euclaise/mathqa_programs huggingface dataset:
Problem: how many positive factors do 180 and 90 have in common ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 180 and 90 is 90 number of factors of 90 = 12 answer : b"
Answer: b
Python program:
a = 90 - 10
b = a / 10
Problem: the population of a town is 10000 . it increases annually at the rate of 27 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 16129 , d ) 14600 , e ) 14700
Rationale: "formula : 10000 × 127 / 100 × 127 / 100 = 16129 answer : c"
Answer: c
Python program:
a = 10000 * 27
b = a / 100
c = b * 2
d = 10000 + c
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 5 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 85.5 % , d ) 70 % , e ) 72 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 5 % , price = 81 - 4.05 = 76.95 which is 76.95 / 90 * 100 of the sale price on day 1 = ~ 8 answer c"
Answer: c
Python program:
a = 5 / 100
b = 1 / 10
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: the captain of a cricket team of 11 members is 30 years old and the wicket keeper is 5 years younger . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?
Options: a ) 20 , b ) 23 , c ) 32 , d ) 19 , e ) 29
Rationale: "let the average of the whole team be x years . 11 x - ( 30 + 25 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer : b"
Answer: b
Python program:
a = 30 + 5 
b = 30 + a 
c = 5 * 5
d = b - c
e = d / 2
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 300 more . what was the sum ?
Options: a ) s . 1200 , b ) s . 1300 , c ) s . 600 , d ) s . 800 , e ) s . 1200
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 300 ( given ) so , at 5 % more rate , the increase in si for 1 year = 300 / 10 = rs . 30 / - i . e . rs . 30 is 5 % of the invested sum so , 1 % of the invested sum = 30 / 5 therefore , the invested sum = 30 × 100 / 5 = rs . 600 answer : c"
Answer: c
Python program:
a = 5 / 100
b = a * 10
c = 300 / b
Problem: in an exam 49 % candidates failed in english and 36 % failed in hindi and 15 % failed in both subjects . if the total number of candidates who passed in english alone is 630 . what is the total number of candidates appeared in exam ?
Options: a ) 2000 , b ) 3000 , c ) 3500 , d ) 3800 , e ) 4000
Rationale: not fail in english = 51 % not fail in hindi = 64 % not fail in both = 30 % ( 49 + 36 - 15 ) pass in english only = 51 - 30 = 21 21 / 100 * x = 630 x = 3000 answer : b
Answer: b
Python program:
a = 36 - 15
b = 100 / a
c = 630 * b
Problem: each of the three people individually can complete a certain job in 4 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 4 / 15 , b ) 7 / 30 , c ) 11 / 30 , d ) 5 / 18 , e ) 7 / 18
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."
Answer: c
Python program:
a = 1 / 5
b = 1 / 6
c = a + b
Problem: find the smallest number which when divided by 11 and 13 leaves respective remainders of 4 and 6 .
Options: a ) 187 , b ) 197 , c ) 207 , d ) 136 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 11 and 13 leaves respective remainders of 4 and 6 . required number = ( lcm of 11 and 13 ) - ( common difference of divisors and remainders ) = ( 143 ) - ( 7 ) = 136 . answer : d"
Answer: d
Python program:
a = 11 * 13
b = 10 + 1 
c = a - b
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 180 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 180 * ( 5 / 18 ) = 50 m / sec time = distance / speed = 100 / 50 = 2 seconds answer : d"
Answer: d
Python program:
a = 180 * const_0_2778
b = 100 / a
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 7.5 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 10 ã — 15 = 150 m â ˆ ´ required time = 150 â  „ 20 = 7.5 sec . answer b"
Answer: b
Python program:
a = 12 * 15
b = a - 15
c = 12 * 15
d = c / 9
e = b / d
Problem: in a box of 8 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 6 / 11 , b ) 8 / 15 , c ) 9 / 20 , d ) 11 / 25 , e ) 15 / 28
Rationale: "p ( neither pen is defective ) = 6 / 8 * 5 / 7 = 15 / 28 the answer is e ."
