euclaise/mathqa_programs huggingface dataset:
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d"
Answer: d
Python program:
a = 90 - 45
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
Problem: the radius of a semi circle is 35 cm then its perimeter is ?
Options: a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b"
Answer: b
Python program:
a = circumface / (
b = a + 2
Problem: an inspector rejects 0.06 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3333
Rationale: "let the number of meters to be examined be x then , 0.06 % of x = 2 ( 6 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 3333 answer is e"
Answer: e
Python program:
a = 2 * 100
b = a / 0
Problem: the present worth of rs . 1404 due in two equal half - yearly installments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) rs . 1600
Rationale: "time = 1 / 2 yr r = 8 % let pw = x si = 1404 - x x * 1 / 2 * 8 / 100 = 1404 - x . ( ref problm 10 of si , rs aggarwal ) x = 1404 * 25 / 26 hence x = 1350 answer : c"
Answer: c
Python program:
a = 1404 / 2
b = 100 + 8 
c = b / 100
d = a / c
e = 1404 / 2
f = 8 / 2
g = 100 + f 
h = g / 100
i = e / h
j = d + i
Problem: a train moves with a speed of 72 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 20 , e ) none
Rationale: "solution speed = 72 kmph = ( 72 x 5 / 18 ) m / sec = 20 m / sec . answer d"
Answer: d
Python program:
a = 72 * const_0_2778
Problem: 40 % of 2 is equal to
Options: a ) 0.2 , b ) 0.8 , c ) 0.6 , d ) 0.7 , e ) 0.9
Rationale: 40 % of 2 = ( 40 / 100 ) * 2 = 0.8 answer : option b
Answer: b
Python program:
a = 40 * 2
b = a / 100
Problem: how many positive integers less than 243 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64
Rationale: "240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d"
Answer: d
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a can finish a piece of work in 5 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 days , b ) 6 days , c ) 7 days , d ) 1 days , e ) 3 days
Rationale: "a 4 days 2 / 5 + ( 2 + x ) / 10 = 1 = > x = 4 days"
Answer: a
Python program:
a = 1 / 5
b = a * 2
c = 1 / 10
d = c * 2
e = b + d 
f = 1 - e
g = 1 / 10
h = f / g
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400
Rationale: let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e
Answer: e
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 = h + 1 
j = 6936 / i
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 59.4 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 20 + 20 + 10 + 5 + 2.5 + 1.25 + 0.6 ans b"
Answer: b
Python program:
a = 20 / 2
b = a / 2
Problem: a rectangular tiled patio is composed of 80 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 80 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 12 , e ) 28
Rationale: "r * c = 80 and ( 12 + 4 ) ( c - 2 ) = 80 - - > r = 12 and c = 7 . answer : d ."
Answer: d
Python program:
a = negate + ( 
b = 4 ** 2
c = 80 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 80 / g
Problem: the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none
Rationale: olution required number of students . = h . c . f of 891 and 810 . â € ¹ = â € º 81 . answer b
Answer: b
Python program:
a = 891 - 810
Problem: what is the slope of a line on a standard xy - plane that passes through the point ( 1 , 3 ) and ( 4 , – 3 ) ?
Options: a ) - 1 , b ) 2 , c ) - 2 , d ) 1 / 2 , e ) - 1 / 2
Rationale: plug the values for the coordinates into the formula for the slope of a line : slope = y 2 - y 1 / x 2 - x 1 = - 3 - 3 / 4 - 1 = - 6 / 3 = - 2 correct answer c ) - 2
Answer: c
Python program:
a = negate - (
b = a / 3
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ?
Options: a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256
Rationale: "ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c"
Answer: c
Python program:
a = 124 - 122
b = 122 * a
c = 124 - 122
d = b * c
Problem: pipe a can fill a tank in 5 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 67 , b ) 10 , c ) 18 , d ) 26 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 5 - 1 / x = 1 / 10 = > 1 / x = 1 / 5 - 1 / 10 = 1 / 10 = > x = 10 . answer : b"
Answer: b
Python program:
a = 10 * 5
b = 10 - 5
c = a / b
Problem: a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 20 * 25 = 500 correct answer b"
Answer: b
Python program:
a = 20 * 25
Problem: find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 .
