euclaise/mathqa_programs huggingface dataset:
Problem: find the compound interest on $ 30000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 2472.96 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 30000 * ( 1 + 2 / 100 ) ^ 4 = 30000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 32472.96 c . i . = 32472.96 - 10000 = $ 2472.96 answer is d"
Answer: d
Python program:
a = 4 / 100
b = a / 2
c = b + 1 
d = c ** 4
e = d * 30000
f = e - 30000
Problem: the average waight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 34 kg , b ) 40 kg , c ) 42 kg , d ) 41 kg , e ) 31 kg
Rationale: ". let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer is e ."
Answer: e
Python program:
a = 40 * 2
b = 45 * 3
c = 43 * 2
d = b - c
e = a - d
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is the correct answer
Answer: d
Python program:
a = 35 / 100
b = 600 * a
c = 40 / 100
d = 600 * c
e = b + d 
f = 50 / 100
g = 600 * f
h = e + g 
i = h - 600
j = 18 / 100
k = j * 600
l = i - k
m = l / 2
Problem: john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?
Options: a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90
Rationale: otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c
Answer: c
Python program:
a = 82 - 62
b = 1 / 2
c = a / b
d = c * 2
Problem: a train running at the speed of 90 km / hr crosses a pole in 10 seconds . find the length of the train .
Options: a ) 150 , b ) 180 , c ) 250 , d ) 200 , e ) 225
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time 25 * 10 = 250 meter answer : c"
Answer: c
Python program:
a = 90 * 1000
b = a / 3600
c = b * 10
Problem: milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches . if the milk does not overflow , how many inches high will the milk reach ?
Options: a ) 60 / π
b ) 24
c ) 40 / π
d ) 10
e ) 3 π
Rationale: let the height of level of milk in the cylinder = h since , volume of milk is constant . therefore 4 * 9 * 10 = π π * 3 ^ 2 * h = > π * h = 40 = > h = 40 / ( π ) answer c
Answer: c
Python program:
a = volume_rectangular_prism / (
b = a / 9
Problem: if 65 % of a number is greater than 5 % of 60 by 23 , what is the number ?
Options: a ) 65 , b ) 40 , c ) 55 , d ) 30 , e ) 60
Rationale: "explanation : 65 / 100 * x - 5 / 100 * 60 = 23 65 / 100 * x - 3 = 23 65 / 100 * x = 26 x = 26 * 100 / 65 x = 40 answer : option b"
Answer: b
Python program:
a = 60 / 100
b = a * 5
c = 23 + b 
d = c / 65
e = 100 * d
Problem: 8 men and 2 boys working together can do 4 times as much work as a man and a boy . working capacity of man and boy is in the ratio
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 2 : 3 , e ) none of these
Rationale: explanation : let 1 man 1 day work = x 1 boy 1 day work = y then 8 x + 2 y = 4 ( x + y ) = > 4 x = 2 y = > x / y = 2 / 4 = > x : y = 1 : 2 option a
Answer: a
Python program:
a = 4 - 2
b = 8 - 4
c = a / b
Problem: the difference between the place value and the face value of 7 in the numeral 856973 is
Options: a ) 63 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: ( place value of 7 ) - ( face value of 7 ) = ( 70 - 7 ) = 63 answer : option a
Answer: a
Python program:
a = 10 * 7
b = a - 7
Problem: if a person walks at 15 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 18 km , d ) 10 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 15 10 x - 100 = > x = 10 km . answer : d"
Answer: d
Python program:
a = 15 - 5
b = 20 / a
c = 5 * b
Problem: the diameter of a cylindrical tin is 4 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 20 , d ) 77 , e ) 21
Rationale: "r = 2 h = 5 π * 2 * 2 * 5 = 20 π cc answer : c"
Answer: c
Python program:
a = 4 / 2
b = volume_cylinder / (
Problem: the sum of 3 consecutive numbers is definitely
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 4 . , d ) divisible by 3 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : d"
Answer: d
Python program:
a = 3 - 1
b = 2 * 1
c = a / b
d = c + 1
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 6 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 4 , c ) 6 , d ) 18 , e ) 60
Rationale: "concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 6 + 18 ) / 2 ] * 7 = 84 h ( 10 ) = ( 6 + 10 ) / 2 ] * 3 = 24 h ( 18 ) / h ( 10 ) = ( 84 ) / ( 24 ) ~ 4 answer : b"
Answer: b
Python program:
a = 18 + 6 
b = 18 - 6
c = b / 2
d = c + 1 
e = a * d
f = e / 2
g = 10 - 6
h = g / 2
i = h + 1 
j = 6 + 10 
k = i * j
l = k / 2
m = f / l
Problem: 20 % of a 6 litre solution and 60 % of 4 litre solution are mixed . what percentage of the mixture of solution
Options: a ) 36 % , b ) 35 % , c ) 34 % , d ) 33 % , e ) 32 %
Rationale: 20 % of 6 litre is ( 6 * 20 / 100 ) = 1.2 litre 60 % of 4 litre is ( 60 * 4 / 100 ) = 2.4 litre the mixture is 3.6 litre so the percentage is ( 3.6 * 100 / 10 ) = 36 % answer : a
Answer: a
Python program:
a = 60 * 4
b = a / 100
c = 20 * 6
d = c / 100
e = b + d 
f = 6 + 4 
g = e / f
h = g * 100
Problem: population of a city decreases by 10 % at the end of first year and increases by 10 % at the end of second year and again decreases by 10 % at the end of third year . if the population of the city at the end of third year is 4455 , then what was the population of the city at the beginning of the first year ?
