euclaise/mathqa_programs huggingface dataset:
Problem: a carpenter worked alone for 1 day on a job that would take him 7 more days to finish . he and another carpenter completed the job in 4 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 16 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 7 more days . means ; carpenter finishes his work in 8 days . let his buddy finish the same task in x days . respective rates per day : 1 / 8 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 8 per day . second one worked for 4 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 8 + 4 * 1 / x = 1 5 x + 32 = 8 x 2 x = 32 x = 16 days . ans : a"
Answer: a
Python program:
a = 1 + 7 
b = 4 * a
c = b / 2
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 55 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 29 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 55 % means total women in company 45 % ( assume total people in company 100 % ) no of men employees attended picnic = 55 x ( 20 / 100 ) = 11 no of women employees attend picnic = 45 x ( 40 / 100 ) = 18 total percentage of employees attend the picnic = 11 + 18 = 29 % answer : a"
Answer: a
Python program:
a = 55 / 100
b = 20 / 100
c = a * b
d = 100 - 55
e = d / 100
f = 40 / 100
g = e * f
h = c + g 
i = h * 100
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 7 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 3 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 7 or 45 * 18 - 45 * x + 36 * x = 7 * 100 or 9 x = - 7 * 100 + 45 * 18 x = 110 / 9 = 12.2 % e"
Answer: e
Python program:
a = 18 / 100
b = 18 / 100
c = 18 * 2
d = b * c
e = 7 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: how many of the positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 42 - 1 , 2,3 , 6,7 , 14,42 factors of 56 - 1,2 , 4,7 , 8,14 , 28,56 comparing both , we have three factors of 42 which are not factors of 56 - 3 , 6,42 . the answer is 3 . pls check your options again - d $ e are same . answer : c"
Answer: c
Python program:
a = 56 / 42
Problem: if taxi fares were $ 10.00 for the first 1 / 5 mile and $ 1.00 for each 1 / 5 mile there after , then the taxi fare for a 10 - mile ride was
Options: a ) $ 55.10 , b ) $ 59.20 , c ) $ 59.40 , d ) $ 59.00 , e ) $ 55.00
Rationale: "in 10 miles , initial 1 / 5 mile charge is $ 10 rest of the distance = 10 - ( 1 / 5 ) = 49 / 5 rest of the distance charge = 49 ( 1.00 ) = $ 49.00 ( as the charge is 1.00 for every 1 / 5 mile ) = > total charge for 4 miles = 10 + 49.00 = 59.00 answer is d"
Answer: d
Python program:
a = 1 / 5
b = 10 / 0
c = b - 1
d = c * 1
e = 10 + 0
Problem: two cubes of tire sides ratio 2 : 3 . find its cube volumes ratio ?
Options: a ) 2 : 27
b ) 3 : 27
c ) 1 : 27
d ) 8 : 27
e ) 5 : 27
Rationale: a ( power 3 ) : b ( power 3 ) = 2 ( power 3 ) : 3 ( power 3 ) = 8 : 27 answer is d .
Answer: d
Python program:
a = volume_cube / (
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7000 , brokerage being 1 / 4 % , is :
Options: a ) 96.97 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 97.22 . = market value of rs . 100 stock = rs . 97.22 - re . 0.25 . = market value of rs . 100 stock = rs . 96.97 answer : a"
Answer: a
Python program:
a = 7000 / 756
b = a * 10
c = 1 / 4
d = b - c
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3600 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 450 , c ) s . 600 , d ) s . 800 , e ) s . 850
Rationale: c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 3600 ) = rs . 450 answer = b
Answer: b
Python program:
a = 1/(3)
b = 1/(8)
c = 1/(6)
d = b + c 
e = a - d
f = e * 3600
g = f * 3
Problem: in town x , 60 percent of the population are employed , and 15 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 75 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "total employed people 60 % , out of which 15 are employed males , hence 45 % are employed females . ( employed females ) / ( total employed people ) = 45 / 60 = 3 / 4 = 75 % answer : b ."