Options: a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512
Rationale: "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c"
Answer: c
Python program:
a = 5 / 34
b = 7 / 48
c = a / b
d = 2 / 13
e = c * d
Problem: if 40 % of a number is greater than 80 % of 5 by 2 , what is the number ?
Options: a ) 3 , b ) 15 , c ) 20 , d ) 2 , e ) 5
Rationale: "explanation : 40 / 100 * x - 80 / 100 * 5 = 2 40 / 100 * x - 4 = 2 40 / 100 * x = 6 x = 6 * 100 / 40 x = 15 answer : option b"
Answer: b
Python program:
a = 5 / 100
b = a * 80
c = 2 + b 
d = c / 40
e = 100 * d
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 additional hours , so harry worked for total of 30 + 5.75 = 35.75 hours . answer : a ."
Answer: a
Python program:
a = 40 + 1 
b = a - 30
c = b / 2
d = c + 30
Problem: in a group of 80 people , 45 have visited iceland and 33 have visited norway . if 41 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 80 = 45 + 33 - 41 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Python program:
a = 45 + 33 
b = a - 41
c = 80 - b
Problem: seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways . hence the probability is 6 / 279936 = 1 / 46656 answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 8000 , brokerage being 1 / 4 % , is :
Options: a ) 110.86 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 8000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 8000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 111.11 = market value of rs . 100 stock = rs . 111.11 - re . 0.25 . = market value of rs . 100 stock = rs . 110.86 . answer : a"
Answer: a
Python program:
a = 8000 / 756
b = a * 10
c = 1 / 4
d = b - c
Problem: p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ?
Options: a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000
Rationale: solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e
Answer: e
Python program:
a = 4000 * 12
b = 3 * a
c = b / 2
d = 12 - 4
e = c / d
Problem: what is the probability of getting exactly 1 head in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Rationale: "one possible case is htttt . p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 1 = 5 possible cases . p ( 1 head ) = 5 * 1 / 32 = 5 / 32 the answer is d ."
Answer: d
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: - 64 * 29 + 468 = ?
Options: a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these
Rationale: = > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d
Answer: d
Python program:
a = negate * (
b = a + 29
Problem: there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 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 ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 70 - - > x = 42 . answer : c ."
Answer: c
Python program:
a = 70 + 14 
b = a / 2
Problem: a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ?
Options: a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22
Rationale: "wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b"
Answer: b
Python program:
a = 1/(14)
b = 2 + 1 
c = a / b
d = 1/(c)
Problem: find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b"
Answer: b
Python program:
a = 165826 / 4
b = math.floor(a)
c = b * 4
d = 165826 - c
Problem: hcf and lcm two numbers are 14 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 154 , d ) 264 , e ) 364
Rationale: "14 * 396 = 36 * x x = 154 answer : c"
Answer: c
Python program:
a = 14 * 396
b = a / 36
Problem: a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec
Rationale: "total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a"
Answer: a
Python program:
a = 60 - 240
b = a * const_0_2778
c = 240 / b
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km .
Options: a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a"
Answer: a
Python program:
a = 40 * 2
b = 40 / 40
c = 2 * 40
d = c / 20
e = b + d 
f = a / e
Problem: if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be
Options: a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a .
Answer: a
Python program:
a = 8 + 1
Problem: a light flashes every 12 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 300 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 12 sec for 1 min = 5 flashes so for 1 hour = 5 * 60 = 300 flashes . answer : b"
Answer: b
Python program:
a = 3600 / 12
Problem: some of the 68 % solution of acid was removed and this was replaced with an equal amount of 11 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 7 / 11 , b ) 7 / 17 , c ) 8 / 17 , d ) 8 / 19 , e ) 11 / 19
Rationale: "let x be the fraction of the original solution that was replaced . 0.68 * ( 1 - x ) + 0.11 ( x ) = 0.35 0.57 x = 0.33 x = 33 / 57 = 11 / 19 the answer is e ."
