euclaise/mathqa_programs huggingface dataset:
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability w that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .
Answer: d
Python program:
a = 3 + 2 
b = 4 * 4
c = a / b
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 170 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 650 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 170 = 1700 3 * 100 + 5 * 150 = 1050 1700 – 1050 = 650 b"
Answer: b
Python program:
a = 3 + 5 
b = a + 2 
c = b * 170
d = 5 * 150
e = c - d
f = 3 * 100
g = e - f
Problem: a grocer has a sale of rs . 5266 , rs . 5768 , rs . 5922 , rs . 5678 and rs . 6029 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) 4637 , b ) 4737 , c ) 4937 , d ) 5937 , e ) 5978
Rationale: "total sale for 5 months = rs . ( 5266 + 5768 + 5922 + 5678 + 6029 ) = rs . 28663 . required sale = rs . [ ( 5600 x 6 ) - 28663 ] = rs . ( 33600 - 28663 ) = rs . 4937 . answer : c"
Answer: c
Python program:
a = 5 + 1 
b = a * 5600
c = 5266 + 5768 
d = c + 5922 
e = d + 5678 
f = e + 6029 
g = b - f
Problem: in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 800 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 40 * 100 = 5 % . we are told that 5 % approximates the percent of tagged fish in the pond . since there are 40 tagged fish , then we have 0.05 x = 40 - - > x = 800 . answer : b ."
Answer: b
Python program:
a = 2 / 40
b = 40 / a
Problem: the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e .
Answer: e
Python program:
a = 327 / 2
b = math.floor(a)
c = b + 1
Problem: a report consists of 20 sheets each of 55 lines and each such line consist of 65 characters . this report is retyped into sheets each of 65 lines such that each line consists of 70 characters . the percentage reduction in number of sheets is closest to
Options: a ) 20 , b ) 5 , c ) 30 , d ) 35 , e ) 67
Rationale: explanation : total no of characters = 20 * 55 * 65 . from the problem it is clear that 20 * 55 * 65 = x * 65 * 70 . we get x = 15.6 ∼ 16 because these are sheets . therefore 4 less sheets . hencde , there is 20 % decrease in number of sheets . answer : a
Answer: a
Python program:
a = 20 * 55
b = a * 65
c = b / 70
d = c / 65
e = 20 - d
f = math.floor(e)
g = f * 100
h = g / 20
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio q of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) q = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Python program:
a = 180 - 170
b = 184 - 180
c = a / b
Problem: 8 / 4 / 2 = ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 4 , e ) 1
Rationale: "8 / 4 / 2 = ( 8 / 4 ) / 2 = 2 / 2 = 1 answer is e ."
Answer: e
Python program:
a = 8 / 4
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.00 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is c ."
Answer: c
Python program:
a = 4 - 0
b = a * 100
c = b / 2
Problem: by weight , liquid x makes up 0.7 percent of solution p and 1.2 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.2 % , b ) 1.1 % , c ) 1.0 % , d ) 0.9 % , e ) 0.8 %
Rationale: "the number of grams of liquid x is 0.7 ( 200 ) / 100 + 1.2 ( 800 ) / 100 = 1.4 + 9.6 = 11 grams . 11 / 1000 = 1.1 % the answer is b ."
Answer: b
Python program:
a = 1 * 2
b = a / 100
c = 1 + b 
d = c / 1000
e = d * 100
Problem: a courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 16000 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2000 × 1600 / 20 × 10 ) = 16000 answer : a"
Answer: a
Python program:
a = 20 * 100
b = 16 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: a car takes 4 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 92 kmph , b ) 98 kmph , c ) 90 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "time = 4 distence = 540 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 540 / 6 = 90 kmph c )"
Answer: c
Python program:
a = 4 * 3
b = a / 2
c = 540 / b
Problem: 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275
Options: a ) 107 , b ) 147 , c ) 10 , d ) 296 , e ) none of these
Rationale: "explanation : let 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275 then , 63 * 15 / 5 + x = 61 + 275 63 * 3 + x = 336 189 + x = 336 x = 147 answer b"
Answer: b
Python program:
a = 3 / 8
b = 168 / 5
c = a * b
d = 2 / 0
e = c * d
f = e * 9
Problem: 36 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 44 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 37
Rationale: "( 36 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 80 80 – 36 = 44 answer : a"
Answer: a
Python program:
a = 36 * 8
b = a / 30
c = b * 50
d = c / 6
e = d - 36
Problem: square a has an area of 121 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 121 , d ) 105 / 121 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 121 - 16 = 105 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 105 / 121 . answer : d ."
