euclaise/mathqa_programs huggingface dataset:
Problem: john bought a total of 20 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 20 mangoes and oranges that john originally purchased was 69 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 20 - x ) 0.60 / 20 = 0.69 solving for x , we get x = 9 - - > mangoes 9 , oranges 11 now , number of oranges to be returned be y 0.80 * 9 + ( 11 - y ) * 0.60 / 20 - y = 0.72 solving for y , y = 5 ans : b"
Answer: b
Python program:
a = 69 / 100
b = a * 20
Problem: a goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 280 m
Rationale: "s = 240 + x / t 72 * 5 / 18 = 240 + x / 26 x = 280 answer : e"
Answer: e
Python program:
a = 72 * const_0_2778
b = a * 26
c = b - 240
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 15 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 ) 3 / 10 , c ) 1 / 4 , 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 - 15 - 2 cmb = 100 b - cb - mb - 2 cmb = 25 hence the probability = 25 / 100 = 1 / 4 . c"
Answer: c
Python program:
a = 50 + 40 
b = a - 15
c = 100 - b
d = c / 100
Problem: when the price of an article was reduced by 40 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 8 % increase , b ) 4 % decrease , c ) 6 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 40 % , the new price is 0.6 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.6 p ) ( 1.8 n ) = 1.08 np , which is 1.08 times the old revenue , so is 8 % greater . answer : a"
Answer: a
Python program:
a = 80 + 100 
b = 100 - 40
c = a * b
d = c / 100
e = d - 100
Problem: how many integers from 101 to 900 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 8 = 8 9 is not possible here because it would result in a number greater than 9 ( i . e 909 , 919 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 8 * 10 = 80 answer is d ."
Answer: d
Python program:
a = 900 / 10
Problem: what is the units digit of 2222 ^ ( 333 ) * 4444 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 10
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 4444 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 8 . final answer : e"
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: the ratio of petrol and kerosene in the container is 3 : 2 when 10 liters of the mixture is taken out and is replaced by the kerosene , the ratio become 2 : 3 . then total quantity of the mixture in the container is :
Options: a ) 33 , b ) 30 , c ) 38 , d ) 37 , e ) 27
Rationale: explanation : pool : kerosene 3 : 2 ( initially ) 2 : 3 ( after replacement ) \ frac { remaining \ : ( or \ : left ) \ : quantity } { initial \ : quantity } = \ left ( 1 - \ frac { replaced \ : quantity } { total \ : quantity } \ right ) ( for petrol ) \ frac { 2 } { 3 } = \ left ( 1 - \ frac { 10 } { k } \ right ) \ rightarrow \ frac { 1 } { 3 } = \ frac { 10 } { k } \ rightarrow k = 30 l therefore the total quantity of the mixture in the container is 30 liters . answer : b ) 30
Answer: b
Python program:
a = 2 / 3
b = 1 - a
c = 10 / b
Problem: what is the greatest 6 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 3 , 4 , 5 , 6 and 7 respectively ?
Options: a ) 456780 , b ) 678910 , c ) 997479 , d ) 997917 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 7 when we divide by 10 , so d is the only possible answer .
Answer: d
Python program:
a = 1000 * 1000
b = a / 10
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent q should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked will be q = 25 % greater than the original number . the answer is c ."
Answer: c
Python program:
a = 10 * 4
b = 100 - 20
c = b / 100
d = c * 10
e = a / d
f = e - 4
g = f / 4
h = g * 100
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 4830 , b ) 5040 , c ) 5250 , d ) 5460 , e ) 5680
Rationale: "7 ! = 5040 the answer is b ."
Answer: b
Python program:
a = math.factorial(6)
Problem: if the sum of a number and its square is 20 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 28 , d ) 4 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 20 ( x + 5 ) ( x - 4 ) = 0 x = 4 answer : d"
Answer: d
Python program:
a = math.sqrt(20)
b = math.floor(a)
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 172 , b ) 180 , c ) 192 , d ) 200 , e ) 216
Rationale: "r = j + 8 = k + 4 r + 4 = 2 ( j + 4 ) ( j + 8 ) + 4 = 2 j + 8 j = 4 r = 12 k = 8 in 4 years ( r + 4 ) ( k + 4 ) = 16 * 12 = 192 the answer is c ."
