euclaise/mathqa_programs huggingface dataset:
Problem: a person can swim in still water at 10 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 9 , e ) 6
Rationale: "m = 10 s = 4 us = 10 - 4 = 6 d = 12 t = 12 / 6 = 2 answer : a"
Answer: a
Python program:
a = 10 - 4
b = 12 / a
Problem: in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 70,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 150,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 320,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 70,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 490,000 - $ 160,000 = $ 150,000 . the correct answer is b ."
Answer: b
Python program:
a = 70 + 20 
b = a * 1000
c = b * 100
d = 70 + 20 
e = d * 1000
f = 20 * e
g = c - f
h = 20 / 2
i = h * 20
j = i * 1000
k = j * 70
l = g - k
m = l / 20
Problem: 2525 * 9
Options: a ) 22725 , b ) 25675 , c ) 22655 , d ) 27575 , e ) none of these
Rationale: "explanation : 2525 * ( 10 - 1 ) = 25250 - 2525 = 22725 option a"
Answer: a
Python program:
a = 2525 / 9
b = a * 100
Problem: rs . 500 amounts to rs . 620 in 2 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 120 , b ) 25 , c ) 614 , d ) 530 , e ) 210
Rationale: "( 500 * 3 * 2 ) / 100 = 30 500 + 30 = 530 answer : d"
Answer: d
Python program:
a = 2 / 100
b = 1 + a 
c = b ** 2
d = c * 500
Problem: if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options: a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
Rationale: "explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b"
Answer: b
Python program:
a = 1 / 3
b = 3 + a 
c = b / 100
d = c + 1 
e = 1 / 2
f = e + 1 
g = f / 100
h = g + 1 
i = 6400 / h
j = d * i
k = j - 6400
Problem: circles x and y are concentric . if the radius of circle x is 6 times that of circle y , what is the probability that a point selected inside circle x at random will be outside circle y ?
Options: a ) 13 , b ) pi / 3 , c ) pi / 2 , d ) 35 / 36 , e ) 8 / 9
Rationale: small circle radius = a , so area = pi a ^ 2 large circle radius = 6 a , so area = 9 . pi a ^ 2 area of shaded region = 36 pi a ^ 2 - pi a ^ 2 = 35 pi a ^ 2 so , probability = ( 35 pi a ^ 2 ) / ( 36 pi a ^ 2 ) = 35 / 36 = answer = d
Answer: d
Python program:
a = 6 ** 2
b = a - 1
c = 6 ** 2
d = b / c
Problem: if x + y = 8 and y − 3 x = 7 , then what is the value of y - x ?
Options: a ) 1 / 7 , b ) 3 , c ) 15 , d ) 15 / 2 , e ) 60 / 7
Rationale: x + y = 8 . . . equation 1 - 3 x + y = 7 . . . equation 2 adding both the equations - 2 x + 2 y = 15 = > y - x = 15 / 2 correct answer option d
Answer: d
Python program:
a = 8 * 3
b = a + 7 
c = 3 + 1 
d = b / c
e = 8 * 3
f = e + 7 
g = 3 + 1 
h = f / g
i = 8 - h
j = d - i
Problem: if 6 / w + 6 / x = 6 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 6 / w + 6 / x = 6 / ywx = y find : ( w + x ) / 2 = ? 6 ( 1 / w + 1 / x ) = 6 ( 1 / y ) - divide both sides by 6 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Python program:
a = 6 + 6 
b = 6 / a
Problem: a cycle is bought for rs . 900 and sold for rs . 1350 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 50 % , e ) 83 %
Rationale: "900 - - - - 450 100 - - - - ? = > 50 % answer : d"
Answer: d
Python program:
a = 1350 - 900
b = a / 900
c = b * 100
Problem: some persons can do a piece of work in 24 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 / ( 2 * 2 ) = 6 days answer : d"
Answer: d
Python program:
a = 1 / 2
b = 24 * a
c = 1 / 2
d = b * c
Problem: if 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 2 / 9 are from africa , 1 / 6 are from asia and the remaining 50 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 120 , b ) 140 , c ) 150 , d ) 160 , e ) 180
Rationale: "1 / 12 + 1 / 4 + 2 / 9 + 1 / 6 = ( 3 + 9 + 8 + 6 ) / 36 = 13 / 18 let x be the number of passengers on the ship . 50 = ( 5 / 18 ) x x = 180 the answer is e ."
Answer: e
Python program:
a = 1 / 12
b = 1 / 4
c = a + b 
d = 1 / 9
e = c + d 
f = 1 / 6
g = e + f 
h = 1 - g
i = 50 / h
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "explanatory answer step 1 : identify the series the smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101 . the next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107 . the largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998 . it is evident that any number in the sequence will be a 3 digit positive integer of the form ( 3 n + 2 ) . so , the given numbers are in an arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3 . step 2 : compute the sum sum of an arithmetic progression ( ap ) = [ first term + last term / 2 ] n we know the first term : 101 we know the last term : 998 . the only unknown is the number of terms , n . in an a . p . , the nth term an = a 1 + ( n - 1 ) * d in this case , therefore , 998 = 101 + ( n - 1 ) * 3 or 897 = ( n - 1 ) * 3 ( n - 1 ) = 299 or n = 300 . sum of the ap will therefore , be [ 101 + 998 / 2 ] ∗ 300 = 164,850 choice b is the correct answer ."
