euclaise/mathqa_programs huggingface dataset:
Problem: the average of first 25 prime numbers is ?
Options: a ) 9.9 , b ) 8.8 , c ) 5.6 , d ) 11.9 , e ) 11.11
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 / 9 = 100 / 9 = 11.11 ( approx ) answer is e"
Answer: e
Python program:
a = 25 + 1
Problem: 14 men can complete a piece of work in 22 days . in how many days can 18 men complete that piece of work ?
Options: a ) 23 days , b ) 26 days , c ) 17 days , d ) 29 days , e ) 20 days
Rationale: "c 17 days 14 * 22 = 18 * x = > x = 17 days"
Answer: c
Python program:
a = 22 * 14
b = a / 18
Problem: what amount does an investor receive if the investor invests $ 7000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 8080 , b ) $ 8130 , c ) $ 8260 , d ) $ 8320 , e ) $ 8470
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 7000 = 1.21 * 7000 = 8470 the answer is e ."
Answer: e
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 7000 * c
Problem: 15 times a number gives 150 . the number is
Options: a ) 11 , b ) 15 , c ) 13 , d ) 14 , e ) can not be determined
Rationale: explanation : let the number be ' n ' 15 × n = 150 ⇒ n = 10 correct option : b
Answer: b
Python program:
a = 150 / 15
b = 150 / a
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 320,000 ?
Options: a ) 30 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 320 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 320,000 = 6 years total 30 years ."
Answer: a
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
Problem: 39 persons can repair a road in 12 days , working 10 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 26
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 10 30 x 6 x x = 39 x 10 x 12 x = ( 39 x 10 x 12 ) / ( 30 x 6 ) x = 26 . answer : e"
Answer: e
Python program:
a = 39 * 12
b = a * 10
c = 30 * 6
d = b / c
Problem: find the lcm of 0.6 , 9.6 and 0.36 .
Options: a ) 26.3 , b ) 35.6 , c ) 32.9 , d ) 25.5 , e ) 28.8
Rationale: "the given numbers are equivalent to 0.60 , 9.60 and 0.36 . now , find the lcm of 60,960 and 36 . which is equal to 2880 . the required lcm = 28.80 . answer is e"
Answer: e
Python program:
a = 0 * 6
b = a - 4
c = b - 4
d = c - 1
Problem: what is the rate percent when the simple interest on rs . 4000 amount to rs . 320 in 2 years ?
Options: a ) 4 % , b ) 4.1 % , c ) 4.2 % , d ) 4.3 % , e ) 4.5 %
Rationale: "interest for 1 year = 320 / 2 = 160 interest on rs 4000 p / a = 160 interest rate = 160 / 4000 * 100 = 4 % answer : a"
Answer: a
Python program:
a = 100 * 320
b = 4000 * 2
c = a / b
Problem: man can row upstream at 30 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 70 , e ) 45
Rationale: "us = 30 ds = 40 m = ( 30 + 40 ) / 2 = 35 answer : b"
Answer: b
Python program:
a = 30 + 40 
b = a / 2
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 10 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 5 : 2
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 10 : 4 = 5 : 2 . answer : e
Answer: e
Python program:
a = math.sqrt(10)
b = math.sqrt(4)
c = a / b
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score q for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean q = 74 . answer : a .
Answer: a
Python program:
a = 58 * 3
b = 98 * 2
c = a + b 
d = 2 + 3 
e = c / d
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50
Rationale: the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b .
Answer: b
Python program:
a = 3 * 2
b = 47 + a 
c = b + 1
Problem: a cycle is bought for rs . 900 and sold for rs . 1120 , find the gain percent ?
Options: a ) 11 , b ) 24 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 220 100 - - - - ? = > 24 % answer : b"
Answer: b
Python program:
a = 1120 - 900
b = a / 900
c = b * 100
Problem: 6.006 / 3.003
Options: a ) 0.002 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 6006 / 3003 = 2 answer e"
Answer: e
Python program:
a = 6 / 6
b = a * 100
Problem: the ratio between the sale price and the cost price of an article is 4 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 1 : 3
Rationale: "let c . p . = rs . 3 x and s . p . = rs . 4 x . then , gain = rs . x required ratio = x : 3 x = 1 : 3 answer : e"
Answer: e
Python program:
a = 4 - 3
b = a / 3
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 seconds . what is the length of each train ( in meters ) ?
Options: a ) 50.5 , b ) 88.5 , c ) 37.5 , d ) 55.5 , e ) 23.5
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 27 seconds , the relative difference in distance traveled is 27 * 25 / 9 = 75 meters this distance is twice the length of each train . the length of each train is 75 / 2 = 37.5 meters the answer is c ."