Answer: e
Python program:
a = 68 + 11 
b = 35 / a
Problem: how many natural numbers between 23 and 137 are divisible by 7 ?
Options: a ) 12 , b ) 17 , c ) 16 , d ) 13 , e ) 15
Rationale: "solution : these numbers are 28 , 35 , 42 , … . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c"
Answer: c
Python program:
a = 137 - 4
b = 23 + 1 
c = a - b
d = c / 7
e = d + 1
Problem: ages of two sisters differ by 9 years . if 5 years ago , the elder one was twice as old the younger one , find their present age
Options: a ) 1228 , b ) 1423 , c ) 1632 , d ) 1834 , e ) 1932
Rationale: explanation : let the age of younger sister be x , then elder sister ' s age is ( x + 9 ) = > 2 ( x - 5 ) = ( x + 9 - 5 ) [ 5 years before ] = > 2 x - 10 = x + 4 = > x = 14 . so older sister ' s age is x + 9 = 23 answer : option b
Answer: b
Python program:
a = 5 * 2
b = a - 5
c = 9 + b 
d = 5 * 2
e = d - 5
f = 9 + e 
g = 9 + f 
h = c / g
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 6 , and the ratio of flour to baking soda is 5 to 1 . if there were 30 more pounds of baking soda in the room , the ratio of flour to baking soda would be 4 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 45 , e ) 70
Rationale: "sugar : flour = 3 : 6 = 1 : 2 = 5 : 10 flour : soda = 5 : 1 = 10 : 2 ; thus we have that sugar : flour : soda = 5 x : 10 x : 2 x . also given that 10 x / ( 2 x + 30 ) = 4 / 1 - - > x = 60 - - > sugar = 5 x = 30 . answer : a"
Answer: a
Python program:
a = 3 / 6
b = 4 * 30
c = 5 - 4
d = b / c
e = 5 * d
f = a * e
Problem: there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27
Rationale: total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of total students = 1 / 5 * 1 / 2 * 100 = 10 . . . answer b
Answer: b
Python program:
a = 100 / 2
b = 1 + 4 
c = a / b
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 130 and $ 160 respectively . charles earns $ 30 more than robin who earns $ 130 . therefore , charles ' wage is 30 / 130 * 100 = 23.07 % . correct choice is ( a )"
Answer: a
Python program:
a = 100 + 60 
b = 100 + 30 
c = a - b
d = 100 + 30 
e = c / d
f = e * 100
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 60 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: a ) 1
Answer: a
Python program:
a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 60 
g = reminder + ( 
h = math.floor(g, 1)
Problem: how many times are the hands of a clock at right angle in 6 hours ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "in 12 hours , they are at right angles 22 times . in 6 hours , they are at right angles 11 times . answer : option c"
Answer: c
Python program:
a = 12 * 2
b = a * 6
c = 12 * 4
d = c - 4
e = b * d
f = 12 * 2
g = e / f
Problem: a and b can do a piece of work in 4 days , b and c in 6 days , c and a in 3 days . how long will c take to do it ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 4 days , e ) 12 days
Rationale: "2 c = 1 / 6 + 1 / 3 – 1 / 4 = 1 / 4 c = 1 / 8 = > 8 days answer : a"
Answer: a
Python program:
a = 4 * 3
b = 4 * 3
c = b / 3
d = 4 * 3
e = d / 4
f = 4 * 3
g = f / 6
h = e + g 
i = c + h 
j = i / 2
k = 4 * 3
l = k / 4
m = j - l
n = a / m
Problem: 45 % of the employees of a company are men . 60 % 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 ) 76.36 % , d ) 90.16 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 45 women = 55 men speaking french = 0.6 * 45 = 27 employees speaking french = 0.55 * 100 = 55 therefore women speaking french = 55 - 42 = 13 and women not speaking french = 55 - 13 = 42 % of women not speaking french = 42 / 55 * 100 = 76.36 % answer c"
Answer: c
Python program:
a = 100 - 45
b = a / 100
c = 40 / 100
d = 45 / 100
e = 60 / 100
f = d * e
g = c - f
h = b - g
i = 100 - 45
j = i / 100
k = h / j
l = k * 100
Problem: a person spent rs . 6,040 from his salary on food and 5,000 on house rent . after that he was left with 80 % of his monthly salary . what is his monthly salary ?
