euclaise/mathqa_programs huggingface dataset:
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 4 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 40 * 2 + 80 * 4 ) / ( 2 + 4 ) = 400 / 6 = 66.6 answer : e"
Answer: e
Python program:
a = 80 * 4
b = 40 * 2
c = a + b 
d = 4 + 2 
e = c / d
f = 100 / 4
g = f - const_0_33
h = e + g
Problem: if each edge of cube increased by 10 % , the percentage increase in
Options: a ) 21 , b ) 22 , c ) 25 , d ) 19 , e ) 15
Rationale: "100 × ( 110 ) / 100 × ( 110 ) / 100 = 121 = > 21 % answer is a ."
Answer: a
Python program:
a = 100 + 10 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: the average of 6 numbers is 3.9 . the average of two of them is 3.4 , while the average of the other two is 3.85 . what is the average of the remaining two numbers ?
Options: a ) 4.7 , b ) 4.45 , c ) 4.2 , d ) 4.1 , e ) 4.9
Rationale: explanation : sum of the remaining two numbers = ( 3.9 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.40 - ( 6.8 + 7.7 ) = 23.40 - 14.5 = 8.90 . required average = ( 8.9 / 2 ) = 4.45 . answer : b ) 4.45
Answer: b
Python program:
a = 3 * 9
b = 3 * 4
c = 3 * 85
d = b + c 
e = a - d
f = e / 2
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 30 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 22 % , b ) 30 % , c ) 42 6 / 7 % , d ) 70 % , e ) 130 %
Rationale: "expensive item = $ 100 ; cheap item = $ 70 ; we must increase $ 70 to $ 100 , so by $ 30 , which is approximately 40 % increase : ( 100 - 70 ) / 70 = 3 / 7 = ~ 0.42 . answer : c ."
Answer: c
Python program:
a = 30 / 100
b = 30 / 100
c = 1 - b
d = a / c
e = d * 100
Problem: a works twice as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work is :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 18 days , e ) none of these
Rationale: solution rates of worktio of raing of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 ∴ a ’ s 1 day ’ s work = 1 / 6 b ’ s 1 day ’ s work = 1 / 12 ( a + b ) ' s 1 day ’ s work = ( 1 / 6 + 1 / 12 ) = 3 / 12 = 1 / 4 so , a and b together can finish the work in 4 days . answer a
Answer: a
Python program:
a = 1 / 12
b = 1 / 12
c = 2 * b
d = a + c 
e = 1/(d)
Problem: p and q started a business investing rs . 25,000 and rs . 20,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 5 : 4 , b ) 5 : 6 , c ) 4 : 3 , d ) 6 : 5 , e ) 17 : 4
Rationale: "p : q = 25000 : 20000 = 5 : 4 . answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 41 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg
Rationale: "a 33 kg let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 41 x 2 ) = 82 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b ' s weight = 33 kg . a"
Answer: a
Python program:
a = 41 * 2
b = 43 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: the salary of a worker is first increased by 40 % and afterwards reduced by 40 % . what is the net change in the worker ' s salary ?
Options: a ) 8 % decrease , b ) 8 % increase , c ) 16 % decrease , d ) 16 % increase , e ) no change
Rationale: "let x be the original salary . the final salary is 0.6 ( 1.4 x ) = 0.84 x the answer is c ."
Answer: c
Python program:
a = 40 + 100 
b = 40 + 100 
c = b * 40
d = c / 100
e = a - d
f = 100 - e
Problem: a tank with a volume of 20 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 8 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2110 , b ) 2220 , c ) 2440 , d ) 2660 , e ) 2880
Rationale: "the tank is emptied at this rate : 9 + 8 - 5 = 12 cubic inches / min the tank has a volume of 20 * 12 * 12 * 12 = 34560 cubic inches . the time it takes to empty the tank is 34560 / 12 = 2880 minutes . the answer is e ."