Answer: b
Python program:
a = 60 - 15
b = a / 60
c = b * 100
Problem: according to a recent student poll , 5 / 6 out of 30 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 1 / 14 , b ) 4 / 49 , c ) 2 / 7 , d ) 28 / 29 , e ) 13 / 14
Rationale: 25 students are interested , 5 are not interested prob = 1 - 5 c 2 / 30 c 2 = 1 - ( 5 * 4 / ( 30 * 29 ) ) = 1 - 20 / 580 = 1 - 1 / 29 = 28 / 29 answer : d
Answer: d
Python program:
a = math.comb(30, 2)
b = 5 / 6
c = 30 * b
d = 30 - c
e = math.comb(d, 2)
f = a - e
g = math.comb(30, 2)
h = f / g
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 80 ?
Options: a ) 24 , b ) 26 , c ) 20 , d ) 22 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 80 4 n < 73 n < 18 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 18 ) combining the two - 1.5 < n < 18.25 n = 1 to 18 ( 18 integers ) and n = - 1 and 0 so 20 integers . c is the answer"
Answer: c
Python program:
a = 80 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: the ratio of pens to pencils is 5 to 6 . there are 6 more pencils than pens . how many pencils are there ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 6 x = 6 the number of pencils is 36 . the answer is b ."
Answer: b
Python program:
a = 6 * 5
b = a + 6
Problem: there is a clock which shows false timing ie it shows 10 minutes less for each 1 hour . . . . if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ?
Options: a ) 16 minutes , b ) 26 minutes , c ) 36 minutes , d ) 46 minutes , e ) 56 minutes
Rationale: for 1 hour , 10 minutes is slower , then for 06 miuntes - 1 minutes is slower 30 minutes - 5 minutes actual time false time 12 12 01 pm 12.50 pm ( 10 minutes slower ) 02 pm 01.40 pm ( 12.50 + 60 min - 10 minutes slower ) 03 pm 02.30 pm ( 01.40 + 60 min - 10 minutes slower ) 03.36 pm 03.00 pm ( 02.30 + 36 min - 6 minutes slower ) so , 36 minutes will be lost when it is showing 3.00 pm . and the actual time is 3.36 pm answer : c
Answer: c
Python program:
a = 3 * const_60
b = const_60 - 10
c = a / b
d = c - 3
e = d * const_60
Problem: in a box of 7 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 7 , e ) 1 / 7
Rationale: "first , there are 5 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 7 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 5 c 3 / 7 c 3 = 10 / 35 = 2 / 7 answer is d"
Answer: d
Python program:
a = 7 - 2
b = math.factorial(a)
c = 7 - 2
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = math.factorial(7)
j = 7 - 3
k = math.factorial(j)
l = math.factorial(3)
m = k * l
n = i / m
o = h / n
Problem: the mean of 50 observations was 36 . it was found later that an observation 90 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 37.3 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 90 - 23 ) = 1867 . correct mean = 1825 / 50 = 37.3 answer : a"
Answer: a
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: how many kilograms of pure water is to be added to 100 kilograms of a 30 % saline solution to make it a 10 % saline solution .
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: let x be the weights , in kilograms , of pure water to be added . let y be the weight , in kilograms , of the 10 % solution . hence x + 100 = y x = 200 kilograms . answer b
Answer: b
Python program:
a = 30 / 100
b = a * 100
c = 10 / 100
d = b / c
e = d - 100
Problem: there is a escalator and 2 persons move down it . a takes 50 steps and b takes 75 steps while the escalator is moving down . given that the time taken by a to take 1 step is equal to time taken by b to take 3 steps . find the no . of steps in the escalator while it is staionary ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e
Answer: e
Python program:
a = 75 / 3
b = 75 + a
Problem: at what price must an article costing rs . 57 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 62.3 , d ) 62.1 , e ) 75
Rationale: "cp = 57 sp = 57 * ( 125 / 100 ) = 71.25 mp * ( 95 / 100 ) = 71.25 mp = 75 answer : e"
Answer: e
Python program:
a = 57 * 25
b = a / 100
c = 57 + b 
d = c * 100
e = 100 - 5
f = d / e
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.2 ) = $ 2.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 2.8 = 3.8 answer is c ."
Answer: c
Python program:
a = 1 / 5
b = 1 / 0
c = b - 1
d = c * 0
e = 1 + 0
Problem: if 3 ^ x * 4 ^ y = 59,049 and x – y = 10 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 59,049 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 10 and y = 0 , then x = 10 . the answer is a ."
