euclaise/mathqa_programs huggingface dataset:
Problem: if the sides of a triangle are 26 cm , 24 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 130 cm 2 , c ) 312 cm 2 , d ) 315 cm 2 , e ) none of these
Rationale: "the triangle with sides 26 cm , 24 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 10 = 120 cm 2 answer : a"
Answer: a
Python program:
a = 24 * 10
b = a / 2
Problem: n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 4,5 and 6 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 1,2 , 3 , 4 , 5 , 6 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 6 in the hundreds places and reserve them for the tens places now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 265 and 314 ( difference is 49 ) or try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . we get 463 and 512 ( difference is 49 ) b"
Answer: b
Python program:
a = 6 - 1
b = a * 10
c = 100 - b
d = c - 1
Problem: of the 150 people at a party , 70 were women , and 40 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 150 women = 70 so men 150 - 70 = 80 no . of pple who tried appetizer = 150 - 50 ( given info ) = 100 no of women who tried appetizer = 40 so remaining ppl ( men ) who tried the appetizer = 100 - 40 = 60 correct option c"
Answer: c
Python program:
a = 150 - 50
b = a - 40
Problem: the breath of a rectangular landscape is 6 times its length . there is a playground in it whose area is 4200 square mtr & which is 1 / 7 th of the total landscape . what is the breath of the landscape ?
Options: a ) 520 , b ) 420 , c ) 320 , d ) 550 , e ) 450
Rationale: "sol . 6 x * x = 7 * 4200 x = 70 length = 6 * 70 = 420 b"
Answer: b
Python program:
a = 4200 * 7
b = a / 6
c = math.sqrt(b)
d = c * 6
Problem: it was calculated that 75 men could complete a piece of work in 25 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 28 days . , b ) 30 days . , c ) 37.5 days . , d ) 40 days . , e ) 36 days .
Rationale: "one day work = 1 / 25 one man ’ s one day work = 1 / ( 25 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 25 * 75 ) the total no . of days required to complete the work = ( 75 * 25 ) / 50 = 37.5 answer : c"
Answer: c
Python program:
a = 75 / 25
b = 25 * a
Problem: a farmer divides his herd of x cows among his 4 sons so that one son gets one half of the herd , the second gets one - fourth , the third gets one - fifth and the fourth gets 7 cows . then x is equal to
Options: a ) 100 , b ) 140 , c ) 180 , d ) 160 , e ) 120
Rationale: no . of cows : : x 1 st son : x / 2 2 nd son : x / 4 3 rd son : x / 5 4 th son : 7 ( x ) + ( x / 4 ) + ( x / 5 ) + 7 = x = > x - ( 19 x / 20 ) = 7 = > ( 20 x - 19 x ) / 20 = 7 = > x = 140 answer : b
Answer: b
Python program:
a = 7 * 4
b = a * 4
c = b + 12 
d = 10 + c
Problem: solve for x and check : x + 5 = 3
Options: a ) 2 , b ) 3 , c ) 1 , d ) - 2 , e ) 4
Rationale: "solution : x + 5 - 5 = 3 - 5 x = - 2 check : x + 5 = 3 - 2 + 5 = 3 3 = 3 answer : d"
Answer: d
Python program:
a = 3 / 5
b = 5 * a
Problem: a trained covered x km at 40 kmph and another 4 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 11.33 kmph , b ) 12.33 kmph , c ) 13.33 kmph , d ) 14.33 kmph , e ) 23.33 kmph
Rationale: "total time taken = x / 40 + 4 x / 20 hours = 9 x / 40 hours average speed = 3 x / ( 9 x / 40 ) = 13.33 kmph answer : c"
Answer: c
Python program:
a = 40 * 3
b = 40 / 40
c = 4 * 40
d = c / 20
e = b + d 
f = a / e
Problem: a rectangular block 8 cm by 24 cm by 56 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 10 , c ) 15 , d ) 40 , e ) 21
Rationale: "volume of the block = 8 * 24 * 56 = 10752 cm ^ 3 side of the largest cube = h . c . f of 8 , 24,56 = 8 cm volume of the cube = 8 * 8 * 8 = 512 cm ^ 3 number of cubes = 10752 / 512 = 21 answer is e"
Answer: e
Python program:
a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d 
f = 3 * 1000
g = 56 * 10
h = f + g 
i = e / h
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 93 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 93 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 93 * 7 ) = 1350 - ( 609 + 651 ) = 1350 - 1260 = 90 answer b"
Answer: b
Python program:
a = 90 * 15
b = 87 * 7
c = 93 * 7
d = b + c 
e = a - d
Problem: find the compound ratio of ( 2 : 3 ) , ( 5 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 5 : 3
Rationale: "required ratio = 2 / 3 * 5 / 11 * 11 / 2 = 2 / 1 = 5 : 3 answer is e"
Answer: e
Python program:
a = 2 / 3
b = 2 / 3
c = 5 / 3
d = b * c
e = a * d
Problem: what is the least common multiple of 15 , 18 , and 34 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 360 , e ) 1530
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 18 = 2 * 3 ^ 2 34 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1530 option e"
Answer: e
Python program:
a = 10 + 2 
b = 3 * 10
c = b - 3
d = math.lcm(a, c)
e = math.lcm(d, 18)
Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 48 , b ) 55 , c ) 58 , d ) 62 , e ) 70
Rationale: "the total number of ways to choose 4 managers is 8 c 4 = 70 we need to subtract the number of groups which include the two managers , which is 6 c 2 = 15 . 70 - 15 = 55 the answer is b ."
