euclaise/mathqa_programs huggingface dataset:
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 3 hammers and 4 wrenches is one - third that of 10 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 1 / 7
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 3 x + 4 y ) = 1 / 3 * ( 10 x + 5 y ) 3 ( 3 x + 4 y ) = ( 10 x + 5 y ) 9 x + 12 y = 10 x + 5 y 7 y = x y = x / 7 ans - e"
Answer: e
Python program:
a = 3 * 2
b = 3 - a
c = 3 * 2
d = c - 4
e = b / d
Problem: if a is an integer greater than 2 but less than 7 and b is an integer greater than 4 but less than 13 , what is the range of a / b ?
Options: a ) 23 / 34 , b ) 57 / 60 , c ) 51 / 67 , d ) 19 / 71 , e ) 75 / 64
Rationale: "the way to approach this problem is 2 < a < 7 and 4 < b < 13 minimum possible value of a is 3 and maximum is 6 minimum possible value of b is 5 and maximum is 12 range = max a / min b - min a / max b ( highest - lowest ) 6 / 5 - 3 / 12 = 57 / 60 hence b"
Answer: b
Python program:
a = 7 - 1
b = 4 + 1 
c = a / b
d = 2 + 1 
e = 13 - 1
f = d / e
g = c - f
Problem: all factors of a positive integer a are multiplied and the product obtained is a ^ 3 . if a is greater than 1 , how many factors does a have ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: answer = d = 6 number . . . . . . . . . . . . . . . . factors . . . . . . . . . . . . . . . . . . . . . . . . product 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 6 . . . . . . . . . . . . . . . . . . . . . . . . . 36 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 , 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 , 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 4 , 6 , 12 . . . . . . . . . . . . . . . . . 12 * 12 * 12 number which we are looking for = 12 answer = d
Answer: d
Python program:
a = 2 * 2
b = a * 2
c = b * 2
d = c * 3
e = 2 * 2
f = e * 2
g = d / f
Problem: when 5 + 1 = 56 , 6 + 1 = 67 , 7 + 1 = 78 , then 8 + 1 = ?
Options: a ) 85 , b ) 98 , c ) 89 , d ) 105 , e ) 129
Rationale: "5 + 1 = > 5 x 1 = 5 & 5 + 1 = 6 = > 5 & 6 = > 56 6 + 1 = > 6 x 1 = 6 & 6 + 1 = 7 = > 6 & 7 = > 67 7 + 1 = > 7 x 1 = 7 & 7 + 1 = 8 = > 7 & 8 = > 78 then 8 + 1 = > 8 x 1 = 8 & 8 + 1 = 9 = > 8 & 9 = > 89 answer : c"
Answer: c
Python program:
a = 1 * 1
b = a * 10
c = b + 5
Problem: express 22 mps in kmph ?
Options: a ) 79.2 kmph , b ) 89.2 kmph , c ) 79.6 kmph , d ) 99.2 kmph , e ) 69.2 kmph
Rationale: "22 * 18 / 5 = 79.2 kmph answer : a"
Answer: a
Python program:
a = 22 / 1000
b = a * 3600
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 58 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 4
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 58 * ( n + 1 ) - - > n = 4 . or as 40 extra units increased the average for n + 1 days by 8 units per day then 40 / ( n + 1 ) = 8 - - > n = 4 . answer : e ."
Answer: e
Python program:
a = 90 - 50
b = 58 - 50
c = a / b
d = c - 1
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 32 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 21.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) solve the equation . 262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) 8 , 411.2 + 3 , 104.35 x = 44 , 782.4 + 1 , 399.45 x 8 , 411.2 + 1 , 704.9 x = 44 , 782.4 1 , 704.9 x = 36 , 371.2 x ≈ 21.3 answer is b ."