Answer: c
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 27
e = d / 2
Problem: the average of 35 numbers is 25 . if each number is multiplied by 5 , find the new average ?
Options: a ) 125 , b ) 189 , c ) 297 , d ) 267 , e ) 298
Rationale: "sum of the 35 numbers = 35 * 25 = 875 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : a"
Answer: a
Python program:
a = 25 * 5
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 20 , b ) 27 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 10 x = > x = 20 . answer : a"
Answer: a
Python program:
a = 90 * 5
b = 5 * 50
c = a - b
d = 90 - 80
e = c / d
Problem: if n = 5 ^ 11 – 5 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 5 ^ 3 - 5 . now 5 ^ 3 has last digit 5 . we subtract 5 from 5 = 0 is the answer . option a
Answer: a
Python program:
a = math.log(5)
b = 5 ** 11
c = math.log(b)
d = a / c
Problem: p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 1600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b"
Answer: b
Python program:
a = 2 / 3
b = 1 + a 
c = 4000 / b
d = 2 / 3
e = c * d
Problem: 8500 + ( 1600 ÷ ? ) of 1 / 5 = 8501
Options: a ) 310 , b ) 312 , c ) 320 , d ) 325 , e ) 345
Rationale: "explanation : = > 8500 + ( 1600 / ? ) × 1 / 5 = 8501 = > 1600 / ? × 1 / 5 = 8501 - 8500 = 1 = > ? = 1600 / 5 = 320 answer : option c"
Answer: c
Python program:
a = 1600 / 1
b = 8500 + a
Problem: 8.008 / 4.004
Options: a ) 2 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 4004 = 2 answer a"
Answer: a
Python program:
a = 8 / 8
b = a * 100
Problem: two friends a , b decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 4 time , no apples were left . how many apples were there ?
Options: a ) 250 , b ) 255 , c ) 254 , d ) 253 , e ) 251
Rationale: whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 8 times . so answer is ( 2 ^ 8 ) - 1 = 255 answer : e
Answer: e
Python program:
a = 4 * 2
b = 2 ** a
c = b - 1
Problem: find the simple interest on $ 10000 at 9 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 900
Rationale: p = $ 10000 r = 9 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 9 * 1 / 100 = $ 900 answer is e
Answer: e
Python program:
a = 9 / 100
b = 10000 * a
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 5 q + 3 n + 2 = 3 p + 3 = 5 q + 5 n + 2 is a multiple of 3 and 5 , so it is a multiple of 15 . the answer is a ."
Answer: a
Python program:
a = 15 - reminder
Problem: how many multiples of 4 are there between 64 and 256 ?
Options: a ) 47 , b ) 49 , c ) 42 , d ) 41 , e ) 40
Rationale: "it should be mentioned whether 64 and 256 are inclusive . if 64 and 256 are inclusive , then the answer is ( 256 - 64 ) / 4 + 1 = 49 . if 64 and 256 are not inclusive , then the answer is ( 252 - 68 ) / 4 + 1 = 47 . since oa is a , then we have not inclusive case ."
Answer: a
Python program:
a = 256 - 64
b = a / 4
c = b + 1
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 14 million gallons of water . this amount is twice the normal level . if this amount represents 70 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 12 , e ) 15
Rationale: the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 14 mg = 70 % of total . . total = 14 / . 7 = 20 mg . . normal level = 1 / 2 of 20 = 10 mg . . shortage of normal level = 20 - 10 = 10 mg . . c
Answer: c
Python program:
a = 14 / 2
b = 70 / 100
c = a / b
Problem: of the 14,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the number of employees is not reqd . . . 1 / 2 of 2 / 7 are shunted out so 1 / 7 left . . . there are another 5 equal parts ( 5 / 7 ) . . so total remaining parts = 6 , in which 1 part is journeyman . . . . therefore % = 1 / 6 * 100 = 16.67 % answer : b"
Answer: b
Python program:
a = 2 / 7
b = a / 2
c = 2 / 7
d = c / 2
e = 2 / 7
f = 1 - e
g = d + f 
h = b / g
i = h * 100
j = i * 3
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) - 6 , c ) 30 , d ) 32 , e ) 48
Rationale: "1 * 1 * 3 - ( 1 * 1 * 9 ) = 3 - 9 = - 6 ans : b"
Answer: b
Python program:
a = negate * (
b = a * 1
c = b * 1
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 54 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 10 + 29 + 8 ) = 15 % basic astrophysics . 15 % of 360 ° is 54 ° . answer : d ."