Answer: e
Python program:
a = 8 - 2
b = a / 8
c = 8 - 2
d = c - 1
e = 8 - 1
f = d / e
g = b * f
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 500 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 512.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 25,000 . now , put the value of x = 5000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 5000 + 5 % of 5000 = 5250 . 2 nd year , amount = 5250 + 5 % of 5250 = 5512.50 . we can see after 2 years interest = 5512.50 - 5000 = 512.50 hence , it satisfies the question . hence c is the correct answer"
Answer: c
Python program:
a = 500 / 2
b = a ** 2
c = 512 - 50
d = b / c
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 5 xy / 3 = ?
Options: a ) a ) 5 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 5 * 3 * 1 ) / 3 = 15 / 3 = 5 a"
Answer: a
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 5
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 2880 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 3645
Rationale: "2880 * 9 / 8 * 9 / 8 = 3645 answer : e"
Answer: e
Python program:
a = 1 / 8
b = a * 2880
c = 2880 + b 
d = 1 / 8
e = 1 / 8
f = e * 2880
g = 2880 + f 
h = d * g
i = c + h
Problem: a man is walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . answer : d"
Answer: d
Python program:
a = 15 / const_60
b = 5 * a
c = b * 1000
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg , what is his percent ?
Options: a ) 19 , b ) 25 , c ) 77 , d ) 88 , e ) 11
Rationale: "840 - - - 160 100 - - - ? = > 19 % answer : a"
Answer: a
Python program:
a = 100 / 840
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: a train 500 m long passes a man , running at 9 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 105 , b ) 95 , c ) 90 , d ) 99 , e ) 100
Rationale: "speed of the train relative to man = 500 / 20 m / sec = 25 m / sec . = 25 x 18 / 5 km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 9 ) km / hr . x - 9 = 90 = 99 km / hr . answer : d"
Answer: d
Python program:
a = 9 * const_0_2778
b = a * 9
c = 500 - b
d = c / 9
e = d / const_0_2778
Problem: the cost price of a radio is rs . 4800 and it was sold for rs . 4400 , find the loss % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "4800 - - - - 400 100 - - - - ? = > 8 % answer : a"
Answer: a
Python program:
a = 4800 - 4400
b = a / 4800
c = b * 100
Problem: line m lies in the xy - plane . the y - intercept of line m is - 5 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 5 ) means line m is parallel to x axis slope m = - 3 ans : a"
Answer: a
Python program:
a = 4 - 8
b = a / 2
c = b + 5 
d = 2 + 6 
e = d / 2
f = c / e
Problem: a certain machine produces 1,100 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 6 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 100,000 , e ) 158,400
Rationale: since 6 days consist of 24 * 6 hours the total is 144 hours . since every hour the machine produces 1100 units of product p the total product during 144 hours is 144 * 1100 = 158,400 . correct option : e
Answer: e
Python program:
a = 4 * 10
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 150 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "if linda spent 3 / 4 of her savings on furniture , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 150 . so 1 / 4 of her savings is $ 150 . so her original savings are 4 times $ 150 = $ 600 correct answer b"
Answer: b
Python program:
a = 3 / 4
b = 1 - a
c = 150 / b
Problem: if 8 people can eat a gallon of ice cream in 10 days , how long would it take 5 people to eat a gallon of ice cream ?
Options: a ) 12 days , b ) 14 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: 8 * 10 = 5 * x x = 16 answer : c
Answer: c
Python program:
a = 8 * 10
b = a / 5
Problem: 8 x 2.4 - 5 x 1.4 / 1.5 = ?
Options: a ) 9.46 , b ) 2.03 , c ) 50.4 , d ) 14.65 , e ) 12.85
Rationale: "given expression = ( 19.2 - 5 x 1.4 ) / 1.5 = 14.2 / 1.5 = 14.2 / 1.5 = 9.46 answer is a"
Answer: a
Python program:
a = 8 * 2
b = 5 * 1
c = a - b
d = c / 1
Problem: in what time will a train 20 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 0.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 20 / 40 = 0.5 sec . answer : c"
Answer: c
Python program:
a = 144 * const_0_2778
b = 20 / a
Problem: the sum of number of boys and girls in a school is 150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 150 = 150 x + x / 100 * 150 = 150 5 / 2 * x = 150 x = 150 * 2 / 5 = 60 answer is c"
Answer: c
Python program:
a = 150 / 100
b = a + 1 
c = 150 / b
Problem: two trains a and b are 175 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 13 s
Rationale: detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 175 + 150 = 325 m . time taken = 325 / 25 = 13 s . correct answer e .