Answer: b
Python program:
a = math.comb(8, 4)
b = 8 - 2
c = math.comb(b, 2)
d = a - c
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 9 is how many times as great as the frequency corresponding to a reading of 3 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 and if richter scale reading goes from 7 to 8 it will be 10 and if richter scale reading goes from 8 to 9 it will be 10 so it will from 3 to 9 i . e 4,5 , 6,7 , 8,9 = 10 * 10 * 10 * 10 * 10 * 10 = 10 ^ 6 answer is e"
Answer: e
Python program:
a = 9 - 3
b = 10 ** a
Problem: the contents of a certain box consist of 72 apples and 30 oranges . how many oranges must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 68 , b ) 78 , c ) 88 , d ) 138 , e ) 108
Rationale: "apple = ( apple + orange + x ) * 0.3 72 = ( 30 + 72 + x ) * 0.3 x = 138 answer : d"
Answer: d
Python program:
a = 72 + 30 
b = 30 / 100
c = 72 / b
d = a - c
Problem: a factory produces 6000 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 ) 1500 toys , c ) 6113 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 . 6000 / 4 = 1500 toys correct answer b"
Answer: b
Python program:
a = 6000 / 4
Problem: two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 9 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 32 / 9 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 9 combined = 5 / 18 work done in 2 days = 5 / 9 work left = 4 / 9 rate * time = work left 1 / 8 * time = 4 / 9 time = 32 / 9 b"
Answer: b
Python program:
a = 4 + 2 
b = 1 / a
c = 1 / 9
d = b + c 
e = d * 2
f = 1 - e
g = 1 / 9
h = f / g
i = max(h)
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box , what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: the sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls ( odd + odd + odd = odd ) or two even numbered balls and one odd numbered ball ( even + even + odd = odd ) ; p ( ooo ) = ( 1 / 2 ) ^ 3 ; p ( eeo ) = 3 * ( 1 / 2 ) ^ 2 * 1 / 2 = 3 / 8 ( you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways : eeo , eoe , or oee ) ; so finally p = 1 / 8 + 3 / 8 = 1 / 2 . answer : c .
Answer: c
Python program:
a = 1 / 2
b = a ** 3
c = 1 / 2
d = c ** 2
e = 3 * d
f = 1 / 2
g = e * f
h = b + g
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 8 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 33 : 1 , b ) 33 : 7 , c ) 33 : 8 , d ) 33 : 5 , e ) 33 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 1 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 1 = 33 / 4 = 8.25 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 8.25 : 1.75 = 33 : 7 . answer : b"
Answer: b
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 2 - g
i = 87 * 5
j = i / 100
k = 8 - j
l = h + k 
m = e / l
Problem: the average age of a class of 39 students is 15 years . if the age of the teacher be included , then the average increases by 3 months . find the age of the teacher .
Options: a ) 20 , b ) 23 , c ) 25 , d ) 21 , e ) 22
Rationale: "total age of 39 persons = ( 39 x 15 ) years = 585 years . average age of 40 persons = 15 yrs 3 months = 61 / 4 years . total age of 40 persons = ( 61 / 4 ) x 40 ) years = 610 years . : . age of the teacher = ( 610 - 585 ) years = 25 years . answer is c ."
