euclaise/mathqa_programs huggingface dataset:
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 50 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 77.27 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 50 * 5 = 250 student ' s average = ( 600 + 250 ) / 11 = 77.27 answer d"
Answer: d
Python program:
a = 6 * 100
b = 5 * 50
c = a + b 
d = 6 + 5 
e = c / d
f = math.floor(e)
Problem: jim ’ s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.5 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d"
Answer: d
Python program:
a = 2 / 5
b = 3 / 6
c = 0 * 35
d = 2 + 35
Problem: a miniature roulette wheel is divided into 9 equal sectors , each bearing a distinct integer from 1 to 9 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun three times , approximately what is the probability that the product of the three winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 83 % , d ) 90 % , e ) 96 %
Rationale: "the only way to have an odd product is if all 3 integers are odd . p ( odd product ) = 5 / 9 * 5 / 9 * 5 / 9 = 125 / 729 p ( even product ) = 1 - 125 / 729 = 604 / 729 which is about 83 % the answer is c ."
Answer: c
Python program:
a = 9 / 2
b = a / 9
c = b ** 2
d = 1 - c
e = d * 100
Problem: local kennel has cats and dogs in the ratio of 2 : 3 . if there are 6 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 24 , b ) 18 , c ) 30 , d ) 15 , e ) 12
Rationale: lets work with the data given to us . we know that there ratio of cats to dogs is 2 : 3 or cats 2 dogs 3 we can write number of cats as 2 x and number of dogs as 3 x and we know that 3 x - 2 x = 6 ( therefore x = 6 ) then # of dogs = 3 x 6 = 18 answer is b
Answer: b
Python program:
a = 6 * 3
Problem: in the coordinate plane a slope of the line k is 3 / 2 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 2 , b ) 2 / 3 , c ) - 2 / 3 , d ) 1 / 4 , e ) 3 / 2
Rationale: as y = 3 / 2 mx + m , from 0 = 3 / 2 mx + m we get x = 2 / 3 . hence , the correct answer choice is b .
Answer: b
Python program:
a = 1 / 3
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 140000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6800 , e ) s . 5600
Rationale: cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 140000 p = rs . [ ( 24 * 4 * 4 * 140000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 53760000 / 9600 ) = > p = rs . 5600 answer : e
Answer: e
Python program:
a = 24 * 4
b = a * 4
c = b * 140000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) s . 933.33 , b ) s . 1009 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 105 % - - - - - - - - 15 % - - - - 140 100 % - - - - ? = > rs . 933.33 answer : a"
Answer: a
Python program:
a = 140 * 100
b = 100 + 5 
c = 100 - 10
d = b - c
e = a / d
Problem: how many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 8 , e ) 10
Rationale: the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be d
Answer: d
Python program:
a = 15 - 2
b = a - 4
c = b - 1
Problem: the sum of all consecutive odd integers from − 31 to 41 , inclusive , is
Options: a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 185
Rationale: "the sum of the odd numbers from - 31 to + 31 is 0 . let ' s add the remaining numbers . 33 + 35 + 37 + 39 + 41 = 5 ( 37 ) = 185 the answer is e ."
Answer: e
Python program:
a = 31 + 2 
b = 31 + 2 
c = b + 2 
d = a + c 
e = 31 + 2 
f = e + 2 
g = f + 2 
h = d + g 
i = h + 41
Problem: find the compound ratio of ( 2 : 5 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 6 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 5 * 6 / 11 * 11 / 2 = 2 / 1 = 6 : 5 answer is d"
Answer: d
Python program:
a = 2 / 5
b = 2 / 5
c = 6 / 5
d = b * c
e = a * d
Problem: if a man lost 4 % by selling oranges at the rate of 24 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 16 , b ) 8 , c ) 9 , d ) 4 , e ) 3
Rationale: "96 % - - - - 24 144 % - - - - ? 96 / 144 * 24 = 16 answer : a"
Answer: a
Python program:
a = 100 - 4
b = a * 24
c = 100 + 44 
d = b / c
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 6 females and 6 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 6 ) = 2 x - 6 x = 12 there were 3 x = 36 people at the party originally . the answer is d ."
