euclaise/mathqa_programs huggingface dataset:
Problem: if 73 ! has 16 zeroes at the end , how many zeroes will 80 ! have at the end ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: prime factoring : you need a 2 and a 5 to make a 10 ( a ` ` zero ' ' ) , and there are tons of 2 ' s so let ' s skip these and focus on the ( rarer ) 5 s : 80 ! = 1 * 2 * 3 * 4 * 5 * 6 . . . * 78 * 79 * 80 since there are 80 consecutive numbers , there are 16 multiples of 5 in there , but if we ' re prime factoring , we need to remember that some multiples of 5 actually contain more than just one 5 . which ? 25 comes to mind - - it ' s got two of them ! so all the multiples of 25 actually contain two 5 ' s ( ie : 50 and 75 ) so , to recap , we have 16 of them , plus 3 more ( the additional 5 ' s in 25 , 50 , and 75 ) , so that makes 19 , and since we have more than enough 2 ' s , we know our number will have exactly 19 zeros at the end . answer : d
Answer: d
Python program:
a = 10 / 2
b = 80 / a
c = b + 3
Problem: in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."
Answer: a
Python program:
a = 2 * 3
b = 10 * a
c = 1990 + b
Problem: 6 bells commence tolling together and toll at the intervals of 24 , 68 , 1012 seconds resp . in 60 minutes how many times they will toll together .
Options: a ) 15 , b ) 16 , c ) 30 , d ) 31 , e ) none of these
Rationale: explanation : lcm of 2 - 4 - 6 - 8 - 10 - 12 is 120 seconds , that is 2 minutes . now 60 / 2 = 30 adding one bell at the starting it will 30 + 1 = 31 answer : option d
Answer: d
Python program:
a = 60 * const_60
b = 10 + 2 
c = b * 10
d = a / c
Problem: in a full deck of 52 cards , there are 13 spades . a game is played whereby a card from is chosen at random from the deck . if the card is a spade , a winner is declared . if the card is not a spade , it is returned to the deck , the deck is reshuffled and another card is drawn . this process is repeated until a spade is drawn . what is the probability that one will pick the first spade on the second draw or later ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 4 , e ) 7 / 8
Rationale: favorable case = the spade is picked in the third draw or later unfavorable case = the spade is picked in either first draw or in second draw probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case : probability of spade picked in first draw = 13 / 52 = 1 / 4 i . e . , favorable probability = 1 - ( 1 / 4 ) = 3 / 4 answer option : d
Answer: d
Python program:
a = 13 / 52
b = 1 - a
Problem: of 600 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 75
Rationale: say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 600 = 1.25 b + b - 0.25 b - - > b = 300 , a = 1.25 b = 375 and { both } = 0.25 b = 75 . the number of students who read only book a is { a } - { both } = 375 - 75 = 300 ; the number of students who read only book b is { b } - { both } = 300 - 75 = 225 ; the difference is 300 - 225 = 75 . answer : e .
Answer: e
Python program:
a = 25 / 100
b = 20 / 100
c = a / b
d = c + 1 
e = 25 / 100
f = d - e
g = 600 / f
h = 25 / 100
i = 20 / 100
j = h / i
k = g * j
l = 20 / 100
m = 1 - l
n = k * m
o = 25 / 100
p = 20 / 100
q = o / p
r = q + 1 
s = 25 / 100
t = r - s
u = 600 / t
v = 25 / 100
w = 1 - v
x = u * w
y = n - x
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4340 , r will receive
Options: a ) 600 , b ) 700 , c ) 840 , d ) 900 , e ) none of these
Rationale: explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4340 * ( 6 / 31 ) = 140 * 6 = 840 . answer : option c
Answer: c
Python program:
a = 4 + 1 
b = 10 + a 
c = b + 10 
d = c + 6 
e = 6 / d
f = 4340 * e
Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are red balls ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 5 / 12 , d ) 5 / 24 , e ) 7 / 24
Rationale: "the number of ways of choosing 3 balls from the jar is 10 c 3 = 120 . the number of ways of choosing 3 red balls is 6 c 3 = 20 . p ( 3 red balls ) = 20 / 120 = 1 / 6 . the answer is b ."