Options: a ) 5000 , b ) 4500 , c ) 4950 , d ) 1000 , e ) 2000
Rationale: m . f = 90 / 100 * 110 * 100 * 90 / 100 = 81 * 11 / 1000 population before 3 yrs = i . q / m . f = 4455 * 1000 / 81 * 11 = 5000 answer : a
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 - f
h = e * g
i = 4455 / h
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
Rationale: 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b
Answer: b
Python program:
a = 7 * 5
b = a + 425 
c = 7 + 5 
d = b / c
e = 30 - d
Problem: stalin and heather are 20 miles apart and walk towards each other along the same route . stalin walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 20 minutes after stalin , how far from the original destination has heather walked when the two meet ?
Options: a ) 4 miles , b ) 6 miles , c ) 9 miles , d ) 10 miles , e ) 12 mile
Rationale: original distance between s and h = 20 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 20 / 60 = t + 2 / 6 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 6 ) + 5 * t = 20 - - - > t = 8 / 11 hours . thus h has traveled for 8 / 11 hours giving you a total distance for h = 5 * 8 / 11 ~ 4 miles . a is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: a
Python program:
a = 1 + 5 
b = a / const_60
c = b * 20
d = 20 - c
e = 1 + 5 
f = 5 + e 
g = d / f
h = g * 5
i = h / 2
Problem: a bag marked at $ 240 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 120 / 240 * 100 = 50 % answer is d"
Answer: d
Python program:
a = 240 - 120
b = a / 240
c = b * 100
Problem: the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg
Rationale: "total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"
Answer: c
Python program:
a = 8 * 2
b = a + 65
Problem: the mean proportional between 4 and 9 is ?
Options: a ) 33 , b ) 77 , c ) 35 , d ) 88 , e ) 29
Rationale: "7 / 20 * 100 = 35 answer : b"
Answer: b
Python program:
a = 4 * 9
b = math.sqrt(a)
Problem: a man buy a book in rs 50 & sale it rs 100 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 100 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 100 profit = 100 - 50 = 50 % = 50 / 50 * 100 = 100 % answer : b"
Answer: b
Python program:
a = 100 - 50
b = a / 50
c = b * 100
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 6 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 287 , c ) 720 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 6 = 720 answer : c"
Answer: c
Python program:
a = 24 * 20
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 20 speak english well , while 60 of them do not speak english . if 60 % of students do not speak french , how many students were surveyed ?
