euclaise/mathqa_programs huggingface dataset:
Problem: john and steve are speed walkers in a race . john is 16 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 36 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 16 + 2 - - - > 0.5 t = 18 - - - > t = 36 seconds . c is the correct answer ."
Answer: c
Python program:
a = 16 + 2 
b = 3 * 7
c = 4 - 2
d = b / c
e = 16 + 2 
f = d + e 
g = f / 4
Problem: a lady builds 9 cm length , 12 cm width , and 3 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 109 , d ) 110 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 9 * 12 * 3 / 3 = 108 cubes answer : b"
Answer: b
Python program:
a = 9 * 12
b = a * 3
c = b / 3
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 58 of gas ?
Options: a ) 242 , b ) 353 , c ) 464 , d ) 575 , e ) 686
Rationale: "58 / 4 = 14.5 gallons 14.5 * 32 = 464 miles the answer is c ."
Answer: c
Python program:
a = 58 * 32
b = a / 4
Problem: of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 9 , c ) 72 , d ) 144 , e ) 216
Rationale: of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for x - 9 ways ; # of permutations of 3 digits in xx - 2 ! / 2 ! total : 9 * 2 ! / 2 ! = 9 . answer : b .
Answer: b
Python program:
a = 10 - 1
b = 10 - 2
c = a * b
d = c * 1
Problem: . 3 + 33 + 333 + 33.3 = ?
Options: a ) 362.33 , b ) 399.6 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: ". 3 33 333 33.3 - - - - - - - - - - 399.6 - - - - - - - - - - answer is b"
Answer: b
Python program:
a = 33 + 333 
b = a + 33 
c = 3 / 10
d = b + c
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 17 is divided by 41 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 22 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 17 = 82 k + 5 + 17 = 82 k + 22 or x + 17 = 22,104 , 186 etc . when divided by 41 , we will get the remainder 22 . d"
Answer: d
Python program:
a = 5 + 17
Problem: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 15 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 15 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 9
Rationale: let number of apples = a number of oranges = b a + b = 15 - - - 1 . 48 = ( . 4 a + . 6 b ) / 15 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 9 b = 6 let the number of oranges put back = c 45 * ( 15 - c ) = 40 * 9 + 60 ( 6 - c ) = > c = 3 answer c
Answer: c
Python program:
a = 48 * 15
b = 45 * 15
c = a - b
d = 60 - 45
e = c / d
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3 ?
Options: a ) 100 , b ) 200 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 so it will from 3 to 5 i . e 4,5 = 10 * 10 = 10 ^ 2 answer is a
Answer: a
Python program:
a = 5 - 3
b = 10 ** a
Problem: the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 19 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 92 + ( 30 / 100 ) * 90 = $ 119 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 119 , the mark up is simply 19 % ans : b ."
Answer: b
Python program:
a = 4 * 8
b = 30 / 100
c = a * b
d = 4 * 8
e = c + d 
f = e - 100
Problem: 115 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 46 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 115 = 69 liters water = 46 liters 69 : ( 46 + p ) = 3 : 4 138 + 3 p = 276 = > p = 46 46 liters of water are to be added for the ratio become 3 : 4 . answer : c"
Answer: c
Python program:
a = 3 + 2 
b = 115 / a
c = b * 2
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1406 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 100 , d ) s . 95 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1406 74 x = 1406 = > x = 19 5 x = 95 rs . answer : d"
Answer: d
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1406 / e
g = 5 * f
Problem: efrida and frazer who live 10 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is four miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : a ."
Answer: a
Python program:
a = 10 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
Problem: 2 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.05555 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 2 / 36 = . 05 something answer ( b )"
Answer: b
Python program:
a = 2 / 0
b = 2 / 0
c = a + b 
d = 1/(c)
Problem: if p ( a ) = 4 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 35 , d ) 2 / 13 , e ) 3 / 17
Rationale: p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 7 . 2 / 5 p ( a n b ) = 8 / 35 . c
Answer: c
Python program:
a = 4 / 7
b = 2 / 5
c = a * b
Problem: bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.003 , e ) $ 0.005
Rationale: "cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e"
Answer: e
Python program:
a = 3 / 0
b = 6 / 25
c = a - b
Problem: for what value of “ k ” will the equation ( 2 kx 2 + 5 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 5 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 25 answer : c
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 2
d = 5 * 5
e = c / d
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams w ?
Options: a ) w = 16 , b ) w = 32 , c ) 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Python program:
a = 8 * 4
Problem: it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill one sixteenth of the dish ?
Options: a ) 16 days , b ) 26 days , c ) 27 days , d ) 28 days , e ) 29 days
Rationale: the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . the answer is b .
