euclaise/mathqa_programs huggingface dataset:
Problem: if 1.5 x = 0.04 y then the value of ( y - x ) / ( y + x ) is
Options: a ) 730 / 77 , b ) 73 / 77 , c ) 7.3 / 77 , d ) 7.3 / 770 , e ) 7.3 / 77
Rationale: x / y = 0.04 / 1.5 y / x = 1.5 / 0.04 by componendo dividendo rule ( y + x ) / ( y - x ) = 1.54 / 1.46 ( y - x ) / ( y + x ) = 1.46 / 1.54 = 73 / 77 answer : b
Answer: b
Python program:
a = 1 * 5
b = a / 2
c = b - 2
d = 1 * 5
e = d / 2
f = e + 2 
g = c / f
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 8 ) , how many units is p from the y - axis ?
Options: a ) 20 , b ) 16 , c ) 8 , d ) 4 , e ) 2
Rationale: the x - axis is 8 units from the point p . thus the y - axis is 16 units from the point p . the answer is b .
Answer: b
Python program:
a = 8 * 2
Problem: 150 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 90 liters , b ) 20 liters , c ) 50 liters , d ) 20 liters , e ) 70 liters
Rationale: "milk = 3 / 5 * 150 = 90 liters water = 50 liters 90 : ( 50 + p ) = 3 : 4 150 + 3 p = 360 = > p = 70 50 liters of water are to be added for the ratio become 3 : 4 . answer : c"
Answer: c
Python program:
a = 3 + 2 
b = 150 / a
c = b * 2
Problem: two years ago , john put $ 5000 into a savings account . at the end of the first year , his account had accrued $ 500 in interest bringing his total balance to $ 5500 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has john ' s account balance increased from his initial deposit of $ 5000 ?
Options: a ) 19 % , b ) 21 % , c ) 20 % , d ) 22 % , e ) 25 %
Rationale: investment 5000 dollars 1 st year total gained = 500 total amount end of first year = 5500 second year account increased by 10 % = 5500 * 0.1 = 550 therefore total amount by second year end = 6050 so total percentage increase in money = ( 6050 - 5000 ) * 100 / 5000 = 21 % correct answer b = 21 %
Answer: b
Python program:
a = 5000 / 500
b = a + 10 
c = b + 1
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 6 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 6.5 , b ) 7.0 , c ) 7.5 , d ) 8.0 , e ) 8.5
Rationale: "in one hour , the crow eats 1 / 30 of the nuts . ( 1 / 4 ) / ( 1 / 30 ) = 7.5 hours the answer is c ."
Answer: c
Python program:
a = 1 / 4
b = 2 + 3 
c = 1 / b
d = c / 6
e = a / d
Problem: how much is 65 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 12 , e ) 6
Rationale: "( 65 / 100 ) * 40 – ( 4 / 5 ) * 25 26 - 20 = 6 answer : e"
Answer: e
Python program:
a = 65 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number r and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number r of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Python program:
a = 144 + 119 
b = a - 232
c = 119 - b
Problem: if the numerator of a fraction be increased by 12 % and its denominator decreased by 2 % the value of the fraction becomes 6 / 7 . thus , the original fraction is :
Options: a ) 1 / 4 , b ) 2 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 3
Rationale: if original fraction is x / y , then 1.12 x / 0.98 y = 6 / 7 ( 8 / 7 ) * ( x / y ) = 6 / 7 x / y = 6 / 8 = 3 / 4 answer : c
Answer: c
Python program:
a = 100 - 2
b = a * 6
c = 100 + 12 
d = c * 7
e = b / d
Problem: 3 - fourth of two - third of 3 - seventh of a number is 27 . what is 10 % of that number ?