Answer: c
Python program:
a = 8 - 4
b = 8 + a 
c = b + 4 
d = 8 - 4
e = 8 + d 
f = 8 / 2
g = e - f
h = g + 4 
i = c * h
Problem: an investor deposited $ 5,000 to open a new savings account that earned 4 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5050.50 , b ) $ 5100.50 , c ) $ 5200.50 , d ) $ 5300.50 , e ) $ 5400.50
Rationale: the amount in the account after 6 months is 1.01 * 1.01 ( $ 5,000 ) = $ 5100.50 the answer is b .
Answer: b
Python program:
a = 2 + 3 
b = a * 100
c = 2 + 3 
d = c * 2
e = b * d
f = 4 / 4
g = f / 100
h = g + 1 
i = h ** 2
j = e * i
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 48 people were made to stand in a column , how many columns could be formed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 16 * 30 = 48 * n n = 10 the answer is a .
Answer: a
Python program:
a = 48 / 16
b = 30 / a
Problem: 18 buckets of water fill a tank when the capacity of each bucket is 60 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 5 litres ?
Options: a ) 216 , b ) 200 , c ) 212 , d ) 220 , e ) 210
Rationale: "capacity of the tank = ( 18 ã — 60 ) litre number of buckets required of capacity of each bucket is 17 litre = 18 ã — 60 / 5 = 18 ã — 12 = 216 answer is a"
Answer: a
Python program:
a = 60 * 18
b = a / 5
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 50 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 55 , b ) 60 , c ) 75 , d ) 80 , e ) 90
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 100 + ( d / 2 ) / v d / 150 = d / 2 v and so v = 75 km / hr the answer is c ."
Answer: c
Python program:
a = 50 * 60
b = 50 - 60
c = b * 60
d = a / c
e = 60 * d
f = 60 / 10
g = e / f
Problem: james took a 3 - hour bike ride . in the second hour he traveled 36 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 111.0 , d ) 157.0 , e ) 163.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 36 , x = 30 . now , the distance travelled in the 3 rd hour = 36 + 1 / 4 â ˆ — 36 = 45 . 36 + 30 + 45 = 111 answer : c"
Answer: c
Python program:
a = 100 - 20
b = a / 100
c = b * 36
d = c + 36 
e = 100 + 25 
f = e / 100
g = f * 36
h = d + g
Problem: a large tanker can be filled by two pipes a and b in 30 and 15 hours respectively . how many hours will it take to fill the tanker from empty state if a and b fill it together ?
Options: a ) 8 hr , b ) 10 hr , c ) 12 hr , d ) 9 hr , e ) 5 hr
Rationale: part filled by a in 1 hr = 1 / 30 part filled by b in 1 hr = 1 / 15 part filled by a + b = 1 / 30 + 1 / 15 = 1 / 10 both the pipes can fill the tank in = 10 hours answer is b
Answer: b
Python program:
a = 1/(30)
b = 1/(15)
c = a + b 
d = 1/(c)
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 440 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 64 , d ) 88 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 440 breadth = 22 feet area to be fenced = 2 b + l = 2 ( 22 ) + 20 = 64 feet answer : c"
Answer: c
Python program:
a = 440 / 20
b = a * 2
c = b + 20
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) 280
Rationale: "given that the area of the square = 3600 sq . units = > side of square = √ 3600 = 60 units the radius of the circle = side of the square = 60 units length of the rectangle = 2 / 5 * 60 = 24 units given that breadth = 10 units area of the rectangle = lb = 24 * 10 = 240 sq . units answer : option a"
Answer: a
Python program:
a = math.sqrt(3600)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: if l is the least positive integer that is divisible by every integer from 1 to 9 inclusive , then l / 2 is =
Options: a ) 5040 , b ) 2520 , c ) 1890 , d ) 1260 , e ) 630
Rationale: the integer should be divisible by : 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 , that is 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 and 3 ^ 2 . the least common multiple of these integers is the product of 7 , 5 , 3 ^ 2 and 2 ^ 3 . then , l / 2 is ( 7 * 5 * 3 ^ 2 * 2 ^ 3 ) / 2 = 7 * 5 * 9 * 4 = 1260 . answer : d .
