euclaise/mathqa_programs huggingface dataset:
Problem: the cost of 8 pens and 4 pencils is rs . 200 and the cost of 2 pens and 2 pencils is rs . 48 . find the cost of each pen ?
Options: a ) rs . 32 , b ) rs . 36 , c ) rs . 42 , d ) rs . 26 , e ) rs . 104
Rationale: "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 8 p + 4 q = 200 - - - ( 1 ) 2 p + 2 q = 48 4 p + 4 q = 96 - - - ( 2 ) ( 1 ) - ( 2 ) = > 4 p = 104 = > p = 26 answer : d"
Answer: d
Python program:
a = 8 * 4
b = 8 + 2 
c = 200 / b
d = a * c
Problem: if the product of 4 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the product of 4 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 3 correct option : b
Answer: b
Python program:
a = 4 - 1
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 4.32 , b ) 4.42 , c ) 4.52 , d ) 4.62 , e ) 4.72
Rationale: "m = 9 s = 1.2 ds = 9 + 1.2 = 10.2 us = 9 - 1.2 = 7.8 x / 10.2 + x / 7.8 = 1 x = 4.42 . answer : b"
Answer: b
Python program:
a = 9 + 1 
b = 9 - 1
c = a * b
d = 9 + 1 
e = 9 - 1
f = d + e 
g = c / f
h = g * 2
Problem: if 12 men can reap 120 acres of land in 36 days , how many acres of land can 44 men reap in 54 days ?
Options: a ) 820 acres , b ) 660 acres , c ) 620 acres , d ) 720 acres , e ) 920 acres
Rationale: "12 men 120 acres 36 days 44 men ? 54 days 120 * 44 / 12 * 54 / 36 10 * 44 * 3 / 2 44 * 15 = 660 answer : b"
Answer: b
Python program:
a = 44 / 12
b = 54 / 36
c = a * b
d = 120 * c
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 3 years ?
Options: a ) 3277 , b ) 2977 , c ) 16875 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 ( 34 ) 3 = 1687540,000 ( 34 ) 3 = 16875 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 3
e = b * d
Problem: the wages earned by robin is 50 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 7 %
Rationale: "let wage of erica = 10 wage of robin = 1.5 * 10 = 15 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 15 ) / 15 * 100 % = 1 / 15 * 100 % = 7 % answer e"
Answer: e
Python program:
a = 100 + 60 
b = 100 + 50 
c = a - b
d = 100 + 50 
e = c / d
f = e * 100
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio r of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore r , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10 
f = e / 20
g = 20 - 10
h = f * g
i = h + 10 
j = 3 + 2 
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
Problem: reb normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if reb averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: reb normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Python program:
a = 45 / const_60
b = 40 * a
c = 100 - 20
d = c / 100
e = b * d
f = e / 12
g = f * const_60
h = g - 45
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent p of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp p = = 50 % of cp thus , answer should bec ."
Answer: c
Python program:
a = 100 - 20
b = a - 20
c = 100 - b
Problem: a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,305 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.15 * 4500 = 5175 cost of type b products next year = 1.1 * 8300 = 9130 total 5175 + 9130 = 14305 option a"
Answer: a
Python program:
a = 3 / 4
b = a * 1000
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 28 x + 49 . if the sum of the perimeters of both squares is 72 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 4 ) ^ 2 and ( 2 x - 7 ) ^ 2 . the lengths of the sides are x + 4 and 2 x - 7 . if we add the two perimeters : 4 ( x + 4 ) + 4 ( 2 x - 7 ) = 72 12 x = 84 x = 7 the answer is e ."