Options: a ) 12.6 % , b ) 6.3 % , c ) 27 % , d ) 25.2 % , e ) none of these
Rationale: explanation : solution : assume the number be x . then , 3 / 4 of 2 / 3 of 3 / 7 of x = 27 . x = 27 * 7 / 3 * 3 / 2 * 4 / 3 . x = 126 . ' . 10 % of 126 = 10 / 100 * 126 = 12.6 answer : a
Answer: a
Python program:
a = 27 * 10
b = 3 + 4 
c = 3 / b
d = 3 / 4
e = 2 / 3
f = d * e
g = c * f
h = g * 100
i = a / h
Problem: a shipment of 250 smartphones contains 67 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 14 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: probability of chosing one defective phone from a lot of 250 which ontains 67 defective phones is = ( 67 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 66 ( we already picked one ) defective phones is = ( 66 / 249 ) combined probability of series of events = product of the probabilities = ( 67 / 250 ) * ( 66 / 249 ) 67 / 250 is close to ( 26 / 97 ) and ( 66 / 249 ) = ( 22 / 83 ) so answer is ( 26 / 97 ) * ( 22 / 83 ) = ( 1 / 14 ) so , answer will be b
Answer: b
Python program:
a = 67 - 1
b = 67 * a
c = 250 - 1
d = 250 * c
e = b / d
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 11 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 6 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 11 mph ) / 2 = 6 mph correct option is : a"
Answer: a
Python program:
a = 1 + 11 
b = a / 2
Problem: ( 17 ) 4.25 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 3.75 , e ) none of these
Rationale: "solution let ( 17 ) 4.25 * ( 17 ) x = 178 . then , ( 17 ) 4.25 + x = ( 17 ) 8 . ∴ 4.25 + x = 8 ⇔ x = ( 8 - 4.25 ) ⇔ x = 3.75 answer d"
Answer: d
Python program:
a = 17 * 17
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 75 time from work to home = x / 105 total time = 2 hrs ( x / 75 ) + ( x / 105 ) = 2 solving for x , we get x = 175 / 2 time from home to work in minutes = ( 175 / 2 ) * 60 / 75 = 70 minutes ans = b"
Answer: b
Python program:
a = 105 * 2
b = 75 + 105 
c = a / b
d = c * const_60
Problem: 65 % of x = 20 % of 487.50 . find the value of x ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 180 , e ) 199
Rationale: 65 % of x = 20 % of 487.50 then , 65 / 100 * x = 20 / 100 * 4875 / 10 x = 150 answer is b
Answer: b
Python program:
a = 487 / 5
b = a * 20
c = b * 100
d = c / 65
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 3 / 7 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9
Rationale: we will have a negative product only if 1 , 2 , 3 , 4 , or 5 are selected from set t . p ( negative product ) = 5 / 9 the answer is e .
Answer: e
Python program:
a = 4 + 5 
b = 5 / a
Problem: how many pieces of 85 cm length can be cut from a rod of 42.5 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 4250 / 85 = 850 / 17 = 50 answer is a ."
Answer: a
Python program:
a = 42 * 5
b = a / 85
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 45000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 2100
Rationale: "30 sec approach - solve it using approximation 45000 sheet at full price , 5 cent = 2250 45000 sheet at max discount price , 4 cent = 2000 your ans got to be between these two . ans e it is ."
Answer: e
Python program:
a = 10000 - 2000
b = 1 / 10
c = 1 - b
d = 1 / 10
e = c * d
f = a * e
Problem: a man buys an article for $ 10 . and sells it for $ 15 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %
Rationale: c . p . = $ 10 s . p . = $ 15 gain = $ 5 gain % = 5 / 10 * 100 = 50 % answer is b
Answer: b
Python program:
a = 10 / 100
b = 15 / a
c = b - 100
Problem: there are 10 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 675 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 10 c 2 number of ways of selecting 2 non fiction books = 6 c 2 10 c 2 * 6 c 2 = 45 * 15 = 675 answer : c"
Answer: c
Python program:
a = 10 * 4
b = 6 * 10
c = a * b
d = math.factorial(2)
e = d ** 2
f = c / e
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 5 .
Options: a ) 2 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: 6 * 15 * 5 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 5 + 1 ) = ( √ 8 * 18 ) / 6 = ( √ 144 ) / 6 = 12 / 6 = 2 answer is a
Answer: a
Python program:
a = 6 + 2 
b = 15 + 3 
c = a * b
d = math.sqrt(c)
e = 5 + 1 
f = d / e
Problem: the speed of a car is 120 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 90 kmph , d ) 65 kmph , e ) 77 kmph
Rationale: "s = ( 120 + 60 ) / 2 = 90 kmph c"
Answer: c
Python program:
a = 120 + 60 
b = a / 2
Problem: if a ( a + 6 ) = 7 and b ( b + 6 ) = 7 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 6 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 6 ) = 7 = > we have a = 1 or - 7 also b ( b + 6 ) = 7 = > b = 1 or - 7 given a ≠ b 1 ) when a = 1 , b = - 7 and a + b = - 6 1 ) when a = - 7 , b = 1 and a + b = - 6 answer choice b"
Answer: b
Python program:
a = 7 / 10
b = 7 / 10
c = 7 / b
d = a + c
Problem: fred and sam are standing 50 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 5 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: "relative distance = 50 miles relative speed = 5 + 5 = 10 miles per hour time taken = 50 / 10 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c"
Answer: c
Python program:
a = 5 + 5 
b = 50 / a
c = 5 * b
Problem: when a number is divided by 6 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 9 = > 2 x = 9 = > x = 4.5 a"
Answer: a
Python program:
a = 9 / 12
b = a * 6
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 12 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 23 , c ) c ) 24 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 12 . . so total who won n = 11 + 12 = 23 . . b"
Answer: b
Python program:
a = 50 - 31
b = a - 3
c = b / 2
d = 3 + c 
e = d + 12
Problem: of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "for total students take lcm of factions = 6 * 5 = 30 let female students = x , so male students = 30 - x now , female stu . on honor roll = 5 / 6 ( x ) and male stu . on honor roll = 2 / 3 ( 30 - x ) as given total female stu . = 3 / 5 ( 30 ) = 18 female stu . = ( 5 / 6 ) * 18 = 15 and male stu . = ( 2 / 3 ) * 12 = 8 fraction of honor student = ( 15 + 8 ) / 30 = 23 / 30 . correct answer is c ."
