euclaise/mathqa_programs huggingface dataset:
Problem: if 10 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 2.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 12.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "c for me 9 people with 2 $ each - > maximum = 12"
Answer: c
Python program:
a = 10 - 2
b = a * 2
c = 30 - 0
Problem: a person borrows rs . 5000 for 2 years at 5 % p . a . simple interest . he immediately lends it to another person at 61 ⁄ 4 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 62.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 5 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 5 × 2 / 100 = 500 he also lends it at 6 1 ⁄ 4 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 25 / 4 × 2 / 100 = 625 his overall gain in 2 years = rs . 625 - rs . 500 = rs . 125 his overall gain in 1 year = 125 / 2 = rs . 62.5 answer : option a"
Answer: a
Python program:
a = 5000 * 61
b = a * 2
c = b / 100
d = 5000 * 5
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: a student chose a number , multiplied it by 6 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 40 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 6 ⋅ x − 138 = 102 6 x = 240 x = 40 answer a"
Answer: a
Python program:
a = 102 + 138 
b = a / 6
Problem: in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 12 or larger is drawn is 1 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 1 / 3 + p ( set 2 ) - 1 / 6 = 1 p ( set 2 ) = 5 / 6 answer ( e )"
Answer: e
Python program:
a = 12 / 6
b = 12 + a 
c = 1 / 6
d = b - c
Problem: 10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "explanation : total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be x years . then , age of the elder child = ( x + 2 ) years . so , x + ( x + 2 ) = 8 ⇔ x = 3 age of younger child = 3 years . answer : c"
Answer: c
Python program:
a = 4 + 2 
b = 24 * a
c = 24 * 4
d = 10 * 4
e = c + d 
f = b - e
g = f - 2
h = g / 2
Problem: if it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park , how many hours would it take 30 workers to do this same job ?
Options: a ) 40 / 3 , b ) 11 , c ) 7 , d ) 7 / 3 , e ) 9 / 7
Rationale: 70 workers = 3 hours then , 1 worker = 3 * 70 hours 30 workers = ( 3 * 70 ) / ( 30 ) = 7 answer : c
Answer: c
Python program:
a = 70 * 3
b = a / 30
Problem: a batsman scored 150 runs which included 5 boundaries and 10 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 46.67 % , c ) 600 / 11 , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 150 − ( 5 × 4 + 10 × 6 ) . = > 150 − 80 = > 70 hence , the required percentage is : - = > 70 / 150 * 100 = > 46.67 % answer : b"
Answer: b
Python program:
a = 5 * 10
b = 10 * 5
c = a + b 
d = 150 - c
e = d / 150
f = e * 100
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 390 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 600 , c ) 510 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 390 = 3510 salary of the new supervisor = 3510 â ˆ ’ 3000 = 510 answer : c"
Answer: c
Python program:
a = 390 * 9
b = 430 * 9
c = b - 870
d = a - c
Problem: a invested $ 400 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 80
Rationale: a : b = 400 * 12 : 200 * 6 a : b = 4 : 1 a ' s share = 100 * 4 / 5 = $ 80 answer is e
Answer: e
Python program:
a = 200 / 2
b = 200 / 2
c = 400 + b 
d = a / c
e = 1 - d
f = 100 * e
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 62 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : b ) 38 km
Answer: b
Python program:
a = 150 - 62
b = 25 + 25 
c = a - b
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 10 % of the money for taxi fare and buys 10 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 10 % of 200 = 20 for taxi fare , so he is left with 180 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 80 ( 180 - 100 ) no of oranges he can buy = 80 / 4 = > 20 so , george can buy 10 oranges . c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 50
d = b - c
e = d * 50
Problem: a ’ s speed is 17 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 16 , b ) 2 / 15 , c ) 2 / 17 , d ) 1 / 8 , e ) 1 / 7
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 15 ) = xd / v ( 15 / 17 ) * d / v = x * d / v x = 15 / 17 b should have a head start of 2 / 17 of the full distance . the answer is c ."
Answer: c
Python program:
a = 17 - 15
b = a / 17
Problem: a box contains 8 apples , 7 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 5 times in a row ) = 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 * 3 / 4 = 3 / 8 < 0.5 the answer is c ."
Answer: c
Python program:
a = 0 * 5
b = a + 1
Problem: a factory produces 8000 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 2000 toys , d ) 2354 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 8000 / 4 = 2000 toys correct answer c"
Answer: c
Python program:
a = 8000 / 4
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 2 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 1 / 7 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 21
Rationale: the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 2 bottles of apple juice is 6 c 2 * 4 c 4 = 15 * 1 = 15 p ( selling 2 bottles of apple juice ) = 15 / 210 = 5 / 70 = 1 / 14 the answer is c .
Answer: c
Python program:
a = math.comb(6, 2)
b = math.comb(10, 6)
c = a / b
Problem: if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 89 ) = ?
