euclaise/mathqa_programs huggingface dataset:
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 30 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 30 = 70 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 70 / 100 ) * 100 = ( 0.7 ) * 100 = 70 % . d"
Answer: d
Python program:
a = 100 - 30
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 5 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 4 , e ) 0
Rationale: "5 ” 3 = 9 - 5 = 4 answer : d"
Answer: d
Python program:
a = 3 ** 2
b = a - 5
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 44 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 39 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 2640 ( this number is convenient because it is divisible by 80 , 24 and 44 ) so : 2640 = 80 * t 1 = 33 hrs 2640 = 24 * t 2 = 110 hrs 2640 = 44 * t 3 = 60 hrs t = t 1 + t 2 + t 3 = 203 hrs d = rt ( 2640 * 3 ) = r * 203 r = 39 answer : a"
Answer: a
Python program:
a = 1 / 80
b = 1 / 24
c = a + b 
d = 1 / 44
e = c + d 
f = 3 / e
Problem: there are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 312 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 312 / 24 = 17 + 13 = 30 answer : d"
Answer: d
Python program:
a = 408 + 312 
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
Problem: in 20 years , a will be twice as old as b was 20 years ago . if a is now 10 years older than b , the present age of b is ?
Options: a ) 35 yrs , b ) 40 yrs , c ) 50 yrs , d ) 60 yrs , e ) 70 yrs
Rationale: "let b ' s present age = x years then a ' s present age = x + 10 years x + 10 + 20 = 2 ( x - 20 ) x + 30 = 2 x - 40 x = 70 years answer is e"
Answer: e
Python program:
a = 2 * 20
b = a + 20 
c = b + 10
Problem: a boat running downstream covers a distance of 44 km in 8 hours while for covering the same distance upstream , it takes 10 hours . what is the speed of the boat in still water ?
Options: a ) 5 kmph , b ) 4.95 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "explanation : speed downstream = 44 / 8 = 5.5 kmph speed upstream = 44 / 10 = 4.4 kmph speed of the boat in still water = ( 5.5 + 4.4 ) / 2 = 4.95 kmph answer : option b"
Answer: b
Python program:
a = 44 / 8
b = 44 / 10
c = a + b 
d = c / 8
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 105 , how much more remains to be paid ?
Options: a ) $ 945 , b ) $ 965 , c ) $ 1025 , d ) $ 1050 , e ) $ 1105
Rationale: "90 % remains to be paid so the remaining amount is 9 * 105 = $ 945 . the answer is a ."
Answer: a
Python program:
a = 100 / 10
b = 105 * a
c = b - 105
Problem: the volume v of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e
Answer: e
Python program:
a = square_area * (
Problem: calculate the dividend from caleb ' s stock , if caleb he invested rs . 2500 at 79 to obtain an income of rs . 200 .
Options: a ) 6.32 , b ) 5.32 , c ) 7.32 , d ) 2.32 , e ) 1.32
Rationale: by investing rs . 2500 , income = rs . 200 by investing rs . 79 , income = 200 ã — 79 / 2500 = 6.32 ie , dividend = 6.32 % answer is a .
Answer: a
Python program:
a = 2500 / 79
b = 200 / a
Problem: in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10,800 petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000
Rationale: 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Answer: c
Python program:
a = 100 * 100
b = a * 100
c = 5 * 4
d = 100 * 100
e = 4 * 2
f = e * 100
g = d + f 
h = c / g
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent r should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked r will be 25 % greater than the original number . the answer is c ."
Answer: c
Python program:
a = 10 * 4
b = 100 - 20
c = b / 100
d = c * 10
e = a / d
f = e - 4
g = f / 4
h = g * 100
Problem: at what rate percent per annum will a sum of money double in 16 years .
Options: a ) 2.45 % , b ) 5.62 % , c ) 5.35 % , d ) 6.9 % , e ) 6.25 %
Rationale: "let principal = p then s . i . = p t = 16 yrs rate = ( 100 * p ) / ( p * 16 ) = 25 / 4 = 6.25 % p . a . answer is e"
Answer: e
Python program:
a = 100 / 16
Problem: a grocery shop has a sale of rs . 6535 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4891 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6535 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6535 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34109 + x = 39000 = > x = 39000 − 34109 = 4891 answer : d"
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6535 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: how many times will the digit 7 be written when listing the integers from 1 to 1000 ?