Answer: c
Python program:
a = 5 * 2
b = a * 2
c = b + 2 
d = 3 * 5
e = 2 * d
f = c / e
Problem: the average of 10 numbers is 23 . if each number is increased by 3 , what will the new average be ?
Options: a ) 36 , b ) 26 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 3 , the total increase = 3 * 10 = 40 the new sum = 230 + 30 = 260 the new average = 260 / 10 = 26 . answer : b"
Answer: b
Python program:
a = 23 * 3
Problem: in an election , candidate a got 60 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 285600 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 60 % therefore , the number of valid votes polled in favour of candidate a = 60 % of 476000 = 60 / 100 × 476000 = 28560000 / 100 = 285600 a )"
Answer: a
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 60 / 100
e = c * d
Problem: the duplicate ratio of 2 : 6 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 9 , d ) 1 : 18 , e ) 1 : 13
Rationale: "2 ^ 2 : 6 ^ 2 = 4 : 36 = 1 : 9 answer : c"
Answer: c
Python program:
a = 2 ** 2
b = 6 ** 2
c = a / b
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 5 is :
Options: a ) 545 , b ) 488 , c ) 542 , d ) 548 , e ) 560
Rationale: required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 5 = 540 + 5 = 545 . answer : a
Answer: a
Python program:
a = 54 * 10
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 43 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 16 min , c ) 20 min , d ) 8.4 min , e ) 40 min
Rationale: "d 8.4 min due to stoppages , it covers 7 km less . time taken to cover 9 km = ( 7 / 50 x 60 ) min = 8.4 min"
Answer: d
Python program:
a = 50 - 43
b = a / 50
c = const_60 * b
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 7000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) 49000
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 7000 = > total profit = 7000 * 7 = 49000 . answer : option e"
Answer: e
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 7000 / e
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 36 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 19 , e ) 21
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 36 - x now , 50 * x + 500 * ( 36 - x ) = 10350 50 x + 18000 - 500 x = 10350 - 450 x = - 7650 x = 17 . no . of 50 rupees note = 17 . answer : option c"
Answer: c
Python program:
a = 500 * 36
b = a - 10350
c = 500 - 50
d = b / c
Problem: a part of certain sum of money is invested at 8 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 3 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 4 : 9
Rationale: "12 : 8 = 3 : 2 answer : a"
Answer: a
Python program:
a = 12 / 100
b = a * 8
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 3 : 5 . what is the ratio of the smaller number to the larger ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
Rationale: "let the numbers be a , b acc . to problem , ( a + b ) / 2 ∗ a ( a + b ) / 2 ∗ a = 3 / 53 / 5 1 / 21 / 2 + b / 2 ∗ ab / 2 ∗ a = 3 / 53 / 5 b / ab / a = 1 / 51 / 5 ans . a"
Answer: a
Python program:
a = 3 / 5
b = 1 / 2
c = a - b
d = c * 2
Problem: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 20 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 5 : 4 , d ) 13 : 11 , e ) 14 : 8
Rationale: correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5 : 4
Answer: c
Python program:
a = 25 - 20
b = 20 - 16
c = a / b
Problem: a sum of money deposited at c . i . amounts to rs . 3000 in 3 years and to rs . 3600 in 4 years . find the rate percent ?
Options: a ) 25 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 20 %
Rationale: "3000 - - - 600 100 - - - ? = > 20 % answer : e"
Answer: e
Python program:
a = 3600 - 3000
b = a / 3000
c = b * 100
Problem: the product z of two prime numbers is between 15 and 36 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24 , then what is z ?