Answer: b
Python program:
a = 32 * 1399
b = 32 * 262
c = a - b
d = 3104 - 35
e = c / d
Problem: the sum of the squares of 3 numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c
Answer: c
Python program:
a = 100 * 2
b = 241 + a 
c = math.sqrt(b)
Problem: two goods trains each 720 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 88 sec , c ) 48 sec , d ) 18 sec , e ) 72 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : e"
Answer: e
Python program:
a = 45 + 30
Problem: if w / x = 1 / 6 and w / y = 1 / 5 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 11 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 6 = > x = 6 w and w / y = 1 / 5 = > y = 5 w ( x + y ) / y = ( 6 w + 5 w ) / 5 w = 11 w / 5 w = 11 / 5 correct option : d"
Answer: d
Python program:
a = 1 / 1
b = 5 / 6
c = a / b
d = c + 1
Problem: 35 liters of a mixture is created by mixing liquid p and liquid q in the ratio 4 : 3 . how many liters of liquid q must be added to make the ratio 5 : 7 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: let x be the amount of liquid q to be added . ( 3 / 7 ) * 35 + x = ( 7 / 12 ) * ( 35 + x ) 1260 + 84 x = 1715 + 49 x 35 x = 455 x = 13 the answer is d .
Answer: d
Python program:
a = 5 + 7 
b = 35 * 4
c = 4 + 3 
d = b / c
e = a * d
f = e / 5
g = f * 7
h = 5 + 7 
i = g / h
j = 35 * 3
k = 4 + 3 
l = j / k
m = i - l
Problem: a jar contains a mixture of ab in the ratio 4 : 1 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 32 , d ) 20 , e ) 25
Rationale: "20 litres of mixture that is replaced will contain 16 litres of a and 4 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 16 ] / [ k - 4 + 20 ] = 2 / 3 = > 12 k - 48 = 2 k - 8 + 40 = > 10 k = 80 solve for k which is k = 8 so initial volume of liquid a = 4 k = 32 litres answer : c"
Answer: c
Python program:
a = 3 * 2
b = 2 * 2
c = a + b 
d = 3 * 2
e = d - 1
f = 20 / e
g = c * f
h = 4 + 1 
i = g / h
j = i * 4
Problem: two trains 140 m and 160 m long run at the speed of 60 kmph and 40 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 40 = 100 kmph * 5 / 18 = 250 / 9 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec answer is c"
Answer: c
Python program:
a = 140 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: for a certain exam , a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "mean - 2 sd = 60 mean + 3 sd = 100 by solving above we get , sd ( absolute value ) = 8 mean = 76 ans . b"
Answer: b
Python program:
a = 60 * 3
b = 100 * 2
c = a + b 
d = 2 + 3 
e = c / d
Problem: the sum of the present age of henry and jill is 48 . what is their present ages if 9 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 9 years ago be x , age of henry be 2 x x + 9 + 2 x + 9 = 48 x = 10 present ages will be 19 and 29 answer : d"
Answer: d
Python program:
a = 48 + 9 
b = a / 3
c = 48 - b
Problem: the average of 15 numbers is calculated as 20 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 30 , b ) 26 , c ) 16 , d ) 97 , e ) 12
Rationale: "15 * 20 + 36 – 26 = 300 / 10 = 30 answer : a"
Answer: a
Python program:
a = 36 - 26
b = a / 15
c = 20 + b
Problem: what is the area of a square field whose diagonal of length 16 m ?
Options: a ) 128 , b ) 289 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 16 * 16 ) / 2 = 128 answer : a"
Answer: a
Python program:
a = square_area / (
Problem: the avg age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasingthe avg by 4 year . find what was the original strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 19
Rationale: let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b
Answer: b
Python program:
a = 32 - 12
b = 40 - 32
c = a - b
Problem: what distance will be covered by a bus moving at 108 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 276 , e ) 900
Rationale: "108 kmph = 108 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : e"
Answer: e
Python program:
a = 108 * const_0_2778
b = a * 30
Problem: vijay sells a cupboard at 12 % below cost price . had he got rs . 1500 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 6250 , d ) 6000 , e ) none of these
Rationale: "explanation : cost price = 1500 / ( 0.12 + 0.12 ) = 1500 / 0.24 = rs . 6250 answer c"
Answer: c
Python program:
a = 100 + 12 
b = 100 - 12
c = a - b
d = c / 100
e = 1500 / d
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 30 men in 3 days ?
Options: a ) 65 mtr . , b ) 84 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: 20 men is 6 days can build 112 metres 30 men in 3 days can build = 112 * ( 30 / 20 ) x ( 3 / 6 ) = 84 meters answer : b .