Options: a ) 55,200 , b ) 65,200 , c ) 75,200 , d ) 85,200 , e ) 95,200
Rationale: "total money spent on food and house rent = 6,040 + 5,000 = 11,040 which is 100 - 80 = 20 % of his monthly salary ∴ his salary = 11040 x 100 / 20 = 55200 answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a * 100
c = b + 80 
d = math.sqrt(100)
e = c / d
Problem: if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: 7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b
Answer: b
Python program:
a = 7 / 8
b = 3 / 4
c = a - b
d = 1 / c
e = 5 * d
Problem: the number of singles that a baseball player hit increased 11 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 1 : 3 , b ) 9 : 11 , c ) 1 : 1 , d ) 2 : 1 , e ) 11 : 3
Rationale: "soln : - 1.11 s + 0.99 d = 1.02 [ s + d ] 0.09 s = 0.03 d s / d = 1 / 3 answer : a"
Answer: a
Python program:
a = 100 - 1
b = 100 + 11 
c = a / b
Problem: trail mix consists of chex cereal , m & m ' s , raisins , and assorted nuts . if one serving consists of 4 cups chex cereal , 3 cups m & m ' s , 2 cups rains , and 4 cups assorted nuts , and the ratio of the chex is doubled to to the m & m ' s , what is the ratio of chex to the rest of the dish ?
Options: a ) 10 : 5 , b ) 15 : 9 , c ) 7 : 17 , d ) 19 : 23 , e ) not enough information given for the answer
Rationale: the answer to this question is way too long for such a simple question , but there ' s really not enough information to tell , so the answer is e .
Answer: e
Python program:
a = 4 + 3 
b = a + 2 
c = b + 4 
d = 4 / c
Problem: which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 16 is 6 ?
Options: a ) 168 , b ) 172 , c ) 170 , d ) 174 , e ) 176
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 6 will be { 336 + 6 , 336 x 2 + 6 , 336 x 3 + 6 , . . . } the largest such number less than or equal to 1856 is 336 x 5 + 6 or 1686 to obtain this you need to subtract 170 . c"
Answer: c
Python program:
a = math.lcm(7, 12)
b = math.lcm(a, 16)
c = math.gcd(1856, b)
d = math.lcm(7, 12)
e = math.lcm(d, 16)
f = c * e
g = 6 + f 
h = 1856 - g
Problem: find 96 × × 98
Options: a ) 92 / 8 , b ) 92 / 12 , c ) 92 / 13 , d ) 92 / 10 , e ) 92 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 4 and - 2 compared with 100 . so answer : a"
Answer: a
Python program:
a = 96 / 98
Problem: a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) 32 yrs , b ) 36 yrs , c ) 40 yrs , d ) 48 yrs , e ) none
Rationale: "explanation : let the mother ' s present age be x years . then , the person ' s present age = ( 2 / 5 ) * x years . ( ( 2 / 5 ) * x ) + 8 = ( 1 / 2 ) ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 . answer : c"
Answer: c
Python program:
a = 2 + 3 
b = 8 - a
c = 1 / 2
d = 2 + 3 
e = 2 / d
f = c - e
g = b / f