Answer: e
Python program:
a = 8 / 2
b = 4 * a
c = b - 8
d = 72 - c
e = d / 8
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 50
Rationale: "there are 10 books less ( 75 - 65 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 50 answer e"
Answer: e
Python program:
a = 75 - 65
b = 80 / 100
c = 1 - b
d = a / c
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 95 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 155 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 186
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 186 min * leg a - b - - - > d = 95.186 / 60 = 17670 / 60 * leg b - a - - - - > d = 155 * 114 / 60 = 17670 / 60 so the correct ans . ise"
Answer: e
Python program:
a = 95 * 5
b = 95 + 155 
c = a / b
d = 5 - c
e = d * const_60
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8091 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 2977 , c ) 2871 , d ) 6725 , e ) 6525
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 8091 ( 100 / 124 ) = rs . 6525 . answer : e"
Answer: e
Python program:
a = 24 / 100
b = 1 + a 
c = 8091 / b
Problem: what is the smallest number which when diminished by 10 , is divisible 2 , 6 , 12 and 24 ?
Options: a ) 35 , b ) 34 , c ) 20 , d ) 35 , e ) 342
Rationale: "required number = ( lcm of 2 , 6 , 12 and 24 ) + 12 = 24 + 10 = 34 option b"
Answer: b
Python program:
a = math.lcm(2, 6)
b = math.lcm(12, 24)
c = math.lcm(a, b)
d = c + 10
Problem: the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 108 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c"
Answer: c
Python program:
a = 1 / 4
b = 108 - 25
Problem: if n is the greatest positive integer for which 4 ^ n is a factor of 8 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "8 ! = 40320 e . 4 ^ 10 = 1048576 ( 40320 / 1048576 ) - this is not a factor of 8 ! d . 4 ^ 8 = 65536 ( 40320 / 65536 ) - this is not a factor of 8 ! c . 4 ^ 6 = 4096 ( 40320 / 4096 ) - this is not a factor of 8 ! b . 4 ^ 4 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! a . 4 ^ 2 = 16 ( 40320 / 16 ) - this is a factor of 8 !"
Answer: a
Python program:
a = 8 / 2
b = a - 1
Problem: if the average ( arithmetic mean ) of a and b is 215 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 110 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 215 = = = > a + b = 430 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 430 - 320 = = = > a + b - b - c = 110 = = = > a - c = 110 answer : d"
Answer: d
Python program:
a = const_60 * 0
b = 215 * 2
c = a - b
Problem: 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is w , what is the difference between the probability that w is even and the probability that w is odd ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2
Rationale: age of boys w : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 1311 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 1714 9 combinations of sum between sets ( 10 , 1211 ) ( 13 , 1714 ) = 23 , 2724 - 16 , 3017 - 24 , 2825 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
Answer: a
Python program:
a = 1 / 3
b = 1 / 3
c = a * b
d = 2 / 3
e = 2 / 3
f = d * e
g = c + f 
h = 1 / 3
i = 2 / 3
j = h * i
k = 1 / 3
l = 2 / 3
m = k * l
n = j + m 
o = g - n
Problem: a can do a job in 30 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 26 days , c ) 30 days , d ) 31 days , e ) 39 days
Rationale: "c 1 / 30 + 1 / 30 = 1 / 15 15 * 2 = 30 days"
Answer: c
Python program:
a = 1 / 30
b = 1 / 30
c = a + b
Problem: 8 x 2.25 - 5 x 0.85 / 2.5 = ?
Options: a ) 3.8 , b ) 10 , c ) 5 , d ) 5.5 , e ) 7.5
Rationale: "given expression = ( 18 - 4.25 / 2.5 = 13.75 / 2.5 = 137.5 / 25 = 5.5 answer is d ."
Answer: d
Python program:
a = 8 * 2
b = 5 * 0
c = a - b
d = c / 2
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 20000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4800 , e ) 7291
Rationale: 20 : 25 = > 4 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 4 / 9 = 3840 + 960 = 4800 answer : d
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 9600 * b
d = 20000 + 25000 
e = 25000 / d
f = c * e
g = 9600 - f
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 170 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 170 and so k = 170 - l l + 10 = 1.5 k = 1.5 ( 170 - l ) 2.5 l = 245 l = 98 the answer is d ."
Answer: d
Python program:
a = 100 + 50 
b = a / 100
c = 170 * b
d = c - 10
e = 100 + 50 
f = e / 100
g = f + 1 
h = d / g
Problem: 12 * 18 * 6 is the volume of some material . how many cubes of edge 3 can be insert into it ?
