euclaise/mathqa_programs huggingface dataset:
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 16 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "in 16 liters , red = 5 / 8 * 16 = 10 and blue = 6 so , 10 / ( 6 + x ) = 3 / 6 or , x = 14 ( answer c )"
Answer: c
Python program:
a = 5 + 3 
b = 5 / a
c = 16 * b
d = 5 + 3 
e = 3 / d
f = c / e
g = 5 + 3 
h = 6 / g
i = f * h
j = 5 + 3 
k = 5 / j
l = 16 * k
m = 16 - l
n = i - m
Problem: the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 98 . what is the rate of interest per annum ?
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 6 % , e ) 5 %
Rationale: "$ 98 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 98 x = 0.07 the answer is c ."
Answer: c
Python program:
a = math.sqrt(98)
Problem: in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 3 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.01
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 3 = ~ 4.14 passengers using logan airport = 4.14 / 4 = ~ 1.01 so e"
Answer: e
Python program:
a = 37 / 3
b = 4 * 3
c = a / b
Problem: ( 4300431 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764813 , d ) 1675123 , e ) none of them
Rationale: "let 4300431 - x = 2535618 then x = 4300431 - 2535618 = 1764813 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 4300431 * b
Problem: by selling 18 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "85 % - - - 18 115 % - - - ? 85 / 115 * 18 = 13 answer : b"
Answer: b
Python program:
a = 100 + 15 
b = 100 - 15
c = 1 / b
d = a * c
e = 1 / d
f = e * 18
Problem: a contractor undertakes to do a piece of work in 40 days . he engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time . if he had not engaged the additional men , how many days behind schedule would it be finished ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: explanation : \ inline \ fn _ jvn [ ( 100 \ times 35 ) + ( 200 \ times 5 ) ] men can finish the work in 1 day \ inline \ fn _ jvn \ therefore 4500 men can finish the work in 1 day . 100 men can finish it in \ inline \ fn _ jvn \ frac { 4500 } { 100 } = 45 days . this is 5 days behind schedule answer : b
Answer: b
Python program:
a = 100 * 35
b = 2 + 3 
c = 100 * 2
d = b * c
e = a + d 
f = e / 100
g = f - 40
Problem: how many integers are between 4 and 88 / 9 , inclusive ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "88 / 9 = 9 . xx we are not concerned about the exact value of 88 / 9 as we just need the integers . the different integers between 4 and 88 / 9 would be 4 , 5 , 6 , 7 , 8 , 9 total number of integers = 6 option d"
Answer: d
Python program:
a = 88 / 9
b = a - 4
c = b + 1
Problem: how many integers from 1 to 100 ( both inclusive ) have odd number of factors ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) greater than 10
Rationale: all perfect squares have odd # of factors . squaring integers 1 - 10 produces 1 , 4 , 9 , 16 , . . . 100 which all have odd # of factors . answer is d
Answer: d
Python program:
a = 100 / 10
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 278 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "consider sister weight now as x jakes weight ( 2 times + 8 ) = 2 x + 8 ( 2 x + 8 ) + ( x ) = 278 x = 90 jake ' s weight is . . . . 188 correct answer is e"
Answer: e
Python program:
a = 278 - 8
b = a / 3
c = b * 2
d = c + 8
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 12000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 14520
Rationale: "the required population is = 12000 ( 1 + 10 / 100 ) ^ 2 = 12000 * 11 / 10 * 11 / 10 = 14520 answer is e"
Answer: e
Python program:
a = 10 + 100 
b = a / 100
c = b * 12000
d = 10 + 100 
e = d / 100
f = c * e
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 65.50 , his capital is ?
Options: a ) 24,602 , b ) 26,200 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 65.50 32 x - 31 x = 6550 * 4 x = 26,200 . answer : b"
Answer: b
Python program:
a = 4 / 4
b = 65 / 50
Problem: a monkey start climbing up a tree 19 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 16 hrs it wil be 16 ft . bt since the height of the tree is 19 ft , so if the monkey hops up the tree in the next hr i . e 17 th hr then it reaches at the top of the tree . hence it takes 17 hrs for monkey to reach at the top answer : d"
Answer: d
Python program:
a = 3 - 2
b = 19 / a
c = b - 2
Problem: find the value of y from ( 12 ) ^ 2 x 6 ^ 3 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 72
Rationale: "72 e"
Answer: e
Python program:
a = 12 ** 2
b = 6 ** 3
c = a * b
d = c / 432
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 6.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 10 , d ) 1 / 78 , e ) 30
Rationale: "pete covered 6.5 * 60 = 390 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 390 = 1 / 78 . answer : d ."
Answer: d
Python program:
a = 6 / 5
b = a * 60
c = 1 / b
Problem: a cistern 12 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 64 , b ) 72 , c ) 80 , d ) 88 , e ) 96
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 12 x 1.25 ) + 12 x 4 ] = 88 the answer is d ."