Answer: b
Python program:
a = 30 * 3
b = 20 * 6
c = a / b
d = 112 * c
Problem: if the speed of a man is 57 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 475 m , d ) 420 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 57 * ( 5 / 18 ) * 30 = 475 m answer : c"
Answer: c
Python program:
a = 57 * const_0_2778
b = a * 30
Problem: victor gets 90 % marks in examinations . if these are 405 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 450 , e ) 271
Rationale: "let the maximum marks be m then 90 % of m = 405 ⇒ 90 / 100 × m = 405 ⇒ m = ( 405 × 100 ) / 90 ⇒ m = 40500 / 90 ⇒ m = 450 therefore , maximum marks in the examinations are 450 answer : d"
Answer: d
Python program:
a = 90 / 100
b = 405 / a
Problem: there are 3 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 45 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 3 c 2 number of ways of selecting 2 non fiction books = 6 c 2 3 c 2 * 6 c 2 = 3 * 15 = 45 answer : c"
Answer: c
Python program:
a = 3 * 4
b = 6 * 3
c = a * b
d = math.factorial(2)
e = d ** 2
f = c / e
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 16 so , 134.08 = 134 + 16 / j so , j = 200 ans e"
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 8
e = 16 / d
Problem: ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) =
Options: a ) 8.4 , b ) 840 , c ) 84.0 , d ) 0.84 , e ) 0.084
Rationale: ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = 0.0048 * 350 / 5 ( 0.1 ) ( 0.004 ) = 0.048 * 70 / 1 ( 0.004 ) = 48 * 70 / 4 = 12 * 70 = 840 answer : b
Answer: b
Python program:
a = 0 * 48
b = 0 * 5
c = b * 0
d = a / c
Problem: a batsman in his 17 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 17 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: average score before 17 th innings = 85 - 3 × 17 = 34 average score after 17 th innings = > 34 + 3 = 37 answer : b
Answer: b
Python program:
a = 3 * 17
b = 85 - a
c = b + 3
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190 , b ) 180 , c ) 150 , d ) 200 , e ) 300
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 300 - x ) = 7500 or 25 x = 7500 - 4500 , x = 3000 / 25 = 120 vip = 120 general 200 d"
Answer: d
Python program:
a = 3 + 4 
b = a * 1000
c = 2 + 3 
d = c * 100
e = b + d 
f = 300 * 15
g = e - f
h = 2 + 3 
i = 2 + 3 
j = h * i
k = g / j
l = 300 - k
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 4 miles per hour and 6 hours - 24 miles total 18 + 20 + 24 - 62 answer : option e .
Answer: e
Python program:
a = 3 + 1 
b = 18 / 3
c = b - 1
d = a * c
e = 18 + d 
f = 18 / 3
g = 3 + 1 
h = f * g
i = e + h
Problem: sum of two numbers is 30 . two times of the first exceeds by 10 from the three times of the other . then the numbers will be ?
Options: a ) 14 , 16 , b ) 16 , 14 , c ) 18 , 12 , d ) 12 , 18 , e ) 17 , 13
Rationale: "explanation : x + y = 30 2 x ã ¢ â ‚ ¬ â € œ 3 y = 10 x = 16 y = 14 answer : b"
Answer: b
Python program:
a = 10 / 2
b = 30 - a
c = b / 2
d = 30 - c
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 4 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 4 t 1 = 4 and so t 2 = 8 . the answer is c ."
Answer: c
Python program:
a = 40 / 2
b = a / 4
c = 40 / b
Problem: a man can do a job in 15 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.4 days , b ) 4.4 days , c ) 5.4 days , d ) 8.4 days , e ) 2.4 days
Rationale: a 6.4 days 1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 25 ) = 47 / 300 so , all three together will complete the work in 300 / 47 = 6.4 days . -
Answer: a
Python program:
a = 1 / 25
b = 1 / 15
c = 1 / 20
d = b + c 
e = a + d 
f = 1 / e
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 272 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 8
Rationale: required run rate = 272 - ( 3.2 x 10 ) = 240 = 6 40 40 a
Answer: a
Python program:
a = 3 * 2
b = 272 - a
c = b / 40
Problem: two numbers are less than third number by 34 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 22 %
Rationale: "let the third number is x . then first number = ( 100 - 34 ) % of x = 66 % of x = 66 x / 100 second number is ( 63 x / 100 ) difference = 66 x / 100 - 63 x / 100 = 3 x / 100 so required percentage is , difference is what percent of first number ( 3 x / 100 * 100 / 63 x * 100 ) % = 22 % answer : e"
Answer: e
Python program:
a = 37 - 34
b = 100 - 34
c = a / b
d = c * 100
e = d - 10
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 30 % iodine solution ?