Answer: a
Python program:
a = 10 * 1
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 18 seconds . what is the length of the train in meters ?
Options: a ) 180 meters , b ) 1111 meters , c ) 1777 meters , d ) 1822 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 18 seconds distance = speed * time 36000 * 18 / 3600 = 180 meters . a is the answer ."
Answer: a
Python program:
a = 100 - 64
b = a * const_0_2778
c = b * 18
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 11 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 11 x = 45 - - > 10 / 9 * x = 45 - - > x = 45 * 9 / 10 = 1500 / 37 = ~ 41 . answer : d ."
Answer: d
Python program:
a = 100 + 11 
b = 100 / a
c = b * 45
Problem: when you multiply a number by 4 and then subtract 3 , the result is the same as if you first subtracted 7 from the same number and then multiplied by 9 . what is the number ?
Options: a ) a ) 23 , b ) b ) 13 , c ) c ) 19 , d ) d ) 12 , e ) e ) 10
Rationale: let x equal the number and then change the words into an equation and solve for x : 4 x – 3 = 9 ( x – 7 ) 4 x – 3 = 9 x – 63 60 = 5 x 12 = x correct answer d ) 12
Answer: d
Python program:
a = 9 * 7
b = a - 3
c = 9 - 4
d = b / c
Problem: a man can row his boat with the stream at 25 km / h and against the stream in 13 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 6 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 25 us = 13 s = ? s = ( 25 - 13 ) / 2 = 6 kmph answer : c"
Answer: c
Python program:
a = 25 - 13
b = a / 2
Problem: an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is :
Options: a ) 2 , b ) 9 , c ) 8 , d ) 7 , e ) 4
Rationale: explanation : in sixteen kg of alloy 10 kg of zinc and 6 kg copper is present to make the ratio 3 : 1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper so answer is 8 . answer : c
Answer: c
Python program:
a = 5 + 3 
b = 3 / a
c = 10 + 6 
d = b * c
e = d * 3
f = 5 + 3 
g = 5 / f
h = 10 + 6 
i = g * h
j = e - i
Problem: what is the cp of rs 100 stock at 5 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 95.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 5 + 1 / 5 95.2 thus the cp is rs 95.2 . answer : c"
Answer: c
Python program:
a = 100 - 5
b = 1 / 5
c = a + b
Problem: a monkey start climbing up a tree 21 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 18 hrs it wil be 18 ft . but since the height of the tree is 21 ft , so if the monkey hops up the tree in the next hr i . e 19 th hr then it reaches at the top of the tree . hence it takes 19 hrs for monkey to reach at the top answer : c"
Answer: c
Python program:
a = 3 - 2
b = 21 / a
c = b - 2
Problem: john makes $ 50 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 15 % , b ) 16.66 % , c ) 50 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 25 / 50 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c"
Answer: c
Python program:
a = 75 - 50
b = a / 50
c = b * 100
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 6400 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 22888
Rationale: "6400 * 9 / 8 * 9 / 8 = 8100 answer : a"
Answer: a
Python program:
a = 1 / 8
b = a * 6400
c = 6400 + b 
d = 1 / 8
e = 1 / 8
f = e * 6400
g = 6400 + f 
h = d * g
i = c + h
Problem: oil cans x and y are right circular cylinders and the height and radius of y are each thrice those of x . if the oil in can x filled to capacity sells for $ 4 , how much does the oil in y sell for if y is only 1 / 3 rd filled ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 36 , d ) $ 40 , e ) $ 28
Rationale: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 27 * vy y when 1 / 3 rd filled will cost 9 times x so ans is c"
Answer: c
Python program:
a = 4 ** 1
b = a * 4
Problem: an alloy weighing 60 ounces is 20 percent copper . how many ounces of copper must be added to create an alloy that is 60 percent copper ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "an alloy of 60 oz which is 20 % copper means there is 12 oz of gold . to get to an alloy that is 60 % copper , let ' s use this expression : ( 12 + x ) / ( 60 + x ) = 0.60 with x representing the amount of pure copper that must be added to get to 60 % . the expression we are using represents the new total weight of pure copper over the new total weight of the alloy and this fraction should represent 60 % or 0.6 . you will see that 60 is the correct answer , as 72 / 120 = 0.6 choose c"
Answer: c
Python program:
a = 60 / 100
b = a * 60
c = 20 / 100
d = b / c
Problem: by selling 16 pens for a rupee a woman loses 5 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65
Rationale: d 95 % - - - 16 118 % - - - ? 95 / 118 * 16 = 13
Answer: d
Python program:
a = 100 - 5
b = 100 / a
c = b / 16
d = 100 - 5
e = 100 / d
f = e / 16
g = f * 18
h = g / 100
i = c + h 
j = 1/(i)
Problem: a and b complete a work in 30 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1873 days , c ) 0.0673 days , d ) 0.0583 days , e ) 0.0773 days
Rationale: "1 / 30 + 1 / 40 = 0.0583 days answer : d"
Answer: d
Python program:
a = 1/(30)
b = 1/(40)
c = a + b 
d = 1/(c)
Problem: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1200 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 2700 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1200 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1200 - - > { not on display } = 1800 . according to ( i ) 2 / 3 * { total } = 1800 - - > { total } = 2700 . answer : b ."
