:
a = 320 / 2
b = 340 - a
c = 320 / 2
d = b - c
e = 100 * d
f = 320 / 2
g = e / f
Problem: if x , y , and z are positive real numbers such that x ( y + z ) = 62 , y ( z + x ) = 82 , and z ( x + y ) = 100 , then xyz is
Options: a ) 120 , b ) 50 , c ) 60 , d ) 70 , e ) 90
Rationale: "xy + xz = 62 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 82 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 100 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 82 + 18 xz + zy = yz + yx + 18 xz = yx + 18 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 80 xz = 40 xyz has to be multiple of 40 , only 120 fits in answer = a"
Answer: a
Python program:
a = 82 - 62
b = 100 - a
Problem: of the families in city x in 1992 , 30 percent owned a personal computer . the number of families in city x owning a computer in 1999 was 50 percent greater than it was in 1992 , and the total number of families in city x was 5 percent greater in 1999 than it was in 1994 . what percent of the families in city x owned a personal computer in 1999 ?
Options: a ) 43 % , b ) 42.85 % , c ) 45.25 % , d ) 46.23 % , e ) 41.66 %
Rationale: "say a 100 families existed in 1992 then the number of families owning a computer in 1992 - 30 number of families owning computer in 1999 = 30 * 150 / 100 = 45 number of families in 1999 = 105 the percentage = 45 / 105 * 100 = 42.85 % . answer : b"
Answer: b
Python program:
a = 50 + 100 
b = a * 30
c = b / 100
d = 100 + 5 
e = c / d
f = 100 * e
Problem: of the votes cast on a certain proposal , 70 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 350 , b ) 375 , c ) 400 , d ) 425 , e ) 450
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 70 0.2 x = 70 x = 350 the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = b - c
e = 70 / d
Problem: a man can do a piece of work in 4 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 12 days , b ) 6 days , c ) 5 days , d ) 4 days , e ) none of these
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 3 − 1 / 4 ) = ( 4 − 3 ) / 12 = 1 / 12 so son will do whole work in 12 days answer : a"
Answer: a
Python program:
a = 4 * 3
b = 4 - 3
c = a / b