Options: a ) 6150 , b ) 6200 , c ) 6050 , d ) 6075 , e ) 5075
Rationale: "explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 89 = 1 + ( n - 1 ) 2 = > n = 45 use value of n in ( 1 ) then , sn = ( 45 / 2 ) ( 1 + 89 ) = 2025 ans : - 3 ( sn ) = 6075 answer : d"
Answer: d
Python program:
a = 89 + 1 
b = 89 * a
c = b / 2
d = 89 - 1
e = d / 2
f = 89 - 1
g = f / 2
h = g + 1 
i = e * h
j = c - i
k = j * 3
Problem: in what time will a railway train 120 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 12 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 10 sec
Rationale: "t = 120 / 36 * 18 / 5 = 12 sec answer : a"
Answer: a
Python program:
a = 36 * const_0_2778
b = 120 / a
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent q of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , q = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1400 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 15,600 , d ) rs . 28,875 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1400 x 20.625 ) = rs . 28875 . answer d"
Answer: d
Python program:
a = 5 * 5
b = 1400 * a
Problem: find the smallest positive integer n such that 11 n - 1 is divisible by 105 .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the last digit of 11 n − 1 is 0 , so 5 always divides 11 n − 1 . also , checking the remainders when the powers of 11 are divided by 3 and 7 we get that 3 divides 11 n − 1 exactly when n is even , and 7 divides 11 n − 1 exactly when 3 divides n . correct answer d
Answer: d
Python program:
a = 2 * 3
b = a * 105
c = b / 105
Problem: there are 89 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 59 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 89 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 89 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 59 answer : d"
Answer: d
Python program:
a = 15 + 10 
b = a + 5 
c = b + 3 
d = 89 - c
e = d + 3
Problem: a sum of rs . 2691 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1656 , c ) 1277 , d ) 6298 , e ) 1279
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2691 - x ) * 3 * 5 ) / 100 24 x / 100 = 40365 / 100 - 15 x / 100 39 x = 40365 = > x = 1035 second sum = 2691 â € “ 1035 = 1656 answer : b"
Answer: b
Python program:
a = 3 * 5
b = a * 2691
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2691 - f
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 155 , b ) $ 225 , c ) $ 510 , d ) $ 850 , e ) $ 1250
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 × $ 0.5 = $ 225 the answer is b ."
Answer: b
Python program:
a = 1000 * 1000
b = 2 * 16
c = 20 * 20
d = c * 12
e = b / d
f = e * 0
Problem: a can do a piece of work in 15 days and b in 20 days . they began the work together but 5 days before the completion of the work , a leaves . the work was completed in ?
Options: a ) 8 days , b ) 10 days , c ) 15 days , d ) 11 3 / 7 days , e ) none of these
Rationale: "explanation : ( x â € “ 5 ) / 15 + x / 20 = 1 x = 11 3 / 7 days answer is d"
Answer: d
Python program:
a = 1 / 15
b = 5 * a
c = 1 / 20
d = 5 * c
e = b + d 
f = 1 - e
g = 1 / 20
h = f / g
i = h + 5
Problem: a is half good a work man as b and together they finish a job in 10 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 15 , d ) 36 , e ) 48
Rationale: "c 15 wc = 1 : 2 2 x + x = 1 / 10 = > x = 1 / 30 2 x = 1 / 15 = > 15 days"
Answer: c
Python program:
a = 3 / 2
b = 10 * a
Problem: rohit walked 25 m towards south . then he turned to his left and walked 20 m . he then turned to his left and walked 25 m . he again turned to his right and walked 15 m . at what distance is he from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m east , e ) 55 m east
Rationale: ! 20 ! - - - > 15 ! ! ! - - - > ! 20 + 15 = 35 answer : a
Answer: a
Python program:
a = 20 + 15
Problem: a mixture contains milk and water in the ratio 6 : 3 . on adding 10 litters of water , the ratio of milk to water becomes 6 : 5 . the quantity of milk in the original mixture is ?
Options: a ) 90 , b ) 45 , c ) 110 , d ) 40 , e ) 50
Rationale: "explanation : milk : water = 6 : 3 6 x : 3 x + 10 = 6 : 5 5 [ 6 x ] = 6 [ 3 x + 10 ] 30 x = 18 x + 60 30 x - 18 x = 60 12 x = 60 x = 5 the quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9 x = 45 short cut method - 2 : for only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio - - - - - - - > 10 liters 9 part of ratio - - - - - - - > 45 liters answer : option b"
Answer: b
Python program:
a = 3 / 3
b = 10 * a
c = 6 + 3 
d = 5 / c
e = 6 + 3 
f = 3 / e
g = 3 / 6
h = f * g
i = d - h
j = b / i
Problem: if the numerator of a fraction be increased by 20 % and its denominator be diminished by 10 % , the value of the fraction is 20 / 21 . find the original fraction ?