Answer: d
Python program:
a = 6 * 2
b = a * 3
c = 6 * 2
d = b - c
e = d / 2
f = 6 * 2
g = f * 3
h = 6 * 2
i = g - h
j = e + i
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 6 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 109 min , d ) 114 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 so they complete one robot in 2 / 5 th of an hour , i . e . 24 minutes - ( 3 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 3 so they complete one robot in 1 / 3 th of an hour , i . e . 20 minutes - ( 4 ) and now we have 5 robots so total = ( 1 ) + ( 2 ) + ( 3 ) + ( 4 ) = 114 minutes answer - d"
Answer: d
Python program:
a = 1/(1)
b = 1/(2)
c = a + b 
d = 1/(2)
e = c + d 
f = 1/(e)
g = 1/(1)
h = 1/(2)
i = g + h 
j = 1/(i)
k = f + j
Problem: john had a stock of 1200 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1200 - n = 1200 - 402 = 798 percentage books not sold / total number of books = 798 / 1200 = 0.665 = 66.5 % correct answer c
Answer: c
Python program:
a = 75 + 50 
b = 64 + 78 
c = a + b 
d = c + 135 
e = 1200 - d
f = e / 1200
g = f * 100
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 16 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 16 . then 4 n < 16 and n < 4 . the largest possible integer is n = 3 . the answer is c ."
Answer: c
Python program:
a = 5 - 1
b = 16 / a
c = math.floor(b)
Problem: find the average of all numbers between 2 and 63 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 32.5 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 ) / 12 = 390 / 12 = 32.5 answer : option d"
Answer: d
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 7 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 14 litres , c ) 30 litres , d ) 22 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 7 ) = 4 / 5 20 x = 4 ( 3 x + 7 ) 8 x = 28 x = 3.5 quantity of alcohol = ( 4 x 3.5 ) litres = 14 litres . answer is b ."
Answer: b
Python program:
a = 7 * 1
Problem: a sum fetched total simple interest of 4016.25 at the rate of 12 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6693.75 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 60 % of p = 4016.25 or , p = 6693.75 answer a"
Answer: a
Python program:
a = 100 * 4016
b = 12 * 5
c = a / b
Problem: a man buys 50 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 5.3 % , b ) 7.6 % , c ) 10.6 % , d ) 12 % , e ) none of these
Rationale: "explanation : let marked price be re . 1 each c . p . of 50 pens = rs . 46 s . p . of 50 pens = 99 % of rs . 50 = rs . 49.50 profit % = ( profit / c . p . ) x 100 profit % = ( 3.50 / 46 ) x 100 = 7.6 % answer b"
Answer: b
Python program:
a = 100 - 1
b = 50 * a
c = 46 * 100
d = b - c
e = 46 * 100
f = d / e
g = 100 * f
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord w , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . w = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Python program:
a = 30 / 3
Problem: what is the least value of x , so that 2 x 5475 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 5 = 23 + x least value of x may be ' 4 ' , so that the total 23 + 4 = 27 is divisible by 9 . answer : option c"
Answer: c
Python program:
a = math.lcm(2, 5475)
b = a / 5475
c = b / 4
d = c / 4
Problem: in the rectangular coordinate system , if the line x = 5 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 7
Rationale: "x = 5 y + 5 , and thus y = x / 5 - 1 the slope is 1 / 5 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 5 and thus p = 2 / 5 the answer is d ."