Answer: b
Python program:
a = 30 - 4
Problem: some persons can do a piece of work in 8 days . two times the number of these people will do half of that work in ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "8 / ( 2 * 2 ) = 2 days answer : a"
Answer: a
Python program:
a = 1 / 2
b = 8 * a
c = 1 / 2
d = b * c
Problem: rectangular tile each of size 35 cm by 30 cm must be laid horizontally on a rectangular floor of size 1000 cm by 210 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 600
b ) 400
c ) 200
d ) 500
e ) 100
Rationale: area of tile = 35 * 30 = 1050 area of floor = 1000 * 210 = 210000 no of tiles = 210000 / 1050 = 200 so , the no of tile = 200 answer : c
Answer: c
Python program:
a = 1000 * 210
b = 35 * 30
c = a / b
Problem: ( 1000 ) 7 ÷ ( 10 ) 18 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 18 = ( 10 ) 21 / ( 10 ) 18 = 10 ( 3 ) = 1000 option c"
Answer: c
Python program:
a = 1000 * 10
Problem: the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the width and the length of the garden .
Options: a ) 80 , b ) 90 , c ) 100 , d ) 70 , e ) 110
Rationale: "let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 answer c"
Answer: c
Python program:
a = 100 - 4
b = 2 * 4
c = a / b
d = c * 3
e = d + 2
Problem: if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 6 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 3 / 2 , b ) 5 / 4 , c ) 10 / 3 , d ) 20 / 7 , e ) 25 / 9
Rationale: n = 3 d / 5 j = n / 6 = d / 10 the average of november and january is ( n + j ) / 2 = 7 d / 10 / 2 = 7 d / 20 d is 20 / 7 times the average of november and january . the answer is d .
Answer: d
Python program:
a = 3 / 5
b = 3 / 5
c = 1 / 6
d = b * c
e = a + d 
f = e / 2
g = 1 / f
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 462 ?
Options: a ) 25.6 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 462 , discount = 621 - 462 = 159 discount % = 159 / 621 * 100 = 25.6 % answer : a"
Answer: a
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 462
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 16 % ?
Options: a ) 31.25 % , b ) 35.5 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 84 gain % = 20 / 64 * 100 = 31.25 % . a"
Answer: a
Python program:
a = 100 / 64
b = 100 - 16
c = b / 100
d = a * c
e = d - 1
f = e * 100
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.8 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0.8 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.8 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.8 = 0 + 0.8 = 0.8 answer : b"
Answer: b
Python program:
a = 3 ** 2
b = 1 ** 8
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 8
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 64.50 , his capital is ?
Options: a ) 24,602 , b ) 28,888 , c ) 25,800 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 64.50 32 x - 31 x = 6450 * 4 x = 25,800 . answer : c"
Answer: c
Python program:
a = 4 / 4
b = 64 / 50
Problem: what is the sum of all digits for the number 10 ^ 27 - 48 ?
Options: a ) 212 , b ) 222 , c ) 232 , d ) 242 , e ) 252
Rationale: "10 ^ 27 is a 28 - digit number : 1 followed by 27 zeros . 10 ^ 27 - 48 is a 27 - digit number : 25 9 ' s and 52 at the end . the sum of the digits is 25 * 9 + 5 + 2 = 232 . the answer is c ."
Answer: c
Python program:
a = 27 - 10
b = a - 2
c = b / 2
d = c + 10 
e = 27 - 10
f = e + 2 
g = f / 2
h = d * g
Problem: what is the units digit of ( 493 ) ( 913 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 3 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 3 . imo d ."
Answer: d
Python program:
a = math.factorial(493)
b = math.factorial(913)
c = a * b
d = math.factorial(493)
e = math.factorial(756)
f = d * e
g = c + f 
h = g / 493
Problem: the greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 2 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1557 - 7 ) and ( 2037 - 5 ) = h . c . f . of 1550 and 2032 = 2 . answer : c"
Answer: c
Python program:
a = 2037 - 5
b = 1557 - 7
c = math.gcd(a, b)
Problem: there is a right angle triangle inside a circle of diameter 18 cm . inside this triangle , there is another circle of diameter 6 cm . find the perimeter of the triangle .
Options: a ) 24 cm
b ) 36 * 2 ^ 1 / 2 cm
c ) 36 cm
d ) 54 cm
e ) 42 cm
Rationale: 1 ) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = ( a + b - c ) / 2 2 ) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3 ) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = ( a + b ) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * ( 9 + 3 ) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e
Answer: e
Python program:
a = 18 + 6 
b = 18 + a
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 14 % ?
