euclaise/mathqa_programs huggingface dataset:
Problem: b alone can do piece of work in 10 days . a alone can do it in 15 days . if the total wages for the work is rs 5000 , how much should b be paid if they work together for the entire duration of the work ?
Options: a ) 267 , b ) 7 , c ) 76 , d ) 8 , e ) 82
Rationale: answer : a
Answer: a
Python program:
a = 15 + 10 
b = 5000 / a
c = 10 * 4
d = c + 10 
e = d + 10 
f = e + 4 
g = f + 3 
h = b + g
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 1170 , what will be c ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 260 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 1170 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 1170 will be 4 : 3 : 2 . hence , c ' s share will be 2 * 1170 / 9 = 260 correct choice is ( b )"
Answer: b
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 1170 * g
Problem: express a speed of 180 kmph in meters per second ?
Options: a ) 10 mps , b ) 05 mps , c ) 50 mps , d ) 12 mps , e ) 11 mps
Rationale: "c 50 mps 180 * 5 / 18 = 50 mps"
Answer: c
Python program:
a = const_0_2778 * 180
Problem: sum of two numbers is 25 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 25 2 x – 3 y = 5 x = 16 y = 9 b )"
Answer: b
Python program:
a = 5 / 2
b = 25 - a
c = b / 2
d = 25 - c
Problem: rs . 1300 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 600 , c ) s . 528 , d ) s . 540 , e ) s . 549
Rationale: "a + b + c = 1300 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1300 = rs . 600 answer : b"
Answer: b
Python program:
a = 4 + 2 
b = a + 3 
c = 1300 / b
d = 4 * c
Problem: joe went on a diet 4 months ago when he weighed 212 pounds . if he now weighs 188 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 160 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "212 - 188 = 24 pounds lost in 4 months 24 / 4 = 6 , so joe is losing weight at a rate of 6 pounds per month . . . . in approximately how many months will he weigh 160 pounds ? a simple approach is to just list the weights . now : 188 lbs in 1 month : 182 lbs in 2 months : 176 lbs in 3 months : 170 lbs in 4 months : 164 lbs in 5 months : 158 lbs since 160 pounds is halfway between 164 and 158 , the correct answer must be 4.5 months . answer : d"
Answer: d
Python program:
a = 188 - 160
b = 212 - 188
c = b / 4
d = a / c
Problem: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 12 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 54 minutes , e ) 35 minutes
Rationale: "as they arrived 12 minutes earlier than usual , they saved 12 minutes on round trip from home to station ( home - station - home ) - - > 6 minutes in each direction ( home - station ) - - > wife meets husband 6 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 6 minutes = 54 minutes . answer : d"
Answer: d
Python program:
a = 12 / 2
b = const_60 - a
Problem: how many numbers from 29 to 79 are exactly divisible by 11
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 11
Rationale: "29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers option ' a '"
Answer: a
Python program:
a = 79 / 11
b = math.floor(a)
c = b * 11
d = 29 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: calculate the time it will take for a train that is 200 meter long to pass a bridge of 180 meter length , if the speed of the train is 65 km / hour ?
Options: a ) 20 seconds , b ) 4 seconds , c ) 31.04 seconds , d ) 11.04 seconds , e ) 21.04 seconds
Rationale: "speed = 65 km / hr = 65 * ( 5 / 18 ) m / sec = 18.06 m / sec total distance = 200 + 180 = 380 meter time = distance / speed = 380 * ( 100 / 1806 ) = 21.04 seconds answer : e"
Answer: e
Python program:
a = 200 + 180 
b = 65 / const_3_6
c = a / b
Problem: if z is a multiple of 8902 , what is the remainder when z ^ 2 is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z .
Rationale: "2 is a factor of 8902 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
Answer: a
Python program:
a = 8902 / 3
b = a ** 2
c = b / 4
d = 4 - 2
e = 1000 * d
f = e * 100
g = 4 - 2
h = 1000 * g
i = h * 10
j = f + i 
k = 2 * 100
l = j + k 
m = 100 - 2
n = l + m 
o = c - n
p = o * 4
Problem: a person travels from p to q a speed of 50 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 62.5 , b ) 77 , c ) 48 , d ) 99 , e ) 21
Rationale: "speed on return trip = 150 % of 50 = 75 km / hr . average speed of trip = 50 + 75 / 2 = 125 / 2 = 62.5 km / hr answer : a"
Answer: a
Python program:
a = 50 / 100
b = 1 + a 
c = 50 * b
d = c + 50 
e = d / 2
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1600 , then what is the income of p 1 ?