Answer: c
Python program:
a = 39 + 3 
b = 15 + 3 
c = a * b
d = 39 * 15
e = c - d
Problem: a man can row 5 kmph in still water . when the river is running at 2.3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.91 , b ) 3.48 , c ) 2.98 , d ) 3.78 , e ) 4.21
Rationale: "m = 5 s = 2.3 ds = 6.3 us = 2.7 x / 6.3 + x / 2.7 = 1 x = 1.89 d = 1.89 * 2 = 3.78 answer : d"
Answer: d
Python program:
a = 5 + 2 
b = 5 - 2
c = a * b
d = 5 + 2 
e = 5 - 2
f = d + e 
g = c / f
h = g * 2
Problem: a part - time employee whose hourly wage was increased by 15 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13.04 , c ) 10 , d ) 11 , e ) 12
Rationale: "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.15 x now we need to find number of hours worked so that x * y = 1.15 x * z i . e z = 1 / 1.15 y % decrease = ( y - 1 / 1.15 y ) / y * 100 = 13.04 % thus my answer is b ."
Answer: b
Python program:
a = 15 + 100 
b = a / 100
c = b * 15
d = 1 / c
e = d * 100
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , how much r will receive ?
Options: a ) 300 , b ) 600 , c ) 900 , d ) 800 , e ) 500
Rationale: "let p ' s capital be p , q ' s capital be q , and r ' s capital be r then 4 p = 6 q = 10 r 2 p = 3 q = 5 r ⋯ ( a ) from ( a ) , q = 2 p / 3 ⋯ ( 1 ) r = 2 p / 5 ⋯ ( 2 ) p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 × 6 / 31 = 150 × 6 = 900 answer is c ."
Answer: c
Python program:
a = 4 + 1 
b = 10 + a 
c = b + 10 
d = c + 6 
e = 6 / d
f = 4650 * e
Problem: a 260 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 240 mts , b ) 270 mts , c ) 260 mts , d ) 250 mts , e ) none of these
Rationale: explanation : relative speed = 120 + 80 = 200 km / hr . = 200 x 5 / 18 = 500 / 9 m / sec . let the length of the other train be l mts . then , ( l + 260 ) / 9 = 500 / 9 = > l = 240 mts . answer is a
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 260
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes r in this range . answer : a ."
Answer: a
Python program:
a = math.factorial(6)
b = a + 6 
c = math.factorial(6)
d = c + 6 
e = b / d
Problem: 25 people went to a hotel for combine dinner party 15 of them spent rs . 5 each on their dinner and rest spent 4 more than the average expenditure of all the 25 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 158.25 , e ) none of these
Rationale: "solution : let average expenditure of 25 people be x . then , 25 x = 15 * 5 + 10 * ( x + 4 ) ; or , 25 x = 15 * 5 + 10 x + 20 ; or , x = 6.33 ; so , total money spent = 6.33 * 25 = rs . 158.25 . answer : option d"
Answer: d
Python program:
a = 15 * 5
b = 25 - 15
c = b * 4
d = a + c 
e = 25 - 15
f = 25 - e
g = d / f
h = g * 25
Problem: find the number of divisors of 1080 excluding the divisors which are perfect squares .
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: 1080 = 2 ^ 3 * 3 ^ 3 * 5 ^ 1 total no . of divisors = ( 3 + 1 ) * ( 3 + 1 ) * ( 1 + 1 ) = 32 only 4 divisors 1 , 2 ^ 2 = 4 , 3 ^ 2 = 9 & 2 ^ 2 * 3 ^ 2 = 36 are perfect squares so , number of divisors excluding perfect squares divisors = 32 - 4 = 28 answer : a
Answer: a
Python program:
a = 4 * 4
b = a * 2
c = b - 3
Problem: line q has the equation 5 y – 3 x = 60 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "5 y - 3 x = 60 and so y = 3 x / 5 + 12 when x = 0 , then y = 12 . when y = 0 , then x = - 20 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 20 , 0 ) , 0 = - 5 ( - 20 ) / 3 + c the y - intercept is c = - 100 / 3 < - 33 . thus the perpendicular line s can have y - intercepts from - 33 up to 11 . the number of possible lines is 33 + 11 + 1 = 45 the answer is c ."
Answer: c
Python program:
a = 60 / 5
b = a - 2
c = 60 / 3
d = 60 / 5
e = c + d 
f = b + e
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 15 - inch boxes . if the university pays $ 0.70 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 357 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.7 = $ 357 answer b"
Answer: b
Python program:
a = 1000 * 1000
b = 3 * 6
c = 20 * 20
d = c * 15
e = b / d
f = e * 0
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number y of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "y = 7 is the correct answer . good solution buneul . b"
Answer: b
Python program:
a = 25 / 5
b = a + 2
Problem: walking at 5 / 6 of its usual speed , a train is 10 minutes too late . what is usual time to cover the journey ?