Answer: d
Python program:
a = 2 + 1 
b = 2 ** a
c = 2 + 1 
d = c ** 2
e = b * d
f = 2 + 1 
g = f + 2 
h = g + 2 
i = e * h
j = 2 + 1 
k = j + 2 
l = i * k
m = l / 2
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 82 . how much was lent at 5 % ?
Options: a ) 899 , b ) 866 , c ) 878 , d ) 800 , e ) 877
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 82 5 x / 100 + 90 – 6 x / 100 = 82 x / 100 = 8 = > x = 800 answer : d"
Answer: d
Python program:
a = 5 + 6 
b = a * 100
Problem: an athlete runs 200 metres race in 24 seconds . what is his speed ?
Options: a ) 20 km / hr , b ) 30 km / hr , c ) 25 km / hr , d ) 35 km / hr , e ) 40 km / hr
Rationale: speed = dist / time = 200 / 24 200 / 24 * 18 / 5 = 40 * 3 / 4 = 30 km / hr answer b
Answer: b
Python program:
a = 200 / 24
b = a * const_3_6
Problem: if the average ( arithmetic mean ) of a and b is 115 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) − 90 , d ) 135 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 115 = = = > a + b = 230 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 230 - 320 = = = > a + b - b - c = - 90 = = = > a - c = - 90 answer : c"
Answer: c
Python program:
a = 160 * 2
b = 115 * 2
c = a - b
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle ?
Options: a ) 65 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 50 ) = 180 - - > x = 65 . answer : a ."
Answer: a
Python program:
a = 3600 / 10
b = 50 * 2
c = a - b
d = c / 4
Problem: jim is able to sell a hand - carved statue for $ 550 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 407.41 , b ) $ 412.40 , c ) $ 455.40 , d ) $ 474.90 , e ) $ 488.20
Rationale: "550 = 1.35 * x x = 550 / 1.35 = 407.407407 . . . which rounds to $ 407.41 , which is ( a ) ."
Answer: a
Python program:
a = 35 / 100
b = a + 1 
c = 550 / b
Problem: pipe b that can fill a tank in an hour and pipe a that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe a is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 32 mins , b ) 35 mins , c ) 40 mins , d ) 30 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe b was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : d
Answer: d
Python program:
a = 1 * const_60
b = 1 / a
c = 15 * b
d = 1 - c
e = 1 / 2
f = e * const_60
g = 1 / f
h = 1 * const_60
i = 1 / h
j = g + i 
k = d / j
l = k + 15
Problem: working together , tim and tom can type 12 pages in one hour . if they would be able to type 15 pages in one hour if tom increases his typing speed by 30 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 1 / 5 , b ) 5 / 1 , c ) 4 / 1 , d ) 1 / 4 , e ) 1 / 3
Rationale: lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 30 % means he will type 1.3 y pages an hour . so we get x + 1.3 y = 15 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.3 y = 3 so y = 10 . . . so x = 2 ( y / x ) = 10 / 2 = 5 / 1 answer is ( b )
Answer: b
Python program:
a = 15 - 12
b = 100 * 1
c = 30 / b
d = a / c
e = 15 - 12
f = 100 * 1
g = 30 / f
h = e / g
i = 12 - h
j = d / i
Problem: the interest on a certain deposit at 5 % per annum is rs . 101.20 in one year . how much will the additional interest in one year be on the same deposit at 6 % per annum ?