Options: a ) 250 , b ) 225 , c ) 175 , d ) 195 , e ) 200
Rationale: "number of students who speak french are 60 + 20 = 80 of total students , the percentage of students who do not speak french was 60 % - - > percentage of who do is 40 % 80 - - - - - - - 40 % x - - - - - - - 100 % x = 80 * 100 / 40 = 200 = number of all students answer is e"
Answer: e
Python program:
a = 20 + 60 
b = 100 - 60
c = b / 100
d = a / c
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.2 kg . the weight of the new student is
Options: a ) 4 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.2 weight of the new student = ( 30 * 27.2 – 29 * 28 ) = 816 - 812 = 4 answer : a"
Answer: a
Python program:
a = 29 + 1 
b = a * 27
c = 29 * 28
d = b - c
Problem: the average expenditure of a labourer for 6 months was 80 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 80 ) – debt = 480 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 750 average monthly income = 750 ÷ 10 = 75 answer c"
Answer: c
Python program:
a = 80 * 6
b = 60 * 4
c = a + b 
d = c + 30 
e = 6 + 4 
f = d / e
Problem: the length of a rectangle is halved , whileits breadth is tripled . wat is the % change in area ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 65 % , e ) 70 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: a man saves 25 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 175 per month . what is his monthly salary ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 1500 , d ) rs . 3000 , e ) rs . 3100
Rationale: "income = rs . 100 expenditure = rs . 75 savings = rs . 25 present expenditure 75 + 75 * ( 10 / 100 ) = rs . 82.5 present savings = 100 – 82.50 = rs . 17.50 if savings is rs . 17.50 , salary = rs . 100 if savings is rs . 175 , salary = 100 / 17.5 * 175 = 1000 answer : a"
Answer: a
Python program:
a = 175 * 100
b = 100 - 25
c = 100 - 25
d = 10 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: a 15 % stock yielding 12 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
Rationale: "income of rs 12 on investment of rs 100 income of rs 15 on investment of ? = ( 15 * 100 ) / 12 = 125 answer : d"
Answer: d
Python program:
a = 100 / 12
b = a * 15
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 2 march 1 = c - 4 april 1 = c - 8 may 1 = c - 10 june 1 = c - 12 july 1 = c - 14 aug 1 = c - 16 sept 1 = c - 18 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 18 ) = 18 hence answer will be ( a )"
Answer: a
Python program:
a = 10 - 1
b = a * 2
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.92 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d ."
Answer: d
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 92
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
Rationale: [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
Answer: c
Python program:
a = 100 * 10
b = 2 / 5
c = 4000 * b
d = a - c
e = d - 600
f = 2 / 5
g = e / f
Problem: a sum fetched a total simple interest of 4020.75 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 2345 , d ) 6474 , e ) 8935
Rationale: "principal = ( 100 x 4020.75 ) / ( 9 x 5 ) = 402075 / 45 = 8935 . answer e"
Answer: e
Python program:
a = 4020 * 75
b = a / 9
c = b / 5
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 28 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 547 km , d ) 588 km , e ) 653 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 28 + 21 = 49 t = 12 d = 49 * 12 = 588 answer : d"
Answer: d
Python program:
a = 21 - 28
b = 60 / a
c = b * 28
d = 21 - 28
e = 60 / d
f = e * 21
g = c + f
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 11 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 33 , d ) 60 , e ) 65
Rationale: the total number of the people in the room must be a multiple of both 7 and 11 ( in order 3 / 7 and 5 / 11 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 11 , which is 77 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 77 people in the room . therefore there are 3 / 7 * 77 = 33 people in the room under the age of 21 . answer : c .
Answer: c
Python program:
a = 7 * 11
b = a * 3
c = b / 7
Problem: one night 15 percent of the female officers on a police force were on duty . if 300 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 300 number of female officers on duty on that night = 300 / 2 = 150 ( 15 / 100 ) * f = 150 = > f = 1000 answer e"
Answer: e
Python program:
a = 300 / 2
b = 15 / 100
c = a / b
Problem: with # andeach representing different digits in the problem below , the difference between # and # # is 801 . what is the value of ? # - # # ____ 812
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: 100 x - ( 10 x + x ) - - - - - - - - - - - 89 x = 801 x = 9 c
Answer: c
Python program:
a = 812 - 801
b = a - 2
Problem: a cat leaps 5 leaps for every 4 leaps of a dog , but 3 leaps of the dog are equal to 4 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 11 : 15 , b ) 15 : 11 , c ) 16 : 15 , d ) 15 : 16 , e ) 11 : 16
Rationale: "solution : given ; 3 dog = 4 cat ; or , dog / cat = 4 / 3 ; let cat ' s 1 leap = 3 meter and dogs 1 leap = 4 meter . then , ratio of speed of cat and dog = 3 * 5 / 4 * 4 = 15 : 16 . ' ' answer : option d"
Answer: d
Python program:
a = 3 / 4
b = a * 5
c = b / 4
Problem: ( √ 97 + √ 486 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 13 / 3
Rationale: "( √ 96 + √ 486 ) / √ 54 = ( 4 √ 6 + 9 √ 6 ) / 3 √ 6 = 13 √ 6 / 3 √ 6 = 13 / 3 hence , the correct answer is e ."