Answer: d
Python program:
a = 16 / 4
b = a ** 2
c = 121 - b
d = c / 121
Problem: the end of a blade on an airplane propeller is 15 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 450 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 15 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 15 / 5280 = 450 π d is the answer"
Answer: d
Python program:
a = 2 * 100
b = 2 + 3 
c = b * 1000
d = a + c 
e = 15 / d
f = e * 2
g = 2 * 10
h = 2 + g 
i = 3 + 4 
j = h / i
k = f * j
l = k * 1
m = l * const_60
Problem: a man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph , find his average speed for the total journey ?
Options: a ) 5 , b ) 4 , c ) 4.5 , d ) 3.75 , e ) 3
Rationale: "m = 4 s = 1 ds = 5 us = 3 as = ( 2 * 5 * 3 ) / 8 = 3.75 answer : d"
Answer: d
Python program:
a = 4 - 1
b = 4 + a 
c = b / 2
Problem: 20 % of a number is more than 40 % of 140 by 80 . find the number ?
Options: a ) 680 , b ) 620 , c ) 652 , d ) 520 , e ) 458
Rationale: "( 20 / 100 ) * x – ( 40 / 100 ) * 140 = 80 1 / 5 x = 136 x = 680 answer : a"
Answer: a
Python program:
a = 140 * 40
b = a / 100
c = b + 80 
d = c * 100
e = d / 20
Problem: a certain machine produces 550 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 5 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 66,000 , d ) 100,000 , e ) 168,000
Rationale: "since 5 days consist of 24 * 5 hours the total is 120 hours . since every hour the machine produces 550 units of product p the total product during 120 hours is 120 * 550 = 66,000 . correct option : c"
Answer: c
Python program:
a = 4 * 10
Problem: the average salary / head of all the workers ina workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 25
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c
Answer: c
Python program:
a = 7 * 1000
b = 7 * 780
c = a - b
d = 850 - 780
e = c / d
Problem: the average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 3 kg = > ( 80 - x ) / 6 = 3 = > x = 62 answer : a"
Answer: a
Python program:
a = 6 * 3
b = 80 - a
Problem: if 20 honey bees make 20 grams of honey in 20 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 30
Rationale: explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 20 : : 20 : x honey 20 : 1 = > 1 x 20 x x = 20 x 1 x 20 = > x = 20 . answer : c
Answer: c
Python program:
a = 1 / 20
b = 1 / a
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 60 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 7 : 15 , b ) 7 : 10 , c ) 7 : 8 , d ) 7 : 4 , e ) 7 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 60 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.60 = $ 36 cost = 36 / 1.6 = $ 22.5 if he wants a 60 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 22.5 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 22.5 / 33 = 15 / 22 of a liter . if milk is 15 / 22 of the liter , then water is 7 / 22 of the liter , and the ratio of water to milk is 7 : 15 . answer choice ( a )"
Answer: a
Python program:
a = 100 + 60 
b = a / 100
c = 36 / b
d = 33 - c
e = 100 + 60 
f = e / 100
g = 36 / f
h = d / g
Problem: in town x , 65 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 27 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 65 % , out of which 48 are employed males , hence 17 % are employed females . ( employed females ) / ( total employed people ) = 17 / 64 = 27 % answer : b ."
Answer: b
Python program:
a = 65 - 48
b = a / 65
c = b * 100
Problem: out of 3 consecutive odd numbers 9 times the first number is equal to addition of twice the third number and adding 9 to twice the second . what is the first number ?