Options: a ) rs . 20.8 , b ) rs . 19.74 , c ) rs . 20.24 , d ) rs . 19.5 , e ) rs . 19.00
Rationale: explanation : principal , p = 100 × si / rt = 100 × 101.20 / 5 × 1 = 20 × 101.20 = rs . 2024 simple interest for rs . 2024 at 6 % per annum for 1 year , si = 2024 × 6 × 1100 = 121.44 additional interest = rs . 121.44 - rs . 101.20 = rs . 20.24 answer : option c
Answer: c
Python program:
a = 100 * 101
b = a / 5
c = b * 6
d = c / 100
e = d - 101
Problem: in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 309400 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 b )"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 65 / 100
e = c * d
Problem: the profit obtained by selling an article for rs . 86 is the same as the loss obtained by selling it for rs . 42 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 64
Rationale: "s . p 1 - c . p = c . p – s . p 2 86 - c . p = c . p - 42 2 c . p = 86 + 42 ; c . p = 128 / 2 = 64 answer : e"
Answer: e
Python program:
a = 86 + 42 
b = a / 2
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 3 = 12 feet answer : a"
Answer: a
Python program:
a = 16 / 4
b = a * 3
Problem: a batsman in his 12 th innings makes a score of 70 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 37 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 70 ∴ x = 37 answer b"
Answer: b
Python program:
a = 12 * 3
b = 70 - a
c = b + 3
Problem: a train 125 m long passes a man , running at 2 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 28 , d ) 47 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 2 ) km / hr . x - 2 = 45 = = > x = 47 km / hr answer : d"
Answer: d
Python program:
a = 2 * const_0_2778
b = a * 2
c = 125 - b
d = c / 10
e = d / const_0_2778
Problem: 50 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 57 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 50 orange + mango + apple = 4 50 + 10 + 4 - 7 = 57 like apple answer : d"
Answer: d
Python program:
a = 50 - 4
b = a + 7 
c = 10 - 7
d = b + c
Problem: 5 ^ 100 is divided by 18 . then what is the remainder ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: "here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c"
Answer: c
Python program:
a = 18 - 5
Problem: a corporation that had $ 120 billion in profits for the year paid out $ 200 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 4 % , e ) 0.17 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 200 million ) / ( 120 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 120 * 10 ^ 9 ) ] * 100 = ( 1.7 / 1000 ) * 100 = 0.17 % so answer is ( e )"
Answer: e
Python program:
a = 3 + 3 
b = 10 ** a
c = 200 * b
d = 10 ** 9
e = 120 * d
f = c / e
g = f * 100
Problem: a , b and c have rs . 900 between them , a and c together have rs . 400 and b and c rs . 750 . how much does c have ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 350
Rationale: "a + b + c = 900 a + c = 400 b + c = 750 - - - - - - - - - - - - - - a + b + 2 c = 1150 a + b + c = 900 - - - - - - - - - - - - - - - - c = 250 answer : d"
Answer: d
Python program:
a = 400 + 750 
b = a - 900
Problem: dividing by 3 ⁄ 8 and then multiplying by 5 ⁄ 8 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 3
Rationale: "say x / 3 / 8 * 5 / 8 = x * 8 / 3 * 5 / 8 = x * 5 / 3 e"
Answer: e
Python program:
a = 8 / 3
b = 5 / 8
c = a * b
Problem: there are 84 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 10 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 47 , e ) 64
Rationale: "x + ( x - 10 ) = 84 - - > x = 47 . answer : d ."
Answer: d
Python program:
a = 84 + 10 
b = a / 2
Problem: a positive integer , which when added to 1000 , gives a sum which is greater than when it is multiplied by 1000 . this positive integer is
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: solution ( 1000 + n ) > ( 1000 n ) clearly , n = 1 . answer a
Answer: a
Python program:
a = 1000 + 1 
b = 1000 * 1
c = a - b
Problem: the average of 11 numbers is 22 . average of the first 6 of them is 19 and that of the last 6 is 27 . find the 6 th number ?
Options: a ) 12 , b ) 25 , c ) 34 , d ) 29 , e ) 27
Rationale: sum of all the 11 numbers = 11 * 22 = 242 sum of the first 6 of them = 6 * 19 = 114 sum of the last 6 of them = 6 * 27 = 162 so , the 8 th number = 242 + 114 - 162 = 34 . answer : c
Answer: c
Python program:
a = 6 * 27
b = 11 * 22
c = 19 * 6
d = b - c
e = a - d
Problem: 10 men , working 6 hours a day can complete a work in 18 days . how many hours a day must 15 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution let the required number of hours per day be x . more men , less hours per day ( indirect proportion ) less days , more hours per day ( indirect proportion ) ∴ 15 × 12 × x = 10 × 18 × 6 ⇔ x = 10 x 18 x 6 / 15 x 12 = x = 6 . answer a"
Answer: a
Python program:
a = 10 * 6
b = a * 18
c = 15 * 12
d = b / c
Problem: 15 men can complete a piece of work in 30 days . in how many days can 10 men complete that piece of work ?
Options: a ) 45 , b ) 50 , c ) 34 , d ) 27 , e ) 11
Rationale: "15 * 30 = 10 * x = > x = 45 days answer : a"
Answer: a
Python program:
a = 30 * 15
b = a / 10