Answer: d
Python program:
a = 2 / 5
Problem: in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121
Rationale: "20 * 15 * 5 = 1500 answer : d"
Answer: d
Python program:
a = 20 * 15
b = a * 5
Problem: a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is :
Options: a ) 10 , b ) 100 , c ) 50 , d ) 200 , e ) 300
Rationale: 2 kmph = ( 2 x 5 / 18 ) m / sec = 5 / 9 m / sec . 4 kmph = ( 4 x 5 / 18 ) m / sec = 10 / 9 m / sec . let the length of the train be x metres and its speed by y m / sec . then , ( x / y - 5 / 9 ) = 9 and ( x / y - 10 / 9 ) = 10 . 9 y - 5 = x and 10 ( 9 y - 10 ) = 9 x = > 9 y - x = 5 and 90 y - 9 x = 100 . on solving , we get : x = 50 . therefore length of the train is 50 m . answer : c
Answer: c
Python program:
a = 9 / 3600
b = 2 * a
c = 10 / 3600
d = 4 * c
e = b - d
f = 9 / 3600
g = 10 / 3600
h = f - g
i = e / h
j = i - 2
k = 9 / 3600
l = j * k
m = l * 1000
Problem: the sum of the present ages of two persons a and b is 45 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 55 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 45 , a = 2 b 2 b + b = 45 = > b = 15 then a = 30 . 5 years , their ages will be 35 and 20 . sum of their ages = 35 + 20 = 55 . answer : a"
Answer: a
Python program:
a = 45 / 5
b = a * 2
c = b + 5 
d = 45 / 5
e = d + 5 
f = c + e
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 90 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 85.7
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 90 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover this distance at regular speed is 40 + 2 = 42 seconds = 42 / 3,600 hours = 7 / 600 hours ; so , we get that to cover 1 kilometer 1 / ( 7 / 600 ) hours is needed - - > regular speed 85.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."
Answer: e
Python program:
a = 1 / 90
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 11 / 12 , e ) 11 / 15
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 5 / 30 = 1 / 6 . the probability that he will stay in the dark is 1 - 1 / 6 = 5 / 6 the answer is a ."
Answer: a
Python program:
a = 5 * 3
b = 5 / a
c = 1 - b
Problem: on a map , 1 inch represents 28 miles . how many v inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "v inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Python program:
a = 383 / 6
Problem: 36 welders work at a constant rate they complete an order in 5 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: "1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 5 = 180 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 5 of the job . so 24 workers have to finish only 4 / 5 of the job . 5 . total time taken by 24 workers can be got from formula used at ( 2 ) . i . e . , 24 * total time taken = 180 . total time taken by 6 workers to finish the complete job is 180 / 24 = 7.5 days . 6 . time taken by 24 workers to finish 4 / 5 of the job is 4 / 5 * 7.5 = 6 days . the answer is choice e"
Answer: e
Python program:
a = 36 * 5
b = 1 / a
c = b * 36
d = 1 - c
e = 36 - 12
f = d / e
g = 36 * 5
h = 1 / g
i = f / h
Problem: there are 23 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923
Rationale: "23 c 3 = 23 * 22 * 21 / 6 = 1771 the answer is c ."
Answer: c
Python program:
a = 3 / 23
b = 1 - a
c = b * 23
Problem: the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than thevolume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: a ) 40 %
b ) 50 %
c ) 75 %
d ) 80 %
e ) 90 %
Rationale: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c
Answer: c
Python program:
a = 1 / 3
b = 64 ** a
c = 1 / 3
d = 27 ** c
e = b * d
f = 1 / 3
g = 64 ** f
h = e + g 
i = 1 / 3
j = 64 ** i
k = h - j
l = 1 / 3
m = 64 ** l
n = k + m 
o = 1 / 3
p = 64 ** o
q = n - p
r = 1 / 3
s = 64 ** r
t = 1 / 3
u = 27 ** t
v = s * u
w = 1 / 3
x = 64 ** w
y = v + x 
z = 1 / 3
A = 64 ** z
B = y - A
C = 1 / 3
D = 64 ** C
E = B + D 
F = q / E
G = F * 100
Problem: speed of a boat in standing water is 7 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 32.44 hours , b ) 31.44 hours , c ) 30.44 hours , d ) 29.44 hours , e ) 28.44 hours
Rationale: "speed upstream = 5.5 kmph speed downstream = 8.5 kmph total time taken = 105 / 5.5 + 105 / 8.5 = 31.44 hours answer is b"
Answer: b
Python program:
a = 7 + 1 
b = 7 - 1
c = a + b 
d = c * 105
e = 7 + 1 
f = 105 / e
g = 7 - 1
h = 105 / g
i = f + h 
j = 7 + 1 
k = 7 - 1
l = j + k 
m = i - l
n = m * const_60
o = d + n
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 37 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 12 , d ) 83 , e ) 11
Rationale: "explanation : t = 8 / 45 * 60 = 11 answer : option e"
Answer: e
Python program:
a = 37 / 45
b = const_60 * a
c = const_60 - b
Problem: a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 600 = 1800 3 x / 2 = 1200 x = 800 km the answer is b ."