Answer: d
Python program:
a = 14 + 24 
b = a + 10 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: the difference between a 7 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 121 , b ) 11 , c ) 9 , d ) 10 , e ) 3
Rationale: "another approach is to test a number . let ' s say the original number is 1231231 so , the reversed number is 1321321 the difference = 1321321 - 1231231 = 90090 no check the answer choices 90090 is a multiple of 3,9 , 10,11 121 is not a multiple of 90090 answer : a"
Answer: a
Python program:
a = 7 + 4 
b = a ** 4
Problem: two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively . in what time they will cross each other when they are moving in same direction .
Options: a ) 120 sec , b ) 125 sec , c ) 135 sec , d ) 140 sec , e ) none of these
Rationale: explanation : 120 = a * 10 , a = 12 m / sec ( speed of first train ) 150 = b * 15 , b = 10 m / sec ( speed of second train ) 270 = ( 2 ) * t , t = 135 seconds answer – c
Answer: c
Python program:
a = 150 + 120 
b = 120 / 10
c = 150 / 15
d = b - c
e = a / d
Problem: a , b two inlet pipes takes 15,18 minutes to fill the tank and c an oulet pipe takes 45 minutes to empty the tank respectively . in what time the tank be filled if all of them are operated together ?
Options: a ) 11 minutes , b ) 10 minutes , c ) 12 minutes , d ) 13 minutes , e ) 14 minutes
Rationale: lcm = 90 no of days = [ 90 / ( 90 / 15 + 90 / 18 - 90 / 45 ) = [ 90 / ( 6 + 5 - 2 ) ] = [ 90 / 9 ] = 10 minutes answer : b
Answer: b
Python program:
a = 45 / 3
b = 1 / a
c = 45 / 3
d = 3 + c 
e = 1 / d
f = b + e 
g = 1 / 45
h = f - g
i = 1 / h
Problem: a car traveled from san diego to san francisco at an average speed of 63 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 63 x total distance traveled = 2 * 63 x = 126 x total time taken = x + 2 x = 3 x average speed = 126 x / 3 x = 42 answer : d"
Answer: d
Python program:
a = 1/(63)
b = 1/(63)
c = b / 2
d = a + c 
e = 1/(d)
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 6 . if the price per share of stock k was $ 8 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 33.33 %
Rationale: "opening = 6 closing = 8 rise in price = 2 so , percent increase = 2 / 6 * 100 = 33.33 % answer : e"
Answer: e
Python program:
a = 8 / 6
b = a - 1
c = b * 100
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after one year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?
Options: a ) 377 , b ) 197 , c ) 187 , d ) 100 , e ) 822
Rationale: "explanation : 9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 answer : d"
Answer: d
Python program:
a = 9 * 900
b = 3 * 4
c = b * 650
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: how many pieces of 85 cm length can be cut from a rod of 29.75 meters long ?
Options: a ) 55 , b ) 45 , c ) 35 , d ) 25 , e ) 15
Rationale: "number of pieces = 2975 / 85 = 35 the answer is c ."
Answer: c
Python program:
a = 29 * 75
b = a / 85
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 30 ) ?
Options: a ) 2 , b ) 5 , c ) 11 , d ) 13 , e ) 19
Rationale: "f ( 30 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Python program:
a = 30 / 2
b = a - 1
Problem: in a office work is distribute between p persons . if 1 / 3 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 50 %
Rationale: "let total % of work is 100 % total person = p 1 / 3 person are absent of total person . so absent person is 1 / 3 p ie p / 3 . left person is , p - p / 3 = 2 p / 3 . p person do the work 100 % 1 person do the work 100 * p % 2 p / 3 person do the work ( 100 * p * 3 ) / 2 p % = 150 % work increased for each person is = ( 150 - 100 ) % = 50 % answer : e"
Answer: e
Python program:
a = 100 * 3
b = 3 - 1
c = a / b
d = c - 100
Problem: find the area of a parallelogram with base 60 cm and height 16 cm ?
Options: a ) 960 cm 2 , b ) 240 cm 2 , c ) 480 cm 2 , d ) 45 cm 2 , e ) 250 cm 2
Rationale: "area of a parallelogram = base * height = 60 * 16 = 960 cm 2 answer : a"
Answer: a
Python program:
a = 60 * 16
Problem: in front of you lies a figure made up with 20 x 10 square blocks . will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares ?