Answer: b
Python program:
a = math.comb(4, 3)
b = 6 + 4 
c = math.comb(b, 3)
d = a / c
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 100 ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 25 , e ) 26
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 < 100 4 n < 93 n < 23 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 23 ) combining the two - 1.5 < n < 23.25 n = 1 to 23 ( 23 integers ) and n = - 1 and 0 so 25 integers . d is the answer"
Answer: d
Python program:
a = 100 - 7
b = a / 4
c = math.floor(b)
d = 1 - 7
e = d / 4
f = math.floor(e)
g = c - f
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 25 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 50 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 30 hence , the correct answer is c"
Answer: c
Python program:
a = 25 * 2
b = 10 * 2
c = a - b
Problem: if the population of a certain country increases at the rate of one person every 25 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 144 , d ) 180 , e ) 160
Rationale: "answer = 2.4 * 60 = 144 answer is c"
Answer: c
Python program:
a = const_60 / 25
b = a * 1
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 912 , d ) 1200 , e ) 775
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 300 62 % - - - - - - - - ? = > 775 answer : e"
Answer: e
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 300 / c
e = d * 62
f = e / 100
Problem: 10 percent of ram ' s monthly salary is equal to 8 percent of shyam ' s monthly salary . shyam ' s monthly salary is twice abhinav ' s monthly salary . if abhinav ' s annual salary is rs . 1.92 lakhs , find ram ' s monthly salary ?
Options: a ) rs . 18000 , b ) rs . 20000 , c ) rs . 25600 , d ) rs . 32000 , e ) none of these
Rationale: let the monthly salaries of ram and shyam be rs . r and rs . s respectively . 10 / 100 r = 8 / 100 s r = 4 / 5 s monthly salary of abhinav = ( 1.92 lakhs ) / 12 = rs . 0.16 lakhs s = 2 ( 0.16 lakhs ) = 0.32 lakhs r = 4 / 5 ( 0.32 lakhs ) = rs . 25600 answer : c
Answer: c
Python program:
a = 8 * 100
b = 1 / 92
c = b * 2
d = a * c
e = 100 * 10
f = d / e
g = f * 100
h = g * 1000
Problem: during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 10 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 . b"
Answer: b
Python program:
a = 12 / 100
b = a + 1 
c = 20 / 100
d = 1 - c
e = 20 - 10
f = e / 20
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: if the selling price of 50 articles is equal to the cost price of 25 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 50 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 25 . loss % = 25 / 50 * 100 = 50 % answer e"
Answer: e
Python program:
a = 50 - 25
Problem: when the bus started from the first bus stop , the number of male passengers to the number of female passengers was 1 : 3 . at the first stop , 16 passengers got down and 6 more female passengers got in . the ratio of the male to female passengers now became 1 : 2 . what was the total number of passengers in the bus when it started from the first stop ?