Options: a ) rs . 800 , b ) rs . 2400 , c ) rs . 4000 , d ) rs . 3200 , e ) rs . 4200
Rationale: let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1600 … ( i ) and 4 x – 2 y = 1600 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1600 - > x = 800 p 1 ’ s income = rs 5 * 800 = rs . 4000 answer : c
Answer: c
Python program:
a = 1600 / 2
b = a * 3
c = b - 1600
d = c * 5
Problem: what is the area of a square field whose diagonal of length 40 m ?
Options: a ) 287 , b ) 269 , c ) 750 , d ) 200 , e ) 800
Rationale: "d 2 / 2 = ( 40 * 40 ) / 2 = 800 answer : e"
Answer: e
Python program:
a = square_area / (
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 28 cm .
Options: a ) 200 cm 2
b ) 300 cm 2
c ) 400 cm 2
d ) 448 cm 2
e ) 100 cm 2
Rationale: explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 28 x 32 ) cm 2 = 448 cm 2 answer : option d
Answer: d
Python program:
a = 1 / 2
b = a * 28
c = 20 * 20
d = c * 4
e = 28 * 28
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 28
Problem: find the greatest number which is such that when 794 , 858 and 1351 are divided by it , the remainders are all same .
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: given , the remainders are same i . e . differences of that numbers are exactly divisible . hence , you have to find hcf ( x – y , y – z , z – x ) . 858 – 794 = 64 ; 1351 – 794 = 557 ; 1351 – 858 = 493 . hcf of ( 64 , 557 , 493 ) = 1 . answer : a
Answer: a
Python program:
a = 1351 - 794
b = 858 - 794
c = math.gcd(a, b)
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 14000 left with him . find salary . .
Options: a ) $ 10400 , b ) $ 14000 , c ) $ 144000 , d ) $ 1800 , e ) $ 140000
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 14000 , = [ 1 - 9 / 10 ] * total salary = $ 14000 , total salary = $ 14000 * 10 = $ 140000 , correct answer ( e )"
Answer: e
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 3 / 5
e = c + d 
f = 1 - e
g = 14000 / f
Problem: the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 10 years respectively . if the difference between their interests is rs . 144 , find the each sum ?
Options: a ) rs . 117.69 , b ) rs . 147.69 , c ) rs . 137.69 , d ) rs . 157.69 , e ) rs . 127.69
Rationale: "( p * 10 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 = > p = rs . 147.69 answer : b"
Answer: b
Python program:
a = 15 * 10
b = 15 * 3
c = a - b
d = c / 100
e = 144 / d
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 12 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 12 x - 13 / 15 x = 12 2 / 15 x = 12 = > so x = ( 15 / 2 ) * 12 = 90 km answer d
Answer: d
Python program:
a = 1 / 5
b = 2 / 3
c = a + b 
d = 1 - c
e = 1/(d)
f = 12 * e
Problem: what is the sum of the first 30 odd natural numbers
Options: a ) 300 , b ) 400 , c ) 900 , d ) 600 , e ) 700
Rationale: sum of first n odd natural nuber is = n ^ 2 so sum of the first 30 odd natural numbers = ( 30 ) ^ 2 = 900 ans 900 answer : c
Answer: c
Python program:
a = 30 ** 2
Problem: the l . c . m . of 2 numbers is 54 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 45 , d ) 32 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 54 x = 9 the numbers are = 18 and 27 required sum = 18 + 27 = 45 answer is c"
Answer: c
Python program:
a = 54 * 2
b = 2 / a
c = b * 2
d = 54 * 2
e = 2 / d
f = e * 54
g = c + f
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 7 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 18 , d ) 16 , e ) 14
Rationale: "7 * 5 : 7 * x = 7 : 10 x = 14 answer : e"
Answer: e
Python program:
a = 7 / 5
b = 10 / 7
c = a * b
d = c * 7
Problem: if x ^ 2 + 1 / x ^ 2 = √ 12 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = √ 12 andsquareboth sides : ( x ² + 1 / x ² ) ² = 12 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 12 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 12 simplify : x ⁴ + 1 / x ⁴ = 10 answer : a"
Answer: a
Python program:
a = 2 ** 2
b = a - 2
Problem: the ratio of 3 numbers is 5 : 3 : 4 and their sum is 108 . the second number of the 3 numbers is ?