Answer: e
Python program:
a = 175 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: a train traveling with constant speed crosses a 90 m long platform in 12 seconds and a 120 m long platform in 15 seconds . find the length of the train and its speed .
Options: a ) 30 , b ) 40 , c ) 60 , d ) 50 , e ) none
Rationale: let the length of the train be x m and its speed be y m / sec . then , x / y = 12 = > y = x / 12 ( x + 90 ) / 12 = x + 120 / 15 = > x = 30 m . answer : a
Answer: a
Python program:
a = 12 * 120
b = 90 * 15
c = a - b
d = 15 - 12
e = c / d
Problem: if the average ( arithmetic mean ) of a and b is 100 , and c – a = 120 , what is the average of b and c ?
Options: a ) 150 , b ) 140 , c ) 160 , d ) 170 , e ) 180
Rationale: "a + b / 2 = 100 = > a + b = 200 a = c - 120 . . . sub this value c - 120 + b = 200 = > c + b = 320 = > c + b / 2 = 160 answer : c"
Answer: c
Python program:
a = 120 * 2
b = 100 * 2
c = a - b
Problem: how many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 130 + 150 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec a"
Answer: a
Python program:
a = 150 + 130 
b = 36 * const_0_2778
c = a / b
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14 - - > x = $ 17.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17.5 + 21 = $ 38.5 . answer : b ."
Answer: b
Python program:
a = 40 / 100
b = 35 * a
c = b + 35
Problem: find the 18 th term of an arithmetic progression whose first term is 4 and the common difference is 5 .
Options: a ) 45 , b ) 38 , c ) 72 , d ) 74 , e ) 78
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 4 + ( 18 - 1 ) * 4 , = 4 + 68 = 72 . answer : c"
Answer: c
Python program:
a = 18 - 1
b = a * 5
c = b + 4
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 18 - m ) then m = ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 m = 18 - m 3 m = 18 m = 6 the answer is c ."
Answer: c
Python program:
a = 2 + 1 
b = 18 / a
Problem: in a school of 850 boys , 44 % of muslims , 32 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 119 , c ) c ) 153 , d ) d ) 721 , e ) e ) 159
Rationale: "44 + 32 + 10 = 86 % 100 – 84 = 14 % 850 * 14 / 100 = 119 answer : b"
Answer: b
Python program:
a = 44 + 32 
b = a + 10 
c = 100 - b
d = 850 * c
e = d / 100
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 12 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 12 ) years . ( x + 12 + 10 ) = 2 ( x — 10 ) hence x = 42 . present age of b = 42 years answer : option e"
Answer: e
Python program:
a = 2 * 10
b = 12 + 10 
c = a + b
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 3 / 10 , b ) 7 / 10 , c ) 9 / 10 , d ) 9 / 20 , e ) 13 / 20
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 5 ) y = ( 9 / 20 ) y the answer is d ."
Answer: d
Python program:
a = 1 / 5
b = a * 12
c = 12 / 2
d = 1 / 2
e = c * d
f = b + e 
g = f / 12
Problem: the average age of 3 boys is 120 years and their ages are in proportion 2 : 6 : 8 . what is the age in years of the youngest boy ?
Options: a ) 10 , b ) 9 , c ) 15 , d ) 6 , e ) 12
Rationale: 2 x + 6 x + 8 x = 120 x = 7.5 2 x = 15 answer : c
Answer: c
Python program:
a = 2 + 6 
b = a + 8 
c = 120 / b
d = c * 2
Problem: for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 25000 , my total savings for the two - year is
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 10000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 25000 + 35000 ) = 66000 - 60000 = rs . 6000 a"
Answer: a
Python program:
a = 25000 * 5
b = a / 3
c = 42000 - b
d = 42000 * 4
e = d / 7
f = e - 25000
g = c + f
Problem: rahul played weel in this season . his current batting averagge is 50 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "50 x + 78 = 54 ( x + 1 ) = > 4 x = 24 = > x = 6 answer : d"
Answer: d
Python program:
a = 78 - 54
b = 54 - 50
c = a / b
Problem: in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag - the greatest chance of drawing a red ball ?