Options: a ) 48
b ) 49
c ) 50
d ) 51
e ) 52
Rationale: no . of such cubes = volume of material / volume of one cube ( 12 * 18 * 6 ) / ( 3 * 3 * 3 ) = 48 answer : a
Answer: a
Python program:
a = volume_rectangular_prism / (
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.63 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.63 - - > 15 p - 13.5 p = 63 - - > p = 42 . answer : d ."
Answer: d
Python program:
a = 15 / 100
b = 10 / 100
c = 1 - b
d = 15 / 100
e = c * d
f = a - e
g = 0 / 63
Problem: 1904 x 1904 = ?
Options: a ) 3623216 , b ) 3624216 , c ) 3624316 , d ) 3625116 , e ) 3625216
Rationale: "1904 x 1904 = ( 1904 ) 2 = ( 1900 + 4 ) 2 = ( 1900 ) 2 + ( 4 ) 2 + ( 2 x 1900 x 4 ) = 3610000 + 16 + 15200 . = 3625216 . e )"
Answer: e
Python program:
a = 1904 / 1904
b = a * 100
Problem: at what rate percent per annum will sum of money double in 20 years ?
Options: a ) 1.2 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) none of these
Rationale: "explanation : hint : if sum of money becomes ( z times ) in ( t ) years at simple interest , then rate of interest ( r ) can be calculated using the formula : rate of interest ( r ) % = 100 ( z – 1 ) / t here , principal amount is not given . hence , we can directly use the trick to calculate the rate of interest . rate of interest ( r ) % = 100 ( 2 – 1 ) / 20 rate of interest ( r ) % = 5 % p . a . answer is d"
Answer: d
Python program:
a = 100 / 20
Problem: n is a positive integer . when n + 1 is divided by 3 , the remainder is 2 . what is the remainder when n is divided by 3 ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "n + 1 = 3 a + 2 i . e . n + 1 = 5 , 8 , 11 , 14 , . . . etc . i . e . n = 4 , 7 , 10 , 13 , . . . etc . when n is divided by 3 remainder is always 1 answer : a"
Answer: a
Python program:
a = 2 + 3 
b = 3 / a
Problem: i bought two books ; for rs . 490 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337.83 , b ) 285.83 , c ) 284.83 , d ) 266.83 , e ) 299.83
Rationale: "x * ( 85 / 100 ) = ( 490 - x ) 119 / 100 x = 285.83 answer : b"
Answer: b
Python program:
a = 100 + 19 
b = 490 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: if 13 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 52 days
Rationale: "13 * 80 = 20 * x x = 52 days answer : e"
Answer: e
Python program:
a = 13 * 80
b = a / 20
Problem: 9773 + x = 13200 , then x is ?
Options: a ) 3427 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9773 = 3427 option : a"
Answer: a
Python program:
a = 13200 - 9773
Problem: when 5 + 6 = 305 , 6 + 7 = 425 , 7 + 8 = 565 , then 8 + 9 = ?