Answer: e
Python program:
a = 9 ** 5
b = 20 * a
c = 12 + 8 
d = c - 5
e = b / d
Problem: what least number should be added to 1024 , so that the sum is completely divisible by 25 ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 0 , e ) 5
Rationale: "1024 ã · 25 = 40 with remainder = 24 24 + 1 = 25 . hence 1 should be added to 1024 so that the sum will be divisible by 25 answer : option a"
Answer: a
Python program:
a = 25 - reminder
Problem: a student was asked to find the arithmetic mean of the numbers 3 , 117 , 915 , 138 , 1917 , 2114 and x . he found the mean to be 12 . what should be the remainder in the place of x ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: we have ( 3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x ) / 12 = 12 137 + x = 144 x = 7 answer is c
Answer: c
Python program:
a = 4 + 3
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 200 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 500 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 200 ( 40 * 5 = 200 ) 100 % - - - - - > 500 ( 100 * 5 = 500 ) answer : option b"
Answer: b
Python program:
a = 100 * 200
b = 100 - 70
c = 70 - b
d = a / c
Problem: if w is 40 percent less than u , u is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 u , u = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = 1 - c
e = b * d
f = 46 / 100
g = 1 - f
h = e / g
i = h / 100
j = 1 / i
k = j - 100
Problem: the salary of a person was reduced by 15 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 17.6 % , c ) 13.7 % , d ) 15.1 % , e ) 12.3 %
Rationale: "let the original salary be $ 100 new salary = $ 85 increase on 85 = 15 increase on 100 = 15 / 85 * 100 = 17.6 % answer is b"
Answer: b
Python program:
a = 15 / 100
b = 100 * a
c = 15 / 100
d = 100 * c
e = 100 - d
f = b / e
g = f * 100
Problem: which of the numbers 1 , 2 , 3 , 4 , or 5 is nearest in value to the sum 2007 / 2999 + 8001 / 5998 + 2001 / 3999 = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the sum is a little more than ( 2 / 3 ) + ( 8 / 6 ) + ( 2 / 4 ) = 2.5 . correct answer c
Answer: c
Python program:
a = 5 / 10
b = 2007 / 2999
c = 8001 / 5998
d = b + c 
e = 10 * 100
f = 2999 + e 
g = 2001 / f
h = d + g 
i = a + h
Problem: if jake loses 12 pounds , he will weigh twice as much as his sister . together they now weigh 156 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 108 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 12 = 2 * s also , together they weight 156 pounds j + s = 156 solvong the 2 equation , we get j = 108 pounds ! a"
Answer: a
Python program:
a = 156 - 12
b = a / 3
c = b * 2
d = c + 12
Problem: during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 40 candies for the discounted price of 14 candies . the store still makes a profit of 12 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . e
Answer: e
Python program:
a = 12 / 100
b = a + 1 
c = 20 / 100
d = 1 - c
e = 40 - 14
f = e / 40
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65 , then how long is the base of isosceles triangle ?
Options: a ) 10
b ) 15
c ) 20
d ) 25
e ) 30
Rationale: the base of the isosceles triangle is 65 - 20 - 20 = 25 units the answer is d .
Answer: d
Python program:
a = 60 / 3
b = 65 - a
c = 60 / 3
d = b - c
Problem: the average age of a class of 19 students is 20 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 39 , b ) 41 , c ) 40 , d ) 42 , e ) 43
Rationale: total age of all students = 19 ã — 20 total age of all students + age of the teacher = 20 ã — 21 age of the teacher = 20 ã — 21 â ˆ ’ 20 ã — 19 = 20 ( 21 â ˆ ’ 19 ) = 20 ã — 2 = 40 answer is c .
Answer: c
Python program:
a = 19 + 1 
b = 20 + 1 
c = a * b
d = 19 * 20
e = c - d
Problem: the sum of all the integers d such that - 26 < d < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 d = - 49 . d is the answer ."
Answer: d
Python program:
a = negate + ( 
b = a + 1
Problem: there are 9 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 72
Rationale: "every team plays with 8 teams . . . so total no of matches = 9 x 8 = 72 . now , each match is played twice = > 72 x 2 but 2 teams play a match = > 72 x 2 / 2 = 72 . answer : e"
Answer: e
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
Problem: | x + 1 | – | 4 - x | = | 8 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 3 d"
Answer: d
Python program:
a = 4 + 1 
b = a * 2
c = b / 8
Problem: an electric pump can fill a tank in 6 hours . because of a leak in the tank , it took 12 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 the leak will empty the tank in 12 hours answer is b"
Answer: b
Python program:
a = 12 / 1
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 4 ) both lie on the line defined by the equation x = ( y / 2 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 4 / 5 , b ) 1 , c ) 2 , d ) 5 , e ) 8
Rationale: "( m , n ) m = x n = y m = n / 2 - 2 / 5 10 m = 5 n - 4 ( multiplied by 10 to simplify equation ) ( m + p , n + 4 ) m + p = x n + 4 = y m + p = ( n + 4 ) / 2 - 2 / 5 multiplied by 10 again 10 m + 10 p = 5 n + 20 - 4 use both equations to solve for p and you get 10 p = 20 p = 2 answer : c"
Answer: c
Python program:
a = 4 / 2
Problem: lilly has 10 fish and rosy has 14 fish . in total , how many fish do they have in all ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "10 + 14 = 24 the answer is d ."