Answer: d
Python program:
a = 12 * 4
b = 25 / 100
c = 1 + b 
d = 4 * c
e = 2 * d
f = a + e 
g = 25 / 100
h = 1 + g 
i = 12 * h
j = 2 * i
k = f + j
Problem: the instructions state that cheryl needs 2 / 9 square yards of one type of material and 1 / 8 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 4 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 1 / 8 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: total bought = 2 / 9 + 1 / 8 left part 4 / 18 - - - > 2 / 9 so used part 2 / 9 + 1 / 8 - 2 / 9 = 1 / 8 answer : c
Answer: c
Python program:
a = 2 / 9
b = 1 / 8
c = a + b 
d = 4 / 18
e = c - d
Problem: the average age of 17 students of a class is 17 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 17 th student is
Options: a ) 62 , b ) 66 , c ) 18 , d ) 75 , e ) 12
Rationale: "explanation : age of the 17 th student = [ 17 * 17 - ( 14 * 5 + 16 * 9 ) ] = ( 289 - 214 ) = 75 years . answer : d"
Answer: d
Python program:
a = 17 * 17
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: right triangle abc is the base of the prism in the figure above . if ab = ac = √ 2 and the height of the prism is 3 , what is the volume of the prism ?
Options: a ) 1
b ) 3 / 2
c ) 2
d ) 3
e ) 6
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 2 ) * ( square root of 2 ) * 3 = 3 answer : d
Answer: d
Python program:
a = math.sqrt(2)
b = math.sqrt(2)
c = volume_rectangular_prism / (
Problem: in a dairy farm , 20 cows eat 20 bags of husk in 20 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x for one cow = 20 days answer : c"
Answer: c
Python program:
a = 20 / 20
b = a * 20
Problem: the average ( arithmetic mean ) of 4 different integers is 68 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 5 , b ) 19 , c ) 29 , d ) 30 , e ) 33
Rationale: "total of integers = 68 * 4 = 272 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 272 - ( 90 + 89 + 88 ) = 272 - 267 = 5 answer : a"
Answer: a
Python program:
a = 68 * 4
b = a - 90
c = 90 - 1
d = b - c
e = 90 - 2
f = d - e
Problem: how much more would rs . 60000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 725 , c ) 992 , d ) 1446 , e ) 923
Rationale: "60000 ( 11 / 10 ) 4 - 60000 ( 6 / 5 ) 2 = 1446 answer : d"
Answer: d
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 4
e = d * 60000
f = 20 / 100
g = f + 1 
h = g ** 2
i = h * 60000
j = e - i
Problem: ramu bought an old car for rs . 45000 . he spent rs . 12000 on repairs and sold it for rs . 80000 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 40 % , d ) 58 % , e ) 13 %
Rationale: "total cp = rs . 45000 + rs . 12000 = rs . 57000 and sp = rs . 80000 profit ( % ) = ( 80000 - 57000 ) / 57000 * 100 = 40 % answer : c"
Answer: c
Python program:
a = 45000 + 12000 
b = 80000 - a
c = 45000 + 12000 
d = b / c
e = d * 100
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 15 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 6
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 15 / 2.5 ) = 6 hrs answer : e"
Answer: e
Python program:
a = 300 / 40
b = 50 / 10
c = a - b
d = math.floor(c)
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 198 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 13
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 198 - $ 120 = $ 78 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 78 / $ 6 = 13 ans is e"
Answer: e
Python program:
a = 3 * 40
b = 198 - a
c = 3 * 2
d = b / c
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 105 / 14 = 7.5 hours , so at 6 : 00 pm . the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = 70 * a
c = 70 + b 
d = 84 - 70
e = c / d
Problem: a grocery store bought some apples at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples ?
Options: a ) 1 : 7 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 2 , e ) 2 : 5
Rationale: to avoid fractions , assume there were 45 apples . so the store bought them for 45 / 5 = 9 dollars . to break even , the selling price should be $ 9 too . 45 mangoes can be split into 1 : 4 , 2 : 3 or 1 : 2 . so let ' s try these . 45 split in the ratio 1 : 4 gives 9 and 36 . 9 apples split into 3 apples each will give $ 3 . 36 apples split into 6 apples each will give $ 6 . they add up to $ 9 so we have hit the right answer . answer ( c )
Answer: c
Python program:
a = 1 / 4
Problem: if 11 lions can kill 11 deers in 11 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 11 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 11 ( lions ) * 11 ( min ) / 11 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 11 answer : b"
Answer: b
Python program:
a = 11 / 11
b = a * 11
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 6 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 2 , b ) 18 : 3 , c ) 29 : 11 , d ) 29 : 5 , e ) 29 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 6 = 15 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 4 + 7 / 2 = 29 / 4 = 7.25 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.25 : 2.75 = 29 : 11 . answer : c"
Answer: c
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 6 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: what is 1 percent of 12,356 ?
Options: a ) 123.56 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 1 ( 1 / 100 ) 12,356 . the answer is 123.56 . hence , the correct answer is a .