Options: a ) 23 , b ) 27 , c ) 30 , d ) 32 , e ) 34
Rationale: 5 : 3 : 4 total parts = 12 12 parts - - > 108 1 part - - - - > 9 the second number of the three numbers is = 3 3 parts - - - - > 27 b )
Answer: b
Python program:
a = 5 + 3 
b = a + 4 
c = 3 / b
d = c * 108
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 42 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 36 , d ) 17 , e ) 01
Rationale: explanation : as there is meal for 70 adults and 42 have their meal , the meal left can be catered to 28 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 28 adults = 36 children hence , the meal can be catered to 36 children . answer : c
Answer: c
Python program:
a = 70 - 42
b = 90 / 70
c = a * b
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many w minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , w = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Python program:
a = 15 - 10
b = 15 / const_60
c = a * b
d = c * const_60
e = d / 10
f = e / 2
g = f - const_0_25
h = g * 10
Problem: if 40 % of a number is equal to 2 / 3 of another number , what is the ratio of first number to the second number ?
Options: a ) 5 / 3 , b ) 3 / 5 , c ) 3 / 7 , d ) 5 / 7 , e ) 7 / 9
Rationale: "let 40 % of a = 2 / 3 b then , 40 * a / 100 = 2 * b / 3 a / b = 5 / 3 ans - a"
Answer: a
Python program:
a = 1 / 4
b = 40 / 100
c = a / b
Problem: pipe a fills a tank in 20 minutes . pipe b can fill the same tank 4 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "a ' s rate is 1 / 20 and b ' s rate is 1 / 5 . the combined rate is 1 / 20 + 1 / 5 = 1 / 4 the pipes will fill the tank in 4 minutes . the answer is c ."
Answer: c
Python program:
a = 1 / 20
b = 4 / 20
c = a + b 
d = 1/(c)
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 20 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.45 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the amount of chromium in the new 20 + 35 = 55 kg alloy is 0.12 * 20 + 0.08 * 35 = 5.2 kg , so the percentage is 5.2 / 55 * 100 = 9.2 % . answer : a ."
Answer: a
Python program:
a = 12 * 20
b = a / 100
c = 8 * 35
d = c / 100
e = b + d 
f = 20 + 35 
g = e / f
h = g * 100
Problem: the number which exceeds 16 % of it by 42 is ?
Options: a ) 50 , b ) 25 , c ) 52 , d ) 58 , e ) 60
Rationale: "let the number be x . then , x - 16 % of x = 42 . x - 16 / 100 x = 42 x = ( 42 * 25 ) / 21 = 50 answer : a"
Answer: a
Python program:
a = 42 * 100
b = 100 - 16
c = a / b
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 53 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 53 has the form 4 k + 1 , so the units digit of 93 ^ 53 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d .
Answer: d
Python program:
a = reminder * (
b = reminder + (
Problem: in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.66 , b ) 0.72 , c ) 0.78 , d ) 0.84 , e ) 0.9
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.7 * 0.6 x = 0.66 x the answer is a ."
Answer: a
Python program:
a = 40 / 100
b = 40 / 100
c = a * b
d = 30 / 100
e = 40 / 100
f = 1 - e
g = d * f
h = c + g 
i = 1 - h
Problem: a number is doubled and 13 is added . if resultant is trebled , it becomes 93 . what is that number
Options: a ) 8 , b ) 9 , c ) 12 , d ) 14 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 13 ) = 93 = > 2 x + 13 = 31 = > x = 9 option b"
Answer: b
Python program:
a = 3 * 13
b = 93 - a
c = 3 * 2
d = b / c
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value t of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "t - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Python program:
a = 2020 / 2020
b = 2020 / 2020
c = 2020 / 2020
d = b + c 
e = a / d
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 22 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 268 , e ) 312
Rationale: "so 12.2 * 22 = 268 . . imo option d is correct answer . ."
Answer: d
Python program:
a = 12 * 2
Problem: a library has an average of 1000 visitors on sundays and 700 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 740 , b ) 750 , c ) 760 , d ) 770 , e ) 775
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 1000 * 5 + 700 * 25 ) / 30 = 22500 / 30 = 750 answer : b ) 750"
Answer: b
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 1000
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 700
l = e + k 
m = l / 30
Problem: a man can row upstream at 12 kmph and downstream at 38 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 25 , c ) 30 , d ) 88 , e ) 34
Rationale: "us = 12 ds = 38 m = ( 12 + 38 ) / 2 = 25 answer : b"
Answer: b
Python program:
a = 12 + 38 
b = a / 2
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 120 girls , the total number of students in the college is ?