Answer: d
Python program:
a = 10 + 14
Problem: 3 years ago , the ratio of ages of p and q was 4 : 3 . 6 years from now , the ratio of their ages will be 7 : 6 . what is p ' s age at present ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: 3 ( p - 3 ) / 4 = ( q - 3 ) . then q = 3 ( p - 3 ) / 4 + 3 6 ( p + 6 ) / 7 = q + 6 6 ( p + 6 ) / 7 = 3 ( p - 3 ) / 4 + 9 24 p + 144 = 21 p + 189 3 p = 45 p = 15 the answer is c .
Answer: c
Python program:
a = 3 + 6 
b = a * 7
c = 3 + 6 
d = c * 6
e = b - d
f = 3 / 4
g = 7 * f
h = 6 - g
i = e / h
j = i + 3
Problem: a student scored an average of 55 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 165 , c ) 76 , d ) 155 , e ) 26
Rationale: "given m + p + c = 55 * 3 = 165 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 165 = 155 answer : d"
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 55 * 3
e = c - d
Problem: a school has received 30 % of the amount it needs for a new building by receiving a donation of $ 500 each from people already solicited . people already solicited represent 60 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 250 , c ) $ 100 , d ) $ 350 , e ) $ 875
Rationale: "let us suppose there are 100 people . 60 % of them donated $ 30000 ( 500 * 60 ) $ 30000 is 30 % of total amount . so total amount = 30000 * 100 / 60 remaining amount is 70 % of total amount . 70 % of total amount = 30000 * ( 100 / 60 ) * ( 70 / 100 ) = 35000 this amount has to be divided by 40 ( remaining people are 40 ) so per head amount is 35000 / 40 = $ 875 ; answer : e"
Answer: e
Python program:
a = 60 / 100
b = a * 500
c = 30 / 100
d = b / c
e = 60 / 100
f = d * e
g = 30 / 100
h = f / g
Problem: if x / y = 4 and y is not ' 0 ' what % of x is 2 x - y
Options: a ) 150 % , b ) 175 percent , c ) 200 % , d ) 250 % , e ) 350 %
Rationale: let z be the percentt x * z / 100 = 2 x - y zx = 7 y * 100 z = 700 y / 4 y z = 350 / 2 z = 175 % answer : b
Answer: b
Python program:
a = 4 + 1 
b = a + 2 
c = 4 + 1 
d = 4 + 1 
e = c * d
f = b * e
Problem: find the principle on a certain sum of money at 11 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 1000 , b ) 812.88 , c ) 827.78 , d ) 826.82 , e ) 886.08
Rationale: "1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 886.08 answer : e"
Answer: e
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 11
e = d / 100
f = e + 1 
g = 1120 / f
Problem: a bowl was filled with 10 ounces of water , and 0.006 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 3 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 006 * 50 = . 006 * 100 / 2 = . 6 / 2 = . 3 percent of the original amount of water evaporated during this period = ( . 3 / 10 ) * 100 % = 3 % answer d"
Answer: d
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: a city with a population of 160,080 is to be divided into 8 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 18,200 , b ) 18,300 , c ) 18,400 , d ) 18,500 , e ) 18,600
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 160,080 = p + 7 ( 1.1 ) p 8.7 p = 160,080 p = 18,400 the answer is c ."