Options: a ) 64 , b ) 48 , c ) 54 , d ) 46 , e ) can not be determined
Rationale: let , initially the number of males and females in the bus be ’ x ’ and ’ 3 x ’ respectively . at the first stop , suppose ’ m ’ males and ’ f ’ females left the bus . therefore at the first stop the number of males is ’ x - m ’ and the number of females is ’ ( 3 x - f ) + 6 ’ therefore ( x - m ) / [ ( 3 x - f ) + 6 ] = 1 / 2 = > 2 x - 2 m = 3 x - f + 6 also m + f = 16 x = 26 - f as we have 3 variable and 2 equations , a definite value can not be determined . answer : e
Answer: e
Python program:
a = 3 + 1 
b = 16 / a
c = b * 2
d = negate - (
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 15 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 85 % ( 100 - 15 ) . therefore 0.5 x amount of flower - nectar = 0.85 x amount of honey = 0.85 x 1 kg therefore amount of flower - nectar needed = ( 0.85 / 0.51 ) kg = 1.7 kgs answer : c"
Answer: c
Python program:
a = 100 - 15
b = a / 100
c = 50 / 100
d = b / c
Problem: a batsman scored 90 runs which included 2 boundaries and 7 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 30 % , b ) 40 % , c ) 44.44 % , d ) 60 % , e ) 80 %
Rationale: "explanation : number of runs made by running = 90 - ( 2 x 4 + 7 x 6 ) = 90 - ( 50 ) = 40 now , we need to calculate 40 is what percent of 90 . = > 40 / 90 * 100 = 44.44 % option c"
Answer: c
Python program:
a = 2 * 7
b = 7 * 2
c = a + b 
d = 90 - c
e = d / 90
f = e * 100
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability w that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability w = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b
Answer: b
Python program:
a = math.comb(10, 3)
b = 10 + 10 
c = math.comb(b, 3)
d = a / c
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and further to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 6.67 % , d ) 6.25 % , e ) 8.33 %
Rationale: answer initial amount invested = $ x amount at the end of year 3 = $ 300 amount at the end of year 8 ( another 5 years ) = $ 400 therefore , the interest earned for the 5 year period between the 3 rd year and 8 th year = $ 400 - $ 300 = $ 100 as the simple interest earned for a period of 5 years is $ 100 , interest earned per year = $ 20 . therefore , interest earned for 3 years = 3 * 20 = $ 60 . hence , initial amount invested x = amount after 3 years - interest for 3 years = 300 - 60 = $ 240 . rate of interest = ( interest per year / principal ) * 100 = 20 / 240 * 100 = 8.33 % choice is ( e )
Answer: e
Python program:
a = 400 - 300
b = a / 5
c = 400 - 300
d = c / 5
e = d * 3
f = 300 - e
g = b / f
h = g * 100
Problem: 28 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 42 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 28 ã — 13.5 = 378 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 378 â  „ 9 = 42 answer b"
Answer: b
Python program:
a = 13 * 5
b = a / 9
Problem: the average ( arithmetic mean ) of 4 different positive integers is 16 . if the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer , what is the least possible value of the fourth integer ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: let the second integer be x and the fourth be a . then [ 3 x + x + ( x + 2 ) + a ] / 4 = 16 = > 5 x + 2 + a = 64 = > 5 x + a = 62 = > a = 62 - 5 x from the above equation we can see that a is minimum when x is maximum , provided both are positive the maximum value that x can take in the above equation while still keeping a positive is x = 12 this gives us a = 62 - 60 = 2 therefore the minimum value that the fourth integer can have is 2 . option d .
Answer: d
Python program:
a = 16 * 4
b = a - 2
c = 3 + 2 
d = 12 * c
e = b - d
Problem: 36 welders work at a constant rate they complete an order in 3 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 3 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: "1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 3 = 108 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 3 of the job . so 24 workers have to finish only 2 / 3 of the job . 5 . total time taken by 24 workers can be got from formula used at ( 2 ) . i . e . , 24 * total time taken = 108 . total time taken by 6 workers to finish the complete job is 108 / 24 = 4.5 days . 6 . time taken by 24 workers to finish 2 / 3 of the job is 2 / 3 * 4.5 = 3 days . the answer is choice a"
Answer: a
Python program:
a = 36 * 3
b = 1 / a
c = b * 36
d = 1 - c
e = 36 - 12
f = d / e
g = 36 * 3
h = 1 / g
i = f / h
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 200 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 50 , d ) 180 , e ) 240
Rationale: "area = length x breadth 200 = 40 x breadth so , breadth = 5 units fencing required is - breadth + breadth + length 5 + 5 + 40 = > 50 feet answer must be ( c ) 50"
Answer: c
Python program:
a = 200 / 40
b = 200 / 40
c = a + b 
d = c + 40
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 120 marks , the no of questions he attempts correctly is :
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 120 = > 5 x = 180 = > x = 36 answer : b"
Answer: b
Python program:
a = 120 + 60 
b = 4 + 1 
c = a / b
Problem: a certain car increased its average speed by 4 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 20 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 20 + 4 + 5 = 29 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 29 * 1 / 12 = 2.5 miles . answer : d ."