Options: a ) 1 / 8 , b ) 2 / 8 , c ) 3 / 8 , d ) 4 / 8 , e ) 5 / 8
Rationale: "greatest chance . 1 / 2 * 1 + 1 / 2 * 4 / 16 = 5 / 8 answer : e"
Answer: e
Python program:
a = 5 + 12 
b = a - 1
c = 5 / b
d = 2 * 2
e = 5 + 12 
f = e - 1
g = d / f
h = c + g
Problem: a man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 12 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 12 , d = 12 b - 12 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 12 b - 12 c = 4 b + 4 c , - - > b = 2 c , - - > d = 12 b - 6 b = 6 b . interval = \ frac { d } { b } = \ frac { 6 b } { b } = 6 answer : b ( 6 minutes ) ."
Answer: b
Python program:
a = 4 + 12 
b = 12 - 4
c = a / b
d = 12 / c
e = 12 - d
f = e / 1
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8900 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 2900 , b ) s . 3570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8900 = 35600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3600 salary of may is rs . 6500 salary of january = rs . 2900 answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 8900 * 4
c = b - 6500
d = a - c
Problem: ( 3 x + 4 ) ( 2 x - 5 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 15
Rationale: "expanding we have 6 x ^ 2 - 15 x + 8 x - 20 6 x ^ 2 - 7 x - 20 taking coefficients , a = 6 , k = - 7 , n = - 20 therefore a - n + k = 6 - ( - 20 ) - 11 = 26 - 11 = 15 the answer is e ."
Answer: e
Python program:
a = 3 * 4
b = 5 * 4
c = a + b 
d = 4 * 4
e = 5 * 3
f = d - e
g = c + f
Problem: a shopkeeper has 280 kg of apples . he sells 45 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 27 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 45 x 20 % + 60 x 30 % = 27 this profit will remain same for any total quantity unless the % of products remains the same . hence ' c ' is the answer"
Answer: c
Python program:
a = 280 * 45
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = 280 * 60
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 280
m = l * 100
n = m / 280
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 40,000 , how much profit did the business make ?
Options: a ) $ 44,000 , b ) $ 54,000 , c ) $ 64,000 , d ) $ 84,000 , e ) $ 104,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 40000 p = $ 64,000 the answer is c ."
Answer: c
Python program:
a = 1 + 4 
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i 
k = c / j
Problem: 70 % of the employees of a company are men . 50 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 83.33 % , d ) 90.33 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 70 women = 30 men speaking french = 0.5 * 70 = 35 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 35 = 5 and women not speaking french = 30 - 5 = 25 % of women not speaking french = 25 / 30 * 100 = 83.33 % answer c"
Answer: c
Python program:
a = 100 - 70
b = a / 100
c = 40 / 100
d = 70 / 100
e = 50 / 100
f = d * e
g = c - f
h = b - g
i = 100 - 70
j = i / 100
k = h / j
l = k * 100
Problem: a and b are partners in a business . a contributes 1 / 4 of the capital for 15 months and b received 2 / 3 of the profit . for how long b ' s money was used ?
Options: a ) 10 , b ) 37 , c ) 27 , d ) 18 , e ) 19
Rationale: let the total profit be rs . z . then , b ' s share = rs . 2 z / 3 , a ' s share = rs . ( z - 2 z / 3 ) = rs . z / 3 . a : b = z / 3 : 2 z / 3 = 1 : 2 let the total capital be rs , x and suppose b ' s money was used for x months . then . ( 1 ( x ) / 4 * 15 ) / ( 3 x ) / 4 * y ) = 1 / 2 < = > y = ( 15 * 2 / 3 ) = 10 . thus , b ' s money was used for 10 months . answer : a ) 10 months
Answer: a
Python program:
a = 10 + 1 
b = a - 1
Problem: 3 * 15 + 3 * 16 + 3 * 19 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 161
Rationale: "3 * 15 + 3 * 16 + 3 * 19 + 11 = 45 + 48 + 57 + 11 = 161 the answer is e ."
Answer: e
Python program:
a = 3 * 15
b = 3 * 16
c = a + b 
d = 3 * 19
e = c + d 
f = e + 11
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 14 hr , e ) 16 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 1 / 3 ) = 1 / 14 leak will empty the tank in 14 hrs . answer : d"
Answer: d
Python program:
a = 1 / 2
b = 2 * 3
c = b + 1 
d = c / 3
e = 1/(d)
f = a - e
g = 1/(f)