Options: a ) 20 / 21 , b ) 23 / 25 , c ) 24 / 23 , d ) 22 / 5 , e ) 21 / 5
Rationale: description : = > 9 x = 2 ( x + 2 ) + 9 + 2 ( x + 4 ) = > 9 x = 4 x + 21 = > 5 x = 21 x = 21 / 5 answer e
Answer: e
Python program:
a = 9 * 3
b = 2 * 3
c = a - b
d = 3 + 2 
e = c / d
Problem: find the lcm of 23 , 46,827
Options: a ) 227 , b ) 83 , c ) 23 , d ) 827 , e ) none of these
Rationale: explanation : whenever we have to solve this sort of question , remember the formula . lcm = \ \ begin { aligned } \ \ frac { hcf of denominators } { lcm of numerators } \ \ end { aligned } so answers will be option 2 , please also give attention to the difference in formula of hcf and lcm answer : option b
Answer: b
Python program:
a = 23 * 4
b = a - 4
c = b - 4
d = c - 1
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 42 liters of forest green to change it to verdant green ?
Options: a ) 14 , b ) 12 , c ) 15 , d ) 11 , e ) 10
Rationale: "42 liter of forset green have 24 liter of blue and 18 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 24 / ( 18 + x ) = ¾ 54 + 3 x = 96 = > x = 14 answer : a"
Answer: a
Python program:
a = 4 / 3
b = a * 4
c = b - 3
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 300,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,250 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 300000 [ 1 ] 0.04 x = 0.80 * 300000 = 240000 [ 2 ] 240000 + 0.09 y = 300000 - - > 0.09 y = 60000 [ 3 ] 240000 / 12 = 20000 [ 4 ] 60000 / 12 = 5000 [ 5 ] adding [ 4,5 ] we get : 25000 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.25 , ans a"
Answer: a
Python program:
a = 4 * 2
b = 9 - a
Problem: 1,2 , 3,2 , 4,6 , 4,8 , _____
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "divide the series : 1 , 2,3 2 , 4,6 4,8 , ? so it is 12 answer : c"
Answer: c
Python program:
a = negate - (
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 312 votes . find the number of votes casted to the winning candidate ?
Options: a ) 806 , b ) 744 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 312 62 % - - - - - - - - ? = > 806 answer : a"
Answer: a
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 312 / c
e = d * 62
f = e / 100
Problem: 5358 x 52 = ?
Options: a ) 272258 , b ) 272358 , c ) 278616 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 2 ) = 5358 x 50 + 5358 x 2 = 267900 + 10716 = 278616 . c )"
Answer: c
Python program:
a = 5358 / 52
b = a * 100
Problem: if x / ( 9 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 54 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 9 p ) = odd prime number x = odd prime number * 9 p least value of x = lowest odd prime number * 9 * lowest value of p = 3 * 9 * 2 = 54 answer a"
Answer: a
Python program:
a = 3 * 9
b = a * 2
Problem: rs . 900 is divided among maya , annie , saiji so that maya receives half as much as annie and annie half as much as saiji . then saiji ’ s share is :
Options: a ) rs . 200 , b ) rs . 300 , c ) rs . 400 , d ) rs . 600 , e ) rs . 500
Rationale: let saiji = x . then , annie = x / 2 and maya = x / 4 . therefore , maya : annie : saiji = x / 4 : x / 2 : x = 1 : 2 : 4 . therefore , saiji ’ s share = rs . 900 * 4 / 9 = rs . 400 . answer : c
Answer: c
Python program:
a = 900 / 100
b = 4 / a
c = 900 * b
Problem: a company has two models of computers , model m and model n . operating at a constant rate , a model m computer can complete a certain task in 24 minutes and a model n computer can complete the same task in 12 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model m computers were used ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 6
Rationale: let ' s say 1 work is processing 24 gb of data . model m : 1 gb per min model n : 2 gb per min working together , 1 m and 1 n = 3 gb per min so , 8 times as many computers would work at 18 gb per min . so no . of m = 8 answer is d
Answer: d
Python program:
a = 1/(12)
b = 1/(24)
c = a + b 
d = 1/(c)
Problem: a and b together can do a work in 4 days . a alone can do it in 20 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 20 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 20 ) = 5 days answer : option e"
Answer: e
Python program:
a = 1 / 4
b = 1 / 20
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: in a kilometer race , a beats b by 200 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 180 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 40 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 200 = 50 sec . time taken by a = 50 - 10 = 40 sec . answer : e"
Answer: e
Python program:
a = 1 * 1000
b = 200 / 10
c = a / b
d = c - 10
Problem: if a car went the first third of the distance at 80 kmh , the second third at 15 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 30 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 15 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 15 * t 2 = 16 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 24 hrs d = rt ( 240 * 3 ) = r * 24 r = 30 answer : a"
Answer: a
Python program:
a = 1 / 80
b = 1 / 15
c = a + b 
d = 1 / 48
e = c + d 
f = 3 / e
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 15,000 , e ) none
Rationale: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d
Answer: d
Python program:
a = 1 + 4 
b = a * 1000
c = b * 2
d = c / 6
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 100 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 100 5 x - 20 = 100 5 x = 120 x = 24 the answer is a .