Options: a ) 30.5 , b ) 49 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 30 / 100 40 x + 700 = 30 x + 1050 10 x = 305 x = 30.5 lts correct option : a"
Answer: a
Python program:
a = 35 * 20
b = a / 100
c = b * 30
d = 35 * 20
e = d / 100
f = e * 20
g = c - f
h = 40 / 100
i = 20 * h
j = 35 * 20
k = j / 100
l = i - k
m = g / l
n = m + 35
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 5.5 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.5 tax on others = 3 percentage = 5.5 / 100 = 5.5 % answer : a"
Answer: a
Python program:
a = 5 / 100
b = 50 * a
c = 10 / 100
d = 30 * c
e = b + d 
f = e / 100
g = f * 100
Problem: in a certain warehouse , 70 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 120 , d ) 102 , e ) 144
Rationale: if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 70 % of the packages weigh less than 75 pounds so , 70 % oft = number of packages that weigh less than 75 pounds 70 % of 240 = 168 , so 168 packages weigh less than 75 pounds of those 168 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 168 - 48 = 120 = c
Answer: c
Python program:
a = 100 - 80
b = 48 / a
c = b * 100
d = c * 70
e = d / 100
f = e - 48
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b
Answer: b
Python program:
a = 1 / 12
b = a * 3
c = b * 2
d = 30 * 2
e = c * d
Problem: a machine , working at a constant rate , manufactures 18 pens in 30 minutes . how many pens does it make in 1 hr 45 min ?
Options: a ) 63 , b ) 65 , c ) 62 , d ) 60 , e ) 45
Rationale: change 1 hr 45 min to 105 min . for this , we need to set up a simple proportion of pens per time 18 / 30 = s / 105 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can see this post . we can cancel 18 / 30 as 6 / 10 6 / 10 = s / 105 we can cross - multiply . 10 * s = 6 * 105 = 630 if we divide both sides by 10 , s = 63 the machine would be 63 pens in 1 hr 45 min . answer : a
Answer: a
Python program:
a = 1 * const_60
b = a + 45 
c = b / 30
d = c * 18
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 225 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 220 , b ) 200 , c ) 210 , d ) 225 , e ) 230
Rationale: "b 225 * t = 1 km = > t = 1 / 225 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 225 + 2 / 3600 ) = 1 = > v = 200 km / h"
Answer: b
Python program:
a = 1 / 225
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: if ( - 7 ) ^ ( 8 x ) = 7 ^ ( 12 - 5 x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) - 4 , c ) 1 , d ) 2 , e ) 3
Rationale: "since x is an integer , ( - 7 ) ^ ( 8 x ) is always positive . so , 7 ^ 8 x = 7 ^ ( 13 - 5 x ) 8 x = 12 - 5 x 12 x = 12 x = 1 answer : c"
Answer: c
Python program:
a = 12 / 7
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 4 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.8 % , d ) 45.2 % , e ) 73.6 %
Rationale: "fiction novels = 5,508 transferred to another location = 4590 transferred fiction novels = 1530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 4590 ) * 100 = > 28.888 . . . % hence answer will be ( c )"
Answer: c
Python program:
a = 30 / 100
b = 1 / 3
c = 1 - b
d = a * c
e = 1 / 4
f = 1 - e
g = d / f
h = g * 100
Problem: ( 51 + 52 + 53 + … … … + 100 ) is equal to :
Options: a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 3885
Rationale: "( 51 + 52 + 53 + … … … + 100 ) = ( 1 + 2 + 3 + … … . + 100 ) - ( 1 + 2 + 3 + 4 + … … + 50 ) = ( 100 * 101 ) / 2 - ( 50 * 51 ) / 2 = ( 5050 - 1275 ) = 3775 . answer : d"
Answer: d
Python program:
a = 100 + 1 
b = 100 * a
c = b / 2
d = 51 - 1
e = d * 51
f = e / 2
g = c - f