Options: a ) 11647
b ) 11550
c ) 12654
d ) 26537
e ) 32651
Rationale: b 11550 there is just one way to find it out and that is the generic computing method . the number of squares and rectangles formed = ( summation of column numbers ) = ( 1 + 2 + 3 + . . . . . . + 19 + 20 ) * ( 1 + 2 + 3 + . . . . . . + 9 + 10 ) = 210 * 55 = 11550
Answer: b
Python program:
a = 20 + 1 
b = 20 * a
c = b / 2
d = 10 + 1 
e = d * 10
f = e / 2
g = c * f
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8400 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4580 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 4900
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8400 = 33600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1600 salary of may is rs . 6500 salary of january = rs . 4900 answer : e"
Answer: e
Python program:
a = 8000 * 4
b = 8400 * 4
c = b - 6500
d = a - c
Problem: if a light flashes every 6 seconds , how many times will it flash in 2 / 5 of an hour ?
Options: a ) 181 , b ) 211 , c ) 241 , d ) 271 , e ) 301
Rationale: "in 2 / 5 of an hour there are 24 * 60 = 1440 seconds the number of 6 - second intervals = 1440 / 6 = 240 after the first flash , there will be 240 more flashes for a total of 241 . the answer is c ."
Answer: c
Python program:
a = 3600 / 4
b = a * 3
c = b / 6
Problem: the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ?
Options: a ) 32 cm
b ) 48 cm
c ) 50 cm
d ) 28 cm
e ) 30 cm
Rationale: ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b
Answer: b
Python program:
a = 1 / 4
b = 1 / 3
c = a + b 
d = 1 / 2
e = c + d 
f = 104 / e
g = 1 / 2
h = f * g
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 w 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: "w = 7 is the correct answer . good solution buneul . b"
Answer: b
Python program:
a = 25 / 5
b = a + 2
Problem: what is 66.67 % of 804 of 0.1666 ?
Options: a ) 19.33 , b ) 54.55 , c ) 89.33 , d ) 97.21 , e ) 68.77
Rationale: "66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 536 of 0.166 = 536 * ( 1 / 6 ) = 89.33 . . . . ans - c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 66 * 67
p = o / 100
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 870 ?
Options: a ) rs . 700 , b ) rs . 780 , c ) rs . 750 , d ) rs . 1000 , e ) none of these
Rationale: "explanation : 870 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 750 answer : option c"
Answer: c
Python program:
a = 3 * 5
b = a + 3 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 870 / f
Problem: how many multiples of 2 are there between 1 and 60 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 29 , d ) 26 , e ) 28
Rationale: "29 multiples of 2 between 1 and 60 exclusive . from 2 * 1 upto 2 * 29 , ( 1,2 , 3,4 , . . . , 29 ) . hence , 29 multiples ! correct option is c"
Answer: c
Python program:
a = 60 - 1
b = a / 2
c = b + 1
Problem: the bankers discount of a certain sum of money is rs . 576 and the true discount on the same sum for the same time is rs . 480 . the sum due is :
Options: a ) 2880 , b ) 2870 , c ) 2860 , d ) 2850 , e ) 2840
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 576 * 480 ) / 576 - 480 ; 2880 answer : a"
Answer: a
Python program:
a = 480 * 576
b = 576 - 480
c = a / b
Problem: a pair of articles was bought for $ 50 at a discount of 30 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 17.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 70 % of x = 25 x = 25 * . 7 = $ 17.50 answer is b"
Answer: b
Python program:
a = 100 - 30
b = 50 / 2
c = a * b
d = c / 100
Problem: in an intercollegiate competition that lasted for 3 days , 185 students took part on day 1 , 150 on day 2 and 200 on day 3 . if 100 took part on day 1 and day 2 and 110 took part on day 2 and day 3 and 50 took part on all three days , how many students took part only on day 3 ?
Options: a ) 45 , b ) 35 , c ) 55 , d ) 30 , e ) 40
Rationale: "day 1 & 2 = 100 ; only day 1 & 2 ( 100 - 50 ) = 50 , day 2 & 3 = 110 ; only day 2 & 3 ( 110 - 50 ) = 60 , only day 3 = 200 - ( 50 + 60 + 50 ) = 40 answer : e"
Answer: e
Python program:
a = 50 + 100 
b = 100 + 110 
c = b + 50 
d = 150 - c
e = 50 + d 
f = e / 2
g = a + f 
h = 185 - g
Problem: express a speed of 46 kmph in meters per second ?
Options: a ) 10.78 mps , b ) 12.78 mps , c ) 97.78 mps , d ) 17.78 mps , e ) 18.78 mps
Rationale: "46 * 5 / 18 = 12.78 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 46