Options: a ) 1 / 2 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 7 , e ) 7 / 9
Rationale: "let the original fraction be x / y then , 120 % of x / 90 % of y = 20 / 21 120 x / 90 y = 20 / 21 x / y = 5 / 7 answer is d"
Answer: d
Python program:
a = 100 - 10
b = a * 20
c = 100 + 20 
d = c * 21
e = b / d
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?
Options: a ) 1 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 5 / 4 ) * 4 = 1 / 5 the answer is a ."
Answer: a
Python program:
a = 100 - 80
b = 100 + 25 
c = a / b
d = 5 / 4
e = c * d
Problem: a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 200 per month . what is his monthly salary ?
Options: a ) rs . 22,000 , b ) rs . 21,000 , c ) rs . 20,000 , d ) rs . 23,000 , e ) rs . 24,000
Rationale: "income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 10 / 100 ) = rs . 99 present savings = 100 – 99 = rs . 1 if savings is rs . 1 , salary = rs . 100 if savings is rs . 200 , salary = 100 / 1 * 200 = 20000 answer : c"
Answer: c
Python program:
a = 200 * 100
b = 100 - 10
c = 100 - 10
d = 10 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: the median annual household income in a certain community of 21 households is $ 50000 . if the mean w income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ?
Options: a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined
Rationale: answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean w is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified .
Answer: e
Python program:
a = 10 / 2
b = a - 10
c = math.log(b)
Problem: 4 different children have jelly beans : aaron has 5 , bianca has 7 , callie has 8 , and dante has 9 . how many jelly beans must dante give to aaron to ensure that no child has more than 1 fewer jelly beans than any other child ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: since bianca and callie are both within 1 jelly bean of each other and aaron has 5 , dante must provide 3 of his 9 jelly beans so each child has no more than 1 fewer jelly bean than any other child . dante + aaron = 9 + 5 = 14 / 2 = 7 9 - 8 = 1 so dante must provide 3 jelly beans to aaron . answer ( a )
Answer: a
Python program:
a = 9 - 8
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 12 - meter platform and caught it after it had traveled 35.65 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 12 + 12 + 6 + 3 + 1.5 + . 75 + 0.4 ans b"
Answer: b
Python program:
a = 12 / 2
b = a / 2
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 10 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 18 , b ) 27 , c ) 26 , d ) 16 , e ) 12
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 10 days , a can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 10 = 16 . the answer is d ."
Answer: d
Python program:
a = 1 / 30
b = a * 10
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 10
Problem: a present value of a machine is $ 128000 . its value depletiation rate is 25 % per annum then find the machine value after 3 years ?
Options: a ) $ 54000 , b ) $ 48000 , c ) $ 36520 , d ) $ 32450 , e ) $ 42500
Rationale: "p = $ 128000 r = 25 % t = 3 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 128000 * 3 / 4 * 3 / 4 * 3 / 4 = $ 54000 answer is a"
Answer: a
Python program:
a = 25 / 100
b = 1 - a
c = b ** 3
d = 128000 * c
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus f = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Python program:
a = 1 + 2 
b = 2 / a
c = 2 / 9
d = 2 / 9
e = 3 / 4
f = d * e
g = c - f
h = b - g
i = 9 - 2
j = i / 9
k = h / j
Problem: when 1 / 20 % of 8000 is subtracted from 1 / 10 of 8000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400
Rationale: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d
Answer: d
Python program:
a = 8000 / 10
b = 20 * 100
c = 8000 / b
d = a - c
Problem: what is the remainder when 47 * 50 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 13 , d ) 5 , e ) 14
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 47 * 50 ) / 8 } } = remainder of ( 47 / 8 ) * remainder of ( 50 / 8 ) = 7 * 2 = 14 answer : e"
Answer: e
Python program:
a = 100 / 0
b = 47 * 47
c = a - b
Problem: there are 100 students in a class . if 14 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 86 , d ) 129 , e ) 11
Rationale: number of students absent on a particular day = 14 % of 100 i . e . , 14 / 100 × 100 = 14 therefore , the number of students present = 100 - 14 = 86 students . answer : c
Answer: c
Python program:
a = 14 / 100
b = 1 - a
c = b * 100
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 72 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: "72 ° divided by 360 ° equals 0.2 , therefore the sector is equal to 20 % of the total answer : a"
Answer: a
Python program:
a = 3600 / 10
b = 72 / a
c = b * 100
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 25 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 19 , 24 , 26 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 24 , 26 , 28 . . the median of these numbers = center of 24 and 26 = 25 d"
Answer: d
Python program:
a = 24 + 26 
b = a / 2
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.5 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 90 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.015 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced × density of water = ( 0.09 × 1000 ) kg = 90 kg . answer b"
Answer: b
Python program:
a = 3 * 2
b = 1 / 5
c = a * b
d = c * 1000