Answer: c
Python program:
a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f 
h = 8 - 1
i = g * h
j = i + 1 
k = e / j
Problem: if the average ( arithmetic mean ) of 18 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 497 , b ) b ) 518 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 18 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 9 th and 10 th numbers in the set ) . this means that numbers 9 and 10 in this set are 413 and 415 . because we know that number 9 is 413 , we know that the smallest number is 8 odd numbers below this , which means that it is 8 * 2 = 16 below this ( every odd number is every other number ) . therefore 413 - 16 = 397 , answer choice a"
Answer: a
Python program:
a = 414 - 18
b = a + 1
Problem: a number x is multiplied by 7 , and this product is then divided by 5 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 7 / 5 , e ) 9 / 25
Rationale: sqrt ( 7 x / 5 ) to be perfect square x has to 7 / 5 ans : d
Answer: d
Python program:
a = 7 / 5
Problem: in a games hour 4 different types of players came to the ground ? cricket 10 , hokey 12 , football 16 , softball 13 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 51 , d ) 49 , e ) 50
Rationale: total number of players = 10 + 12 + 16 + 13 = 51 answer is c
Answer: c
Python program:
a = 10 + 12 
b = 16 + 13 
c = a + b
Problem: calculate 56581 ÷ ? = 137
Options: a ) 113 , b ) 213 , c ) 413 , d ) 417 , e ) 414
Rationale: "answer let 56581 / x = 137 then x = 56581 / 137 = 413 option : c"
Answer: c
Python program:
a = 56581 * 137
Problem: in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag -
Options: a ) 9 / 18 , b ) 9 / 16 , c ) 9 / 11 , d ) 9 / 12 , e ) 9 / 13
Rationale: ( 1 ) put 1 white in first bag , and all the remaining ball in second bag . probability = 12 × 0 + 12 × 51612 × 0 + 12 × 516 = 532532 ( 2 ) to maximize , we put 1 red in the first bag , and all the remaining in the second . probability = 12 × 1 + 12 × 43212 × 1 + 12 × 432 = 9 / 16 answer : b
Answer: b
Python program:
a = 5 + 12 
b = a - 1
c = 5 / b
d = 2 * 2
e = 5 + 12 
f = e - 1
g = d / f
h = c + g
Problem: sandy leaves her home and walks toward ed ' s house . two hours later , ed leaves his home and walks toward sandy ' s house . the distance between their homes is 52 kilometers , sandy ' s walking speed is 6 km / h , and ed ' s walking speed is 4 km / h . how many kilometers will sandy walk before she meets ed ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: sandy walks 12 km in the first two hours so there are 40 km remaining . when ed starts walking , they complete a total of 10 km per hour . they will meet four hours after ed starts walking . since sandy walks for 6 hours , she walks 36 km . the answer is d .
Answer: d
Python program:
a = 2 * 6
b = 52 - a
c = 6 + 4 
d = b / c
e = d * 6
f = 2 * 6
g = e + f
Problem: two bullet train s 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.88 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 190 ) m = 330 m . required time = 330 x 9 / 250 = 54 / 5 = 11.88 sec . answer c"
Answer: c
Python program:
a = 140 + 190 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a customer purchased a package of ground beef at a cost of $ 1.95 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 35 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.50 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.25 , e ) $ 3.50
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.95 . let x be the price per pound for the steak . then 0.65 x = 195 x = 195 / 0.65 = $ 3.00 the answer is c ."
Answer: c
Python program:
a = const_0_25 * 2
b = const_0_33 * 1
c = a + b 
d = 1 / 95
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 4 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 60
Rationale: "actual number of horses = 12,880 / 230 ( hold it since it is a harder calculation ) ratio multiplier = 1288 / ( 23 * 7 ) actual number of sheep = 1288 / ( 23 * 7 ) * 4 . first divide 1288 by 7 to get : 184 * 4 / 23 use the last digit to figure out that 23 will go 8 times into 184 . confirm . 8 * 4 = 32 answer ( c )"
Answer: c
Python program:
a = 4 * 2
b = a * 10
c = 4 * 2
d = c * 100
e = b + d 
f = 12 * 1000
g = e + f 
h = g / 230
i = h / 7
j = i * 4
Problem: there are 8 books on a shelf , of which 2 are paperbacks and 6 are hardbacks . how many possible selections of 3 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 36 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 8 c 3 - 6 c 3 = 36 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 6 c 2 + 2 c 2 * 6 c 1 = 36 answer is c"
Answer: c
Python program:
a = math.comb(8, 3)
b = math.comb(6, 3)
c = a - b
Problem: the ratio of the volumes of two cubes is 729 : 343 . what is the ratio of their total surface areas ?
Options: a ) 81 : 49 , b ) 81 : 122 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 729 : 3 √ 343 = 9 : 7 ratio of surface areas = 9 ^ 2 : 7 ^ 2 = 81 : 49 answer : option a"
Answer: a
Python program:
a = 729 / 343
b = 1 / 3
c = a ** b
Problem: the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 150 , b ) 300 , c ) 299 , d ) 322 , e ) 345
Rationale: "the numbers are ( 10 x 11 ) and ( 10 x 15 ) . larger number = ( 10 x 15 ) = 150 . answer : a"
Answer: a
Python program:
a = 10 * 15