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1200 / b
d = 1 / 3
e = 1 - d
f = c / e
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12600 after a year ?
Options: a ) 3630 , b ) 3637 , c ) 3630 , d ) 3631 , e ) 3780
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12600 = 3780 answer : e"
Answer: e
Python program:
a = 6300 + 4200 
b = a + 10500 
c = 6300 / b
d = c * 12600
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.45 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 7.30
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.45 ) = $ 6.3 ( as the charge is 0.45 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 6.3 = 7.3 answer is e ."
Answer: e
Python program:
a = 1 / 5
b = 1 / 0
c = b - 1
d = c * 0
e = 1 + 0
Problem: a and b together can do a work in 3 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 4 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 3 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 3 - ( 1 / 12 ) = 4 days answer : option a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 12
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: the distance from city a to city b is 180 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 120 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 45 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 4 hours for the trip . dan needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is b ."
Answer: b
Python program:
a = 180 / 30
b = 120 / const_60
c = a - b
d = 180 / c
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents c watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , c is 21 . d is the correct answer
Answer: d
Python program:
a = 35 / 100
b = a * 600
c = 50 / 100
d = c * 600
e = b + d 
f = 40 / 100
g = f * 600
h = e + g 
i = h - 600
j = 18 / 100
k = j * 600
l = i - k
m = l / 2
Problem: find the lowest positive integer that can be divided by all the even numbers between 14 and 21 .
Options: a ) 4581 , b ) 5040 , c ) 3682 , d ) 1231 , e ) 1563
Rationale: the even numbers between 14 and 21 are 1416 , 1820 . find the lcm of these numbers lcm = 2 ^ 4 * 7 * 3 ^ 2 * 5 the answer is b )
Answer: b
Python program:
a = 14 / 2
b = a + 1 
c = b + 1 
d = math.lcm(10, c)
e = 14 / 2
f = math.lcm(d, e)
g = 14 / 2
h = g + 1 
i = f * h
Problem: by combining number of small cubes , a larger cube is produced . the ratio between volume of larger cube and small cube is 1000 : 8 then how many small cubes are required to produce a larger cube ?
Options: a ) 100
b ) 2
c ) 5
d ) 125
e ) 80
Rationale: the ratio is a 13 : a 23 = 1000 : 8 then number small cubes requiered is 1000 / 8 = 125 so the answre is d
Answer: d
Python program:
a = 1000 / 8
Problem: jacob is now 12 years younger than michael . if 3 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 15 , d ) 21 , e ) 13
Rationale: "jacob = x years , mike = x + 12 years 3 years from now , 2 ( x + 3 ) = x + 15 2 x + 6 = x + 15 x = 9 x + 4 = 13 years answer e"
Answer: e
Python program:
a = 12 + 3 
b = 2 * 3
c = a - b
d = 4 + c
Problem: the area of a triangle will be when a = 2 m , b = 5 m , c = 7 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 2 + 5 + 7 ) / 2 = 7 answer : b"
Answer: b
Python program:
a = 2 + 5 
b = a + 7 
c = b / 5