Options: a ) 70 minutes , b ) 2 hours , c ) 2 / 3 hours , d ) 5 / 6 hours , e ) 85 minutes
Rationale: "et speed be s and time to cover the journey be t s * t = d ( distance of journey ) - - - 1 now as per the question stem we have ( 5 / 6 ) s * ( t + 10 ) = d - - - - 2 equating value of d from ( 1 ) in ( 2 ) we get t = 50 mins or 5 / 6 hrs . answer : d"
Answer: d
Python program:
a = 5 / 6
b = 1/(a)
c = b - 1
d = 10 / c
Problem: a fruit seller sells mangoes at the rate of rs . 6 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 7.41 , b ) rs 9.81 , c ) rs 10.41 , d ) rs 11.81 , e ) none of these
Rationale: "explanation : 85 : 6 = 105 : x x = ( 6 × 105 / 85 ) = rs 7.41 option a"
Answer: a
Python program:
a = 100 + 5 
b = 6 * a
c = 100 - 15
d = b / c
Problem: the salaries of a and b together amount to $ 5000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 3500 , e ) $ 3750
Rationale: "let a ' s salary is x b ' s salary = 5000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 5000 - x ) x = $ 3750 answer is e"
Answer: e
Python program:
a = 100 - 85
b = 100 - 95
c = a / b
d = c + 1 
e = 5000 / d
f = 5000 - e
Problem: when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 12 , e ) 1 / 16
Rationale: on the first toss , the coin will land on one side or the other . on the second toss , the probability of landing on the same side is 1 / 2 . on the third toss , the probability of landing on the same side is 1 / 2 . on the fourth toss , the probability of landing on the same side is 1 / 2 . p ( same side all four times ) = 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 . the answer is c .
Answer: c
Python program:
a = 1 / 2
b = a ** 4
c = 1 / 2
d = c ** 4
e = b + d
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 9 minutes 42 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 9 % , e ) 12 %
Rationale: "bob ' s time = 640 secs . his sis ' time = 582 secs . percent increase needed = ( 640 - 582 / 640 ) * 100 = 58 / 640 * 100 = 9 % . ans ( d ) ."
Answer: d
Python program:
a = 10 * 10
b = 9 * const_60
c = b + 42 
d = 10 * const_60
e = d + 40 
f = c / e
g = 1 - f
h = a * g
Problem: convert 300 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 482802 , e ) 864520
Rationale: "1 mile = 1609.34 meters 300 mile = 300 * 1609.34 = 482802 meters answer is d"
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 300
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 9 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 9 ) = multiply and divide by 2 ^ 4 = 2 ^ 6 / ( 2 ^ 3 * 2 ^ 6 * 5 ^ 9 ) = 2 ^ 6 / 10 ^ 9 = > non zero digits are 64 = > ans b"
Answer: b
Python program:
a = 1 + 2
Problem: the average weight of 5 person ' s increases by 4 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?
Options: a ) 70 , b ) 86.5 , c ) 80 , d ) 88.5 , e ) 75
Rationale: "total increase in weight = 5 × 4 = 20 if x is the weight of the new person , total increase in weight = x − 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : a"
Answer: a
Python program:
a = 5 * 4
b = a + 50
Problem: what is the smallest integer that is multiple of 7 , 12 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 420
Rationale: "correct answer : e it is the lcm of 7 , 12 and 20 which is 420"
Answer: e
Python program:
a = 20 / 3
b = math.floor(a)
c = b + 1
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 17 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 8 + 16 x 6 ) ] = ( 225 - 208 ) = 17 years . answer c"
Answer: c
Python program:
a = 15 * 15
b = 8 * 14
c = 6 * 16
d = b + c 
e = a - d
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 174,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 45 %
Rationale: "increase = 174000 - 120000 = 54000 % increase = 54000 * 100 / 120000 = 45 % answer : option e"
Answer: e
Python program:
a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
Problem: in the faculty of reverse - engineering , 200 second year students study numeric methods , 400 second year students study automatic control of airborne vehicles and 100 second year students study them both . how many students are there in the faculty if the second year students are approximately 60 % of the total ?
Options: a ) 834 , b ) 750 , c ) 633 , d ) 654 , e ) 812
Rationale: "total number of students studying both are 400 + 200 - 100 = 500 ( subtracting the 100 since they were included in the both the other numbers already ) . so 60 % of total is 500 , so 100 % is approx . 834 . answer is a"
Answer: a
Python program:
a = 200 + 400