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 1 * n
p = o / 100
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b .
Answer: b
Python program:
a = 2 ** 2
b = math.comb(4, 2)
c = math.comb(2, 1)
d = b * c
e = a / d
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 35 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 48.3 % , b ) 52.8 % , c ) 55.5 % , d ) 58.3 % , e ) 61.4 %
Rationale: "35 % is 5 % - points above 30 % and 25 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 5 : 1 . 5 / 6 * 70 % = 58.3 % the answer is d ."
Answer: d
Python program:
a = 100 * 2
b = 70 / a
c = b * 100
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 70 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 7 / 48,000 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 70 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 70 / 800 * 1 / 600 = 7 / 48,000 . answer : c ."
Answer: c
Python program:
a = 70 / 800
b = 1 / 600
c = a * b
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 10
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 24 / 60 ) ) km = 10 km . answer : e"
Answer: e
Python program:
a = 24 / const_60
b = 20 + 5 
c = a * b
Problem: the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: "total bought = 4 / 9 + 2 / 3 left part 8 / 18 - - - > 4 / 9 so used part 4 / 9 + 2 / 3 - 4 / 9 = 2 / 3 answer : c"
Answer: c
Python program:
a = 4 / 9
b = 2 / 3
c = a + b 
d = 8 / 18
e = c - d
Problem: a sells a bicycle to b at a profit of 30 % and b sells it to c at a loss of 20 % . find the resultant profit or loss .
Options: a ) 5 % , b ) 4 % , c ) - 4 % , d ) - 12 % , e ) 2 %
Rationale: the resultant profit or loss = 30 - 20 - ( 30 * 20 ) / 100 = 4 % profit = 4 % answer is b
Answer: b
Python program:
a = 30 / 100
b = 1 + a 
c = 20 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: a man can row at 6 kmph in still water . if the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back , how far is the place ?
Options: a ) 5.33 km , b ) 6.33 km , c ) 5.63 km , d ) 7.33 km , e ) 5.93 km
Rationale: "speed in still water = 6 kmph speed of the current = 2 kmph speed downstream = ( 6 + 2 ) = 8 kmph speed upstream = ( 6 - 2 ) = 4 kmph let the required distance be x km total time taken = 2 hour x / 8 + x / 4 = 2 x + 2 x / 8 = 2 3 x / 8 = 2 3 x = 16 x = 5.33 km answer : a"
Answer: a
Python program:
a = 6 - 2
b = a * 3
c = b / 6
Problem: in a survey of 335 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 38 / 67 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 281 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 335 we have to find not part time and not uninsured . in other words not part time and insured = x / 335 = ( 281 - 104 + 13 ) / 335 = 38 / 67 answer is a ."
Answer: a
Python program:
a = 12 * 5
b = 1 * 100
c = a / b
d = 54 - c
e = d + 104 
f = 335 - e
g = f / 335
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1 , 500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 10 5 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the ratio of investments is 500 : 1,500 = 1 : 3 . the deviation from the average return from $ 500 investment and $ 1,500 investment must be in the ration 3 : 1 . $ 500 investment return has the deviation from the mean of 8.5 - 7 = 1.5 % , thus $ 1,500 investment return must have the deviation from the mean equal to 0.5 % , which means that $ 1 , 500 investment has 8.5 + 0.5 = 9 % yearly return . answer : a ."
Answer: a
Python program:
a = 3 * 500
b = 500 + a 
c = 8 / 5
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: 8 : 4 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 8 , c ) 20 , d ) 25 , e ) 30
Rationale: "8 * 4 = 4 * x x = 8 answer : b"
Answer: b
Python program:
a = 8 / 4
b = 4 * a
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 7 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 10500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 7000 * 2 * 45 ) / 60 = 10500 m 3 answer : option c"
Answer: c
Python program:
a = 2 * 45
b = 7 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: at a local appliance manufacturing facility , the workers received a 25 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 125 = 1250 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 125 = 8 so he can reduce his work by 2 hours . which is 20 % . answer c"
Answer: c
Python program:
a = 25 - 1
Problem: if 625 ^ ( - x ) + 5 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . a"
Answer: a
Python program:
a = 1 / 4
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4529 , b ) s . 4586 , c ) s . 4597 , d ) s . 4530 , e ) s . 5436
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 6 = rs . 5436 answer : e"
Answer: e
Python program:
a = 2 * 12
b = 15 + 25 
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 6
Problem: a car dealership has 40 cars on the lot , 10 % of which are silver . if the dealership receives a new shipment of 80 cars , 25 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 21 % , e ) 22 %
Rationale: the number of silver cars is 0.1 * 40 + 0.25 * 80 = 24 the percentage of cars which are silver is 24 / 120 = 20 % the answer is c .
Answer: c
Python program:
a = 10 / 100
b = 40 * a
c = 25 / 100
d = 80 * c
e = b + d 
f = 40 + 80 
g = e / f
h = g * 100