Answer: b
Python program:
a = 1800 * 2
b = a / 3
c = b * 3
d = 2 + 3 
e = c / d
Problem: the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in :
Options: a ) 5.5 min . , b ) 6 min . , c ) 4.9 min . , d ) 5.28 min . , e ) 5 min .
Rationale: "let both of them meet after t min 4500 m are covered by suresh in 60 m . in t min he will cover 4500 t / 60 likewise , in t min suresh ' s wife will cover 3750 t / 60 given , ( 4500 t / 60 ) + ( 3750 t / 60 ) = 726 t = 5.28 minutes answer : d"
Answer: d
Python program:
a = 4 * 5
b = 3 * 75
c = a + b 
d = c / const_60
e = 726 / d
Problem: a and b have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4 . if they save rs . 1800 and rs . 1600 respectively , find the monthly income of b
Options: a ) rs . 3400 , b ) rs . 2700 , c ) rs . 1720 , d ) rs . 7200 , e ) rs . 8200
Rationale: explanation : incomes of a and b = 5 x and 6 x and expenses of a and b = 3 y and 4 y then , savings of a = 5 x - 3 y = 1800 — ? ( 1 ) savings of b = 6 x - 4 y = 1600 — ? ( 2 ) by solving equations ( 1 ) and ( 2 ) y = 1400 monthly income of b = expenses of b + savings of b = 4 y + 1600 = 4 ( 1400 ) + 1600 = rs . 7200 answer : d
Answer: d
Python program:
a = 4 * 1800
b = a / 3
c = b - 1600
d = 4 * 5
e = d / 3
f = e - 6
g = c / f
h = g * 6
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 40 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "lets assume that candidate got 40 % votes and total votes is 100 . candidate won = 40 remaining = 60 to get 50 % , candidate requires 10 votes from 100 which is 10 % and 10 votes from 60 . 10 / 60 = 1 / 6 = . 166 = 16.67 % which is approx 17 % . hence the answer is d"
Answer: d
Python program:
a = 50 / 100
b = 40 / 100
c = a - b
d = 40 / 100
e = 1 - d
f = c / e
g = f * 100
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 16 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 13 / 50 , c ) 1 / 2 , d ) 7 / 10 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 16 - 2 cmb = 100 b - cb - mb - 2 cmb = 26 hence the probability = 26 / 100 = 13 / 50 . b"
Answer: b
Python program:
a = 50 + 40 
b = a - 16
c = 100 - b
d = c / 100
Problem: if it is 5 : 14 in the evening on a certain day , what time in the morning was it exactly 2 , 880702 minutes earlier ? ( assume standard time in one location . )
Options: a ) 5 : 32 , b ) 5 : 36 , c ) 5 : 48 , d ) 5 : 54 , e ) 5 : 58
Rationale: 5 : 14 minus 2 , 880,702 must end with 2 , the only answer choice which ends with 2 is a . answer : a .
Answer: a
Python program:
a = 2 * 1000
b = a * 1000
c = b + 880702 
d = 14 - reminder
e = const_60 + d 
f = 5 / e
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . how far is the place ?
Options: a ) 2.29 , b ) 2.88 , c ) 2.2 , d ) 2.12 , e ) 2.14
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Python program:
a = 6 + 1 
b = 6 - 1
c = a * b
d = 6 + 1 
e = 6 - 1
f = d + e 
g = c / f
h = g * 2
Problem: when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 6 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 4 . . d"
Answer: d
Python program:
a = 100 - reminder