Options: a ) 312 , b ) 356 , c ) 452 , d ) 416 , e ) 512
Rationale: let the number of boys and girls be 8 x and 5 x then , 5 x = 120 x = 24 total number of students = 13 x = 13 * 24 = 312 answer is a
Answer: a
Python program:
a = 8 / 5
b = a * 120
c = b + 120
Problem: there are 20 poles with a constant distance between each pole . a car takes 21 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 36.4543 , b ) 36.2727 , c ) 31.45128 , d ) 36.41288 , e ) 31.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 21 seconds 1 pole ( 21 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 21 / 11 ) seconds = 36.2727 seconds answer : b"
Answer: b
Python program:
a = 21 / 12
b = a * 20
Problem: noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 5 kilometers per hour ?
Options: a ) 15 , b ) 12.5 , c ) 10 , d ) 8 , e ) 7.75
Rationale: let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 5 = 2 * 3 * x / 3 + x x = 15 a is the answer
Answer: a
Python program:
a = 5 * 3
b = 2 * 3
c = b - 5
d = a / c
Problem: if 75 percent of a class answered the first question on a certain test correctly , 65 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 60 %
Rationale: "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 65 % - { both } + 20 % - - > { both } = 60 % . answer : e ."
Answer: e
Python program:
a = 75 + 65 
b = a + 20 
c = b - 100
Problem: two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 11 , b ) 12 , c ) 10.9 , d ) 14 , e ) 15
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 12 = 10 m / sec . relative speed = 12 + 10 = 22 m / sec . required time = ( 120 + 120 ) / 22 = 10.9 sec . answer : option c"
Answer: c
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: the area of a triangle will be when a = 1 m , b = 1 m , c = 2 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 1 + 1 + 2 ) / 2 = 2 answer : a"
Answer: a
Python program:
a = 1 + 1 
b = a + 2 
c = b / 1
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.6 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 7 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.6 - 19 x 15 ) kg = 7 kg . correct option : c"
Answer: c
Python program:
a = 19 + 1 
b = a * 14
c = 19 * 15
d = b - c
Problem: how many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number ? for example if we take 98 then 9 * 8 = 72 , 72 = 7 * 2 = 14 , 14 = 1 * 4 = 4 . consider only 4 prime no . s ( 23 , 57 )
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: we know prime no . are 2 , 3 , 5 , 7 mulply by 1 is prime no 2 = 21 ( 2 * 1 ) = 73 ( 7 * 3 ) 2 = 21 ( 2 * 1 ) = 37 ( 3 * 7 ) 2 = 12 ( 1 * 2 ) = 43 ( 4 * 3 ) or 34 ( 3 * 4 ) or 26 ( 2 * 6 ) or 62 ( 6 * 2 ) . . . similarly for all prime no then u will got it . . . . 12,13 , 15,17 , 21,26 , 31,34 , 35,37 , 43,51 , 53,57 , 62,71 , 73,75 ans is 18 answer : c
Answer: c
Python program:
a = 9 * 2
Problem: each of the integers from 1 to 16 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 9 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: "out of the 16 integers : 8 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 8 odd numbers first 2 . 9 th number will be the first even number so we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 9 . ( a )"
Answer: a
Python program:
a = 16 / 2
b = a + 1
Problem: a taxi owner buys diesel at rs . 8.50 , rs . 9 and rs . 9.50 per litre for 3 successive years . what approximately is the average cost per litre of diesel if he spends rs . 5000 each year ?
Options: a ) 7.98 , b ) 8.98 , c ) 9.98 , d ) 6.98 , e ) 8.12
Rationale: total cost = 5000 × 3 = 15000 total diesel used = 5000 / 8.50 + 5000 / 9 + 5000 / 9.50 = 588 + 555 + 527 = 1670 average cost per litre of diesel = 15000 / 1670 = 8.98 answer : b
Answer: b
Python program:
a = 5000 * 3
b = 5000 / 8
c = 5000 / 9
d = b + c 
e = 5000 / 9
f = d + e 
g = a / f