Options: a ) 35 , b ) 33 , c ) 28 , d ) 21 , e ) 15
Rationale: the smallest possible product is 33 which is 3 * 11 . all other products are too big . the answer is b .
Answer: b
Python program:
a = 15 - 4
b = a * 3
Problem: a sum amounts to rs . 3087 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 2800
Rationale: "ci = 3087 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 3087 = p [ 21 / 20 ] ^ 2 3087 [ 20 / 21 ] ^ 2 2800 answer : e"
Answer: e
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = 3087 / c
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 11 managers ?
Options: a ) 56 , b ) 57 , c ) 58 , d ) 59 , e ) 60
Rationale: "11 / 7 * 37 = 58.1 the answer is c ."
Answer: c
Python program:
a = 37 * 11
b = a / 7
c = math.floor(b)
Problem: rebecca ' s yearly income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s yearly income increase so that it constitutes 55 % of rebecca and jimmy ' s combined income ?
Options: a ) 7000 , b ) 8000 , c ) 9000 , d ) 10000 , e ) 11000
Rationale: total rebecca = x + 15000 ; total = x + 15000 + 18000 ; x + 15000 / x + 33000 = 55 / 100 therefore x = 7000 a
Answer: a
Python program:
a = 18000 - 15000
b = a * 2
c = b + 1000
Problem: a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 75 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 78
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover 1 kilometer at regular speed is 48 + 5 = 53 seconds = 53 / 3,600 hours = 1 / 70 hours ; so , we get that to cover 1 kilometer 1 / 70 hours is needed - - > regular speed 70 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : a"
Answer: a
Python program:
a = 1 / 75
b = 3600 * a
c = b + 5 
d = c / 3600
e = 1 / d
Problem: by investing in 1623 % stock at 64 , one earns rs . 1900 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 5760 , e ) - 7296
Rationale: explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d
Answer: d
Python program:
a = 4 * 2
b = 4 * 2
c = a * b
d = c * 3
e = 100 / 2
f = d / e
g = 4 * 100
h = 1900 - g
i = f * h
Problem: the average of 10 numbers is 23 . if each number is increased by 5 , what will the new average be ?
Options: a ) 36 , b ) 28 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 5 , the total increase = 5 * 10 = 50 the new sum = 230 + 50 = 280 the new average = 280 / 10 = 28 . answer : b"
Answer: b
Python program:
a = 23 * 5
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days m will the work get over ?
Options: a ) 60 , b ) 70 , c ) m = 75 , d ) 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Python program:
a = 10 * 20
b = a / const_0_25
c = 1 - const_0_25
d = b * c
e = 10 - 2
f = d / e
Problem: a train 100 m long crosses a platform 100 m long in 12 sec ; find the speed of the train ?
Options: a ) 60 kmph , b ) 65 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 100 + 100 = 200 t = 12 s = 200 / 12 * 18 / 5 = 60 kmph answer : a"
Answer: a
Python program:
a = 100 * const_0_2778
b = 12 * a
c = b - 100
Problem: if circles x and y have the same area and circle x has a circumference of 14 π , half of the radius of circle y is :
Options: a ) 16
b ) 8
c ) 4
d ) 3.5
e ) 1
Rationale: x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 14 * pi x = 7 thus y = 7 y / 2 = 3.5 ans : d
Answer: d
Python program:
a = 14 / 2
b = a / 2
Problem: the sum of three consecutive integers is 93 . what are the integers ?
Options: a ) 20 , 21,22 , b ) 10 , 11,12 , c ) 30 , 31,32 , d ) 40 , 41,42 , e ) 30 , 31,32
Rationale: "first x make the first number x second x + 1 to get the next numberwe go up one or + 1 third x + 2 add another 1 ( 2 total ) to get the third f + s + t = 93 first ( f ) plus second ( s ) plusthird ( t ) equals 93 ( x ) + ( x + 1 ) + ( x + 2 ) = 93 replace f with x , s with x + 1 , and t with x + 2 x + x + 1 + x + 2 = 93 here the parenthesis aren ′ t needed . 3 x + 3 = 93 combine like terms x + x + x and 2 + 1 − 3 − 3 add 3 to both sides 3 x = 90 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 30 our solution for x first 30 replace x in our origional listwith 30 second ( 30 ) + 1 = 31 the numbers are 30 , 31 , and 32 third ( 30 ) + 2 = 32 correct answer e"
Answer: e
Python program:
a = 93 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 93 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 93 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 93 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x