Answer: d
Python program:
a = 20 + 4 
b = a + 5 
c = 4 / const_60
d = b * c
Problem: an engineer undertakes a project to build a road 10 km long in 15 days and employs 30 men for the purpose . after 5 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 28 , e ) 30
Rationale: "30 workers working already let x be the total men required to finish the task in next 10 days 2 km done hence remaining is 8 km also , work has to be completed in next 10 days ( 15 - 10 = 5 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 5 ) / ( 2 * 10 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : e"
Answer: e
Python program:
a = 10 - 2
b = 30 * a
c = b * 5
d = 15 - 5
e = 2 * d
f = c / e
g = f - 30
Problem: chandigarh express of 100 m runs at a speed of 60 km / hr . what will be the time taken to cross a platform of 150 meters long ?
Options: a ) 11.00 sec , b ) 12.50 sec , c ) 15.00 sec , d ) 15.23 sec , e ) 5.23 sec
Rationale: explanation : given : length of train = 100 m , speed of train = 60 km / hr , length of platform = 150 m 1 ) always remember first step is the conversion of units . convert 60 km / hr into m / s by multiplying it with ( 5 / 18 ) speed of the train = 60 x 5 / 18 = 16.66 m / s 2 ) distance covered by the train in passing the platform = ( length of train + length of platform ) = ( 100 + 150 ) = 250 m therefore , the time taken = distance / speed = 250 / 16.66 = 15 sec answer is c
Answer: c
Python program:
a = 100 + 150 
b = 60 * const_0_2778
c = a / b
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many p cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . p = 4 + 4 + 4 = 12 . answer a"
Answer: a
Python program:
a = 1 / 3
b = 27 ** a
c = 4 * b
Problem: in a school 50 % of the students are younger than 10 , 1 / 20 are 10 years old and 1 / 10 are older than 10 but younger than 12 , the remaining 70 students are 12 years or older . how many students are 10 years old ?
Options: a ) 50 , b ) 60 , c ) 10 , d ) 20 , e ) 30
Rationale: let us write the fraction for each group of students group a : younger than 10 : 50 % = 50 / 100 = 1 / 2 group b : 10 years old : 1 / 20 group c : older that 10 but younger than 12 : 1 / 10 group d : 12 years or older : 70 students the fraction for group a , b and c together is given by 1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator = 13 / 20 , add numerators the fraction for group d is given by 20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students if x is the total number of students , then 7 / 20 of x = 70 or ( 7 / 20 ) * x = 70 solve for x x = 70 * ( 20 / 7 ) = 200 students who are 10 years old have a fraction of 1 / 20 of the total x and their number is equal to ( 1 / 20 ) of 200 = 10 students correct answer c
Answer: c
Python program:
a = 50 / 100
b = 1 - a
c = 1 / 20
d = b - c
e = 1 / 10
f = d - e
g = 70 / f
h = g / 20
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 180 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 270 + l ) / 20 = l / 8 2160 + 8 l = 20 l l = 2160 / 12 = 180 m answer a"
Answer: a
Python program:
a = 20 - 8
b = 270 / a
c = b * 8
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 7 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 240 , e ) 560
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 7 € 40 = 2 * 3 * 40 = 560 hence , answer is e"
Answer: e
Python program:
a = 2 * 7
b = 2 * 4
c = b * 5
d = a * c
Problem: if a farmer wants to plough a farm field on time , he must plough 90 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 1600 , b ) 2490 , c ) 3780 , d ) 4235 , e ) 6179
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 90 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 90 x = 85 ( x + 2 ) + 40 5 x = 210 x = 42 so the farmer planned to have the work done in 6 days , and the area of the farm field is 90 ( 42 ) = 3780 hectares correct answer c"
Answer: c
Python program:
a = 2 * 85
b = 40 + a 
c = 90 - 85
d = b / c
e = d * 90
Problem: the workforce of company x is 60 % female . the company hired 30 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 240 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 30 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 30 ) 0.05 x = 16.5 x = 330 - this is quantity of employees before adding 30 men so after adding it will be 360 answer is d"
Answer: d
Python program:
a = 55 / 100
b = a * 30
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 30