Answer: a
Python program:
a = 2 + 2 
b = 2 + a 
c = 2 + 2 
d = c + 2 
e = b + d 
f = 2 + 2 
g = f + 2 
h = g + 2 
i = e + h 
j = 100 - i
k = j / 5
l = 2 + 2 
m = l + 2 
n = m + 2 
o = k + n
Problem: an article is bought for rs . 600 and sold for rs . 900 , find the gain percent ?
Options: a ) 33 1 / 7 % , b ) 33 1 / 6 % , c ) 50 % , d ) 38 1 / 3 % , e ) 33 2 / 3 %
Rationale: "600 - - - - 300 100 - - - - ? = > 50 % answer : c"
Answer: c
Python program:
a = 900 * 100
b = a / 600
c = 100 - b
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 7 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n = 8 mark sold 1 box and ann sold 6 boxes total 7 < 8 answer : e"
Answer: e
Python program:
a = 7 + 1
Problem: total 15 cows 5 cow gives each 2 liter milk 5 cow gives each 3 / 4 liter milk 5 cow gives each 1 / 4 liter milk this is split into 3 son per each 5 cows & 5 liter milk how ?
Options: a ) 10 , b ) 5 , c ) 15 , d ) 7.5 , e ) 12.5
Rationale: "5 cow 2 liter each = 10 liter 5 cow 3 / 4 liter each = 3 / 4 = 0.75 * 5 = 3.75 5 cow 1 / 4 liter each = 1 / 4 = 0.25 * 5 = 1.25 add 10 + 3.75 + 1.25 = 15 milk split into 3 son each 5 liter then 15 / 3 = 5 answer : b"
Answer: b
Python program:
a = 3 / 4
b = 3 / 4
c = b * 5
d = a + c 
e = const_0_25 * 5
f = d + e
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 19 = f ( x – 4 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 2 ( 3 x - 5 ) - 19 = 3 ( x - 4 ) - 5 3 x = 12 x = 4 the answer is b .
Answer: b
Python program:
a = 2 * 5
b = a + 19 
c = 3 * 4
d = c + 5 
e = b - d
f = 2 * 3
g = 3 * 1
h = f - g
i = e / h
Problem: a committee is reviewing a total of 20 x black - and - white films and 8 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 40 / 41 , b ) 20 / 41 , c ) 30 / 41 , d ) 60 / 41 , e ) 80 / 41
Rationale: "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 8 y = 80 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 80 color films , thus total of 82 films were selected . color films thus compose 80 / 82 = 40 / 41 of the selected films . answer : a"
Answer: a
Python program:
a = 20 / 100
b = a + 8 
c = 8 / b
Problem: if | 4 x + 2 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 1 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 2 = 46 or 4 x + 2 = - 46 = > x = 11 or x = - 12 sum of both the values will be - 12 + 11 = - 1 answer is b"
Answer: b
Python program:
a = 46 - 2
b = a / 4