Options: a ) 705 , b ) 735 , c ) 685 , d ) 665 , e ) 725
Rationale: 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 6 + 7 = > 6 ã — 7 = 42 = > 42 ã — 10 + 5 = 425 7 + 8 = > 7 ã — 8 = 56 = > 56 ã — 10 + 5 = 565 then 8 + 9 = > 8 ã — 9 = 72 = > 72 ã — 10 + 5 = 725 answer : e
Answer: e
Python program:
a = 8 * 9
b = a * 10
c = b + 5
Problem: the population of a town is 7800 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9600 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7800 ã — 100 / 90 ã — 100 / 90 = 9629 a )"
Answer: a
Python program:
a = 10 / 100
b = 7800 * a
c = 7800 - b
d = 10 / 100
e = 7800 * d
f = 7800 - e
g = 10 / 100
h = f * g
i = c - h
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat weavers in 8 days ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : please always remember , that what exactly we need to calculate before applying chain formula . as in this question we need to find how many mats , right ! so we will compare everything with ` ` number of mats ' ' as , more men , more number of mats ( direct proportion ) more days , more number of mats ( direct proportion ) so , it can be solved as , [ weavers 4 4 days 8 8 ] : : 4 : x = > x ∗ 4 ∗ 4 = 8 ∗ 8 ∗ 4 = > x = 16 option c"
Answer: c
Python program:
a = 8 / 4
b = 4 * a
c = 8 / 4
d = b * c
Problem: the floor of a rectangular room is 21 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 128 m 2 , c ) 138 m 2 , d ) 148 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 25 ã — 16 = 400 m 2 area of the inner rectangle = 21 ã — 12 = 252 m 2 required area = ( 400 â € “ 252 ) = 148 m 2 answer d"
Answer: d
Python program:
a = 2 * 2
b = a + 21 
c = 2 * 2
d = 12 + c 
e = rectangle_area - (
Problem: two bullet trains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 11 sec . , b ) 15 sec . , c ) 13.3 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 20 m / sec = 6 m / sec . relative speed = ( 12 + 6 ) = 18 m / sec . required time = ( 120 + 120 ) / 18 sec = 13.3 sec . c"
Answer: c
Python program:
a = 120 + 120 
b = speed + ( 
c = a / b
Problem: in a tree , 3 / 7 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 3 / 5 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 11 / 35 , b ) 14 / 35 , c ) 18 / 35 , d ) 31 / 70 , e ) 37 / 70
Rationale: "the fraction of birds that are male robins is ( 2 / 3 ) ( 3 / 7 ) = 2 / 7 . the fraction of birds that are male bluejays is ( 2 / 5 ) ( 4 / 7 ) = 8 / 35 . the total fraction of male birds is 2 / 7 + 8 / 35 = 18 / 35 . the answer is c ."
Answer: c
Python program:
a = 3 / 7
b = 2 / 0
c = a * b
d = 3 / 7
e = 1 / 3
f = d * e
g = c + f
Problem: the length of a rectangular landscape is 8 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 6 rd of the total landscape . what is the length of the landscape ?
Options: a ) 180 , b ) 270 , c ) 340 , d ) 140 , e ) 240
Rationale: "sol . x * 8 x = 6 * 1200 x = 30 length = 8 * 30 = 240 e"
Answer: e
Python program:
a = 4 * 0
b = a * 10
Problem: ratio and proportion 215 : 474 : : 537 : ?
Options: a ) 26 , b ) 27 , c ) 25 , d ) 22 , e ) 23
Rationale: 2 + 1 + 5 + 4 + 7 + 4 = 23 5 + 3 + 7 + x = 23 = > x = 8 combination that match 8 is 26 since 2 + 6 = 8 answer : a
Answer: a
Python program:
a = 4 + 2 
b = 10 + 10 
c = a + b
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 288 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 288 per week 36 x = 288 x = 8 correct option : d"
Answer: d
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 288 / c
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 200 kg . in the first week 20 percent is cut away . in the second week 25 percent of the remainder is cut away . in the third week the statue is completed when 35 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 97.5 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "a 97.5 kg 250 ã — 0.8 ã — 0.75 ã — 0.65 = 97.5 kg ."
Answer: a
Python program:
a = 35 / 100
b = 1 - a
c = 25 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 200 * f
h = d * g
i = b * h
Problem: an offshore company sells two products , l and m . last year , seventy percent of the units sold were product l , and the price of product l was 25 percent greater than the price of product m . approximately what percent of the total revenue the company received last year was from the sale of product l ?
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 65 % , e ) 74 %
Rationale: percentage of total units that is product l = 70 % price of product l = 25 percent greater than price of product m . now , we can consider this as a weighted average scenario . if the price of both the products l and m was equal , then contribution of product l to total sales would be = 70 % but since , price of product l is greater than m , then contribution of product l to total sales will be greater than 70 % the only option is 74 % answer e
Answer: e
Python program:
a = 3 + 4 
b = a * 10
c = 3 + 4 
d = c * 10
e = 100 - d
f = 25 / 100
g = 1 - f
h = e * g
i = 3 + 4 
j = i * 10
k = h + j 
l = b / k
m = l * 100