Options: a ) 110 , b ) 111 , c ) 271 , d ) 300 , e ) 304
Rationale: another approach : in the range 0 - 100 : 7 as units digit - 10 times ( 7 , 17 , 27 , . . . , 97 ) ; 7 as tens digit - 10 time ( 71 , 72 , 73 , . . . , 79 ) ; so in first one hundred numbers 7 is written 10 + 10 = 20 times . in 10 hundreds 7 as units or tens digit will be written 10 * 20 = 200 times . plus 100 times when 7 is written as hundreds digit ( 700 , 701 , 702 , . . . , 799 ) . total 200 + 100 = 300 . answer : d .
Answer: d
Python program:
a = 1 * 10
b = a * 10
c = b * 3
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 8 inches by 15 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "area of first rectangle is 8 * 15 = 120 hence area of second would be 4 x = 120 x x = 30 answer is d"
Answer: d
Python program:
a = rectangle_area / (
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8450 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4700 , d ) 2981 , e ) 2711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8450 = 33800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1800 salary of may is rs . 6500 salary of january = rs . 4700 . answer : c"
Answer: c
Python program:
a = 8000 * 4
b = 8450 * 4
c = b - 6500
d = a - c
Problem: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 45 more than the correct answer . find the number .
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 45 25 x = 16 x + 900 9 x = 900 x = 100 the answer is c ."
Answer: c
Python program:
a = 4 / 5
b = 45 * a
c = 4 / 5
d = b * c
e = 4 / 5
f = 4 / 5
g = e * f
h = 1 - g
i = d / h
j = 4 / 5
k = i / j
Problem: a quiz has one mcq question with a , b and c as options . and two questions with true / false answers . what is the probability of giving all 3 answers correct ?
Options: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 6
Rationale: probability of getting mcq answer correct = 1 / 3 probability of getting one true / false answer correct = 1 / 2 probability of getting all 3 answers correct = 1 / 3 * 1 / 2 * 1 / 2 = 1 / 12 answer : a
Answer: a
Python program:
a = 1 / 2
b = 1 / 3
c = 1 / 2
d = b * c
e = a * d
Problem: what is the sum of natural numbers between 90 and 100
Options: a ) 1045 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 90 and 100 numbers = 11 = > 100 - 90 = 10 + 1 = 11 sn = 11 / 2 ã — 190 = 11 ã — 95 = 1045 answer : a"
Answer: a
Python program:
a = 100 + 1
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 30 m , b ) 28 m , c ) 26 m , d ) 24 m , e ) 22 m
Rationale: "explanation : between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 1 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 × 2 ) + 1 + 1 = 24 meter answer : d"
Answer: d
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: in the manufacture of a certain product , 9 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.36 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: percent of defective produced = 9 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 9 / 100 ) * 100 % = ( 36 / 10000 ) * 100 % = ( 36 / 100 ) % = . 36 % answer b
Answer: b
Python program:
a = 4 / 100
b = 9 * a
Problem: 70 students are required to paint a picture . 52 use green color and some children use red , 38 students use both the colors . how many students use red color ?
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: 70 = red + green - both red = 70 - green + both = 70 - 52 + 38 = 56 answer : d
Answer: d
Python program:
a = 70 - 52
b = a + 38
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1245 , find the loss % ?
Options: a ) 17 % , b ) 16 % , c ) 19 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 255 100 - - - - ? = > 17 % answer : a"
Answer: a
Python program:
a = 1500 - 1245
b = a / 1500
c = b * 100
Problem: a person buys an article at $ 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 560 , b ) 449 , c ) 600 , d ) 740 , e ) 460
Rationale: "c 600 cost price = $ 500 profit = 20 % of 500 = $ 100 selling price = cost price + profit = 500 + 100 = 600"
Answer: c
Python program:
a = 20 / 100
b = 500 * a
c = 500 + b
Problem: ramu bought an old car for rs . 36400 . he spent rs . 8000 on repairs and sold it for rs . 68400 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 54 % , e ) 13 %
Rationale: "total cp = rs . 36400 + rs . 8000 = rs . 44400 and sp = rs . 68400 profit ( % ) = ( 68400 - 44400 ) / 44400 * 100 = 54 % answer : d"
Answer: d
Python program:
a = 36400 + 8000 
b = 68400 - a
c = 36400 + 8000 
d = b / c
e = d * 100
Problem: i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a gain ?