Options: a ) 20 % , b ) 29 % , c ) 13 1 / 30 % , d ) 12 % , e ) 13 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 86 2 / 3 sp 1 = 86 sp 1 = 129 100 - - - 29 = > 29 % answer : b"
Answer: b
Python program:
a = 100 - 14
b = 2 / 3
c = a / b
d = c - 100
Problem: p and q can complete a work in 10 days and 6 days respectively . p alone started the work and q joined him after 2 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 10 work done by q in 1 day = 1 / 6 work done by p in 2 days = 2 ã — ( 1 / 10 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 10 + 1 / 6 = 4 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 4 / 15 ) = 3 total days = 2 + 3 = 5 answer : option a"
Answer: a
Python program:
a = 2 / 10
b = 1 - a
c = 1/(10)
d = 1/(6)
e = c + d 
f = b / e
g = 2 + f
Problem: david is 18 years older than his daughter rosy . in 6 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 23
Rationale: now : rosy = x , david = x + 18 in 6 years rosy = x + 6 , david = x + 18 + 6 or 2 ( x + 6 ) x + 24 = 2 x + 12 x = 12 rosy is 12 years old answer : a
Answer: a
Python program:
a = 18 + 6 
b = 2 * 6
c = a - b
Problem: you collect pens . suppose you start out with 20 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 65 , d ) 42 , e ) 43
Rationale: solution start with 20 pens . mike gives you 22 pens : 20 + 22 = 42 pens . cindy doubles the number of pens you have : 42 ã — 2 = 84 pens . sharon takes 19 pens from you : 84 - 19 = 65 pens . so you have 65 at the end . correct answer : c
Answer: c
Python program:
a = 22 + 20 
b = a * 2
c = b - 19
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 5
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 it takes a total of nine hours to cover the 210 mile distance . answer : a 6"
Answer: a
Python program:
a = 10 + 20 
b = 30 + a 
c = 210 / b
Problem: sarah is driving to the airport . after driving at 40 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 340 , c ) 210 , d ) 245 , e ) 280
Rationale: "after driving at 40 miles per hourfor one hour , this distance left to cover is d - 40 . say this distance is x miles . now , we know that the difference in time between covering this distance at 40 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 40 - x / 50 = 3 / 2 - - > 5 x / 200 - 4 x / 200 = 3 / 2 - - > x / 200 = 3 / 2 - - > x = 300 . total distance = x + 40 = 340 miles . answer : b"
Answer: b
Python program:
a = 40 - 30
b = 30 - a
Problem: the sum of the 1 st and 3 rd of 3 consecutive odd integers is 131 less than 3 times the second integer . find the 3 integers ?
Options: a ) 121 , b ) 133 , c ) 145 , d ) 150 , e ) 165
Rationale: let x , x + 2 and x + 4 be three integers . the sum of the first x and third x + 4 is given by x + ( x + 4 ) 131 less than three times the second 3 ( x + 2 ) is given by 3 ( x + 2 ) - 131 ` ` the sum of the first and third is 131 less than three times the second ' ' gives x + ( x + 4 ) = 3 ( x + 2 ) - 131 solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 as an exercise , check that the sum of the first and third is 131 less than three times b
Answer: b
Python program:
a = 131 - 3
b = 3 + 3 
c = b - 1
d = a + c
Problem: a local business made a $ 125000 profit on its first $ 1 million in sales and a $ 80000 profit on its next $ 2 million in sales . by approximately what percent did the ratio of profit to sales decrease from the first $ 1 million in sales to the next $ 2 million in sales ?
Options: a ) 100 % , b ) 150 % , c ) 200 % , d ) 250 % , e ) 300 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 1 million in sales , and the second ratio will be for the next 2 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 1 million profit / sales = 125 / 1000 = 1 / 8 next 2 million profit / sales = 8 / 200 = 2 / 50 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 400 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 1 million royalties / sales = ( 1 / 8 ) x 400 = 50 next 2 million royalties / sales = ( 2 / 50 ) x 400 = 16 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 16 – 50 ) / 16 ] x 100 = - 34 / 16 x 100 so approximately a 200 % decrease . answer c .
Answer: c
Python program:
a = 125000 / 100
b = a - 1000
c = 4 * 10
d = c + 10 
e = b - d
Problem: in town x , 64 percent of the population are employed , and 44 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 55 % , c ) 29 % , d ) 40 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 20 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 20 / 64 = 29 c"
Answer: c
Python program:
a = 64 - 44
b = a / 64
c = b * 100
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score t for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean t = 74 . answer : a ."
Answer: a
Python program:
a = 58 * 3
b = 98 * 2
c = a + b 
d = 2 + 3 
e = c / d
Problem: √ 5 percent of 5 √ 5 =
Options: a ) 0.05 , b ) 0.25 , c ) 0.5 , d ) 2.5 , e ) 25
Rationale: "√ / 1005 / 100 * 55 √ 5 = ( 5 * 5 ∗ 5 − − √ 5 ∗ 5 ) / 100 = ( 5 * 5 ) / 100 = 25 / 100 = . 25 answer : b"
Answer: b
Python program:
a = math.sqrt(5)
b = math.sqrt(5)
c = a * b
d = c * 5
e = d / 100
Problem: how many numbers from 10 to 31 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 7 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 . 7 numbers . 10 / 3 = 3 and 31 / 3 = 10 = = > 10 - 3 = 7 . therefore 7 digits d )"
Answer: d
Python program:
a = 31 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1