Answer: e
Python program:
a = math.sqrt(97)
b = math.sqrt(486)
c = a + b 
d = math.sqrt(54)
e = c / d
Problem: a secret can be told only 2 persons in 5 minutes . the same person tells to 2 more persons and so on . how long will take to tell it to 768 persons ?
Options: a ) 25 min , b ) 32 min , c ) 33 min , d ) 34 min , e ) 35 min
Rationale: at start one person will tell to 2 persons , it will take 5 min , now that 1 + 2 = 3 persons will tell this to next 6 persons , then 1 + 2 + 6 = 9 persons will tell to next 18 persons , then 1 + 2 + 6 + 18 = 27 persons to 54 similarly 1 + 2 + 6 + 18 + 54 = 81 persons will tell this to 162 persons similarly 1 + 2 + 6 + 18 + 54 + 162 = 243 persons will tell this to 486 persons , upto this step total persons who have listened this secret = 2 + 6 + 18 + 54 + 162 + 486 = 728 , and total time taken upto this step = 5 * 6 = 30 min , now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min answer : e
Answer: e
Python program:
a = 2 + 5 
b = a * 5
Problem: in what time will a train 110 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.35 sec , b ) 2.85 sec , c ) 7.5 sec , d ) 2.75 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 110 / 40 = 2.75 sec . answer : d"
Answer: d
Python program:
a = 144 * const_0_2778
b = 110 / a
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 6 m / h - - > 3 m in 1 / 2 hr side 2 = 8 m / h - - > 4 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option c"
Answer: c
Python program:
a = 1 / 2
b = 6 * a
c = b ** 2
d = 6 - 2
e = 1 / 2
f = d * e
g = f ** 2
h = c + g 
i = math.sqrt(h)
Problem: find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
Options: a ) 187 , b ) 197 , c ) 184 , d ) 219 , e ) 227
Rationale: let ' n ' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4 . required number = ( lcm of 13 and 15 ) - ( common difference of divisors and remainders ) = ( 195 ) - ( 11 ) = 184 . answer : c
Answer: c
Python program:
a = 13 * 15
b = 10 + 1 
c = a - b
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 420 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "( 406 / 116 ) 120 = 420 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 12 = 420 ( 350 + 70 ) answer a"
Answer: a
Python program:
a = 16 / 100
b = 1 + a 
c = 406 / b
d = 20 / 100
e = 16 / 100
f = 1 + e 
g = 406 / f
h = d * g
i = c + h
Problem: two tains are running in opposite directions with the same speed . if the length of each train is 120 metres and they cross each other in 12 seconds , then the speed of each train ( in km / hr ) is :
Options: a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 38
Rationale: sol . let the speed of each train be x m / sec . then , relative speed of the two trains = 2 x m / sec . so , 2 x = ( 120 + 120 ) / 12 ⇔ 2 x = 20 ⇔ x = 10 . ∴ speed of each train = 10 m / sec = [ 10 * 18 / 5 ] km / hr = 36 km / hr . answer c
Answer: c
Python program:
a = 120 + 120 
b = a / 12
c = b / 2
d = c * const_3_6
Problem: a taxi company charges $ 2.5 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 2.5 for the first quarter - mile , we will have $ 2.40 left to spend on quarter - mile intervals . since $ 2.40 / $ 0.15 = 16 , we can buy 16 more quarter - miles , and will travel 17 quarter miles in all : 17 × 1 / 4 = 4 1 / 4 miles . the correct answer is choice ( b ) ."
Answer: b
Python program:
a = 4 - 90
b = a * 100
c = b / 3
d = c / 4
Problem: a student has to obtain 60 % of the total marks to pass . he got 160 marks and failed by 20 marks . the maximum marks are ?
Options: a ) 210 , b ) 280 , c ) 300 , d ) 320 , e ) 340
Rationale: "let the maximum marks be x then , 60 % of x = 160 + 20 60 x / 100 = 180 60 x = 180 * 100 = 18000 x = 300 answer is c"
Answer: c
Python program:
a = 160 + 20 
b = 60 / 100
c = a / b