Options: a ) a ) 657 , b ) b ) 200 , c ) c ) 438 , d ) d ) 290 , e ) e ) 427
Rationale: "x = price of a book sold at loss x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 price of book sold at gain = 480 - 280 = 200 answer : b"
Answer: b
Python program:
a = 100 + 19 
b = 480 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: a ladder 25 m long reaches a window of building 20 m above the ground . then the distance of the foot of the ladder from the building is ?
Options: a ) 35 m , b ) 45 m , c ) 30 m , d ) 15 m , e ) 25 m
Rationale: let it forms a right angled triangle and follow c ^ 2 = a ^ 2 + b ^ 2 then 25 ^ 2 = 20 ^ 2 + b ^ 2 b ^ 2 = 625 - 400 b = 15 answer : d
Answer: d
Python program:
a = 25 ** 2
b = 20 ** 2
c = a - b
d = math.sqrt(c)
Problem: when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 134.08 , what is value of j ?
Options: a ) 125 , b ) 56 , c ) 78 , d ) 112 , e ) 175
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 = 10 so , 134.08 = 134 + 10 / j so , j = 125 ans a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 8
e = 10 / d
Problem: when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 204.03 , what is value of j ?
Options: a ) 600 , b ) 200 , c ) 400 , d ) 800 , e ) 1000
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 = 204.03 here 204 is the quotient . given that remainder = 18 so , 204.03 = 204 + 18 / j so , j = 600 answer : a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 204 - 3
e = 18 / d
Problem: if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 4 + 8 = ?
Options: a ) 125 , b ) 126 , c ) 127 , d ) 128 , e ) 129
Rationale: 2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 4 ^ 3 + 8 ^ 2 = 128 answer : d
Answer: d
Python program:
a = 4 ** 3
b = 8 ** 2
c = a + b
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.4 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.3 ( 6 ) = 1.8 gallons at the start , the amount of water is 0.7 ( 6 ) = 4.2 gallons after 6 hours , the amount of water is 4.2 - 0.4 ( 6 ) = 1.8 gallons the concentration of water is 1.8 / ( 1.8 + 1.8 ) = 1.8 / 3.6 = 50 % the answer is e ."
Answer: e
Python program:
a = 100 - 30
b = 6 * a
c = b / 100
d = 0 * 4
e = c - d
f = 0 * 4
g = 6 - f
h = e / g
i = h * 100
Problem: by selling 20 pencils for a rupee a man loses 35 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 14 , e ) 10
Rationale: 65 % - - - 20 130 % - - - ? 65 / 130 * 20 = 10 answer : e
Answer: e
Python program:
a = 100 + 30 
b = 100 - 35
c = 1 / b
d = a * c
e = 1 / d
f = e * 20
Problem: 1804 x 1804 = ?
Options: a ) a ) 3254416 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1804 x 1804 = ( 1804 ) 2 = ( 1800 + 4 ) 2 = ( 1800 ) 2 + ( 4 ) 2 + ( 2 x 1800 x 4 ) = 3240000 + 16 + 14400 . = 3254416 . a )"
Answer: a
Python program:
a = 1804 / 1804
b = a * 100
Problem: in order to obtain an income of rs . 500 from 30 % stock at rs . 90 , one must make an investment of
Options: a ) rs . 1550 , b ) rs . 1430 , c ) rs . 1450 , d ) rs . 1400 , e ) rs . 1500
Rationale: "explanation : market value = rs . 90 required income = rs . 500 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 30 ( ie , 30 % of the face value 100 ) , investment = rs . 90 to obtain rs . 15000 , investment = 90 / 30 ã — 500 = rs . 1500 answer : option e"
Answer: e
Python program:
a = 90 / 30
b = a * 500
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Python program:
a = 72 / 2
b = math.sqrt(a)
c = b * 2
Problem: the value of ( 2.502 + 0.064 ) ^ 2 - ( 2.502 - 0.064 ) ^ 2 / 2.502 * 0.064
Options: a ) . 25 , b ) . 235 , c ) 4 , d ) 3 , e ) 2
Rationale: "( 2.502 + 0.064 ) 2 - ( 2.502 - 0.064 ) 2 / 2.502 * 0.064 = ( a + b ) 2 - ( a - b ) / ab = 4 ab / ab = 4 answer : c"
Answer: c
Python program:
a = 2 + 502 
b = a ** 2
c = 2 - 502
d = c ** 2
e = b - d
f = 2 * 502
g = e / f
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 320 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 267 , d ) 20 , e ) 27
Rationale: a + b + c = 500 a + c = 200 b + c = 320 - - - - - - - - - - - - - - a + b + 2 c = 520 a + b + c = 500 - - - - - - - - - - - - - - - - c = 20 answer : d
Answer: d
Python program:
a = 200 + 320 
b = a - 500
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 18 ) ?
Options: a ) - 8 , b ) 10 , c ) 12 , d ) - 4 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 18 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , - 16 , and - 18 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) + ( - 18 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 = 58 - 62 = - 4 hence the correct answer choice is d ."
Answer: d
Python program:
a = 6 - 8
Problem: car a runs at the speed of 70 km / hr & reaches its destination in 10 hr . car b runs at the speed of 35 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 13 : 7 , d ) 15 : 7 , e ) 2 : 1
Rationale: "sol . distance travelled by car a = 70 × 10 = 700 km distance travelled by car b = 35 × 10 = 350 km ratio = 700 / 350 = 2 : 1 answer : e"
Answer: e
Python program:
a = 70 * 10
b = 35 * 10
c = a / b
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 50 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 120 , c ) 140 , d ) 147 , e ) 98
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 50 t t = 2.8 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 2.8 = 98 miles answer : - e"
Answer: e
Python program:
a = 72 / const_60
b = a * 35
c = 50 - 35
d = b / c
e = 35 * d
Problem: a and b together can do a work in 4 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 6 , c ) 77 , d ) 55 , e ) 21
Rationale: 1 / 4 – 1 / 12 = 1 / 6 = > 6 answer : b
Answer: b
Python program:
a = 1 / 4
b = 1 / 14
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 6 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 2 / 3 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 6 x = 5 / 6 x so if gold card balance is transferred then the rest unspent will be 5 / 6 x - x / 6 = 2 / 3 x so the ans is a"
Answer: a
Python program:
a = 1/(3)
b = 1/(2)
c = a * b
d = 1/(6)
e = c + d 
f = 1 - e
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 2 = 2 / 1 = 2 : 1 answer is b"
Answer: b
Python program:
a = 2 / 3
b = 2 / 3
c = 6 / 3
d = b * c
e = a * d
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 30 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 7 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 30 pm + 2 hrs = 7 : 30 pm answer : b . 7 : 30
Answer: b
Python program:
a = 5 + 2 
b = a / 30
Problem: you cook a pot of beef stew for you and your roommate . normally it lasts 7 days between the two of you . if 3 guests are now staying with you and your roommate , how many days will the beef stew now last if everyone eats it ?
Options: a ) 2.8 , b ) 1 , c ) 3.5 , d ) 14 , e ) 1.6
Rationale: first set up a ratio with all the relevant values and also the unknown variable : 2 * 7 = 5 * x now solve by multiplying 2 by 7 and then dividing that product by 5 : 2 * 7 = 14 14 / 5 = x x = 2.8 the value of x represents the amount of days a bot of beef stew will last for 5 total people . answer : a
Answer: a
Python program:
a = 7 * 2
b = 1 / a
c = 2 + 3 
d = b * c
e = 1 / d
Problem: a person can swim in still water at 12 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 2 us = 12 - 2 = 10 d = 10 t = 10 / 10 = 1 answer : a"
Answer: a
Python program:
a = 12 - 2
b = 10 / a