Answer: b
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 3
i = h + 1 
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: if it takes 4 movers 40 minutes to unpack their van , how long would 5 movers take ?
Options: a ) 38 minutes , b ) 35 minutes , c ) 32 minutes , d ) 29 minutes , e ) 26 minutes
Rationale: 4 * 40 = 5 * x x = 32 answer : c
Answer: c
Python program:
a = 40 * 4
b = a / 5
Problem: a person can row at 9 kmph and still water . he takes 5 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 24 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 5.5 = > x / 10 + x / 8 = 11 / 2 = > ( 4 x + 5 x ) / 40 = 11 / 2 = > x = 24 km . answer : d"
Answer: d
Python program:
a = 9 - 1
b = 9 + 1 
c = a * b
d = c * 5
e = 9 + 1 
f = 9 - 1
g = e + f 
h = d / g
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6300 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 7670 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6300 * 6 ) – 30,130 ] = rs . ( 37800 – 30,130 ) = rs . 7670 answer d"
Answer: d
Python program:
a = 5 + 1 
b = a * 6300
c = 5420 + 5660 
d = c + 6200 
e = d + 6350 
f = e + 6500 
g = b - f
Problem: a train moves with a speed of 189 kmph . its speed in metres per second is
Options: a ) 60.8 , b ) 18 , c ) 30 , d ) 52.5 , e ) none
Rationale: "solution speed = 189 kmph = ( 189 x 5 / 18 ) m / sec = 52.5 m / sec . answer d"
Answer: d
Python program:
a = 189 * const_0_2778
Problem: a man has some hens and cows . if the number of heads be 100 and the number of feet equals 180 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 80 , d ) 90 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 100 . . . . ( i ) and 2 x + 4 y = 220 x + 2 y = 110 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 90 , y = 10 . the required answer = 90 . answer : d"
Answer: d
Python program:
a = 100 * 4
b = a - 180
c = b / 2
Problem: if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 3 * x to 1 / 5 * y ?
Options: a ) 25 / 6 , b ) 36 / 25 , c ) 2 , d ) 5 / 6 , e ) 25 / 36
Rationale: 5 x = 6 y = > x / y = 6 / 5 1 / 3 * x to 1 / 5 * y = x / y * 5 / 3 = ( 6 / 5 ) * ( 5 / 3 ) = 2 ans : c
Answer: c
Python program:
a = 1 / 3
b = 1 / 5
c = a / b
d = 6 / 5
e = c * d
Problem: john and jacob set out together on bicycle traveling at 12 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 12 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 2 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 2
Rationale: "john ' s speed - 12 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 12 x 2 / 3 = 8 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 12 - 9 = 3 miles / hr . thus , to cover 7 miles at 3 miles / hr , john will take 7 / 3 = 2 1 / 3 hours answer b"
Answer: b
Python program:
a = 12 - 9
b = 40 / const_60
c = b * 12
d = 40 / const_60
e = d * 9
f = c - e
g = 9 - f
h = a + g 
i = 40 / const_60
j = i * 12
k = 40 / const_60
l = k * 9
m = j - l
n = h / m
Problem: the proportion of water to alcohol in solution a is 5 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 36.7 % , b ) 37.6 % , c ) 38.3 % , d ) 39.8 % , e ) 40.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 6 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 12 + 3 v / 10 = 23 v / 60 . the concentration of alcohol is 23 / 60 = 38.3 % the answer is c ."
Answer: c
Python program:
a = 1 + 3 
b = 5 + 2 
c = 1 + 3 
d = b + c 
e = a / d
f = e * 100
Problem: 51 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 17
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 51 x 12 x 5 = 30 x 6 x x x = 17 hence , the number of days = 17 . answer : e"
Answer: e
Python program:
a = 51 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , and 6 , how many palindromes are possible ?
Options: a ) 36 , b ) 96 , c ) 132 , d ) 216 , e ) 256
Rationale: "there are 6 choices for each of the first three digits . the number of possible palindromes is 6 ^ 3 = 216 . the answer is d ."
Answer: d
Python program:
a = 5 ** 3
Problem: a sells a bicycle to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays rs . 225 for it , the cost price of the bicycle for a is ?
Options: a ) 277 , b ) 268 , c ) 270 , d ) 150 , e ) 282
Rationale: "125 % of 120 % of a = 225 125 / 100 * 120 / 100 * a = 225 a = 225 * 2 / 3 = 150 . answer : d"
Answer: d
Python program:
a = 100 * 225
b = 25 + 100 
c = a / b
d = 100 * c
e = 20 + 100 
f = d / e
Problem: the average marks of a class of 30 students is 50 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 56.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 50 = 1500 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1500 + 3000 = 4500 average marks of all the students = 4500 / 80 = 56.25 answer : a"
Answer: a
Python program:
a = 30 * 50
b = 50 * 60
c = a + b 
d = 30 + 50 
e = c / d
Problem: if equation | x / 2 | + | y / 2 | = 1 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 8 , b ) 50 , c ) 100 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 2 | + | y / 2 | = 1 , so these are lines in four quadrants with x and y intercept as 2 , so it is a rhombus with diagonals of 4 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 4 * 4 = 8 . answer a .
Answer: a
Python program:
a = 2 * 2
b = a ** 2
c = 2 * 2
d = c ** 2
e = b + d
Problem: andrea wants to fill in two sections of her backyard with sod that must be purchased in 2 - x - 2 - foot squares . if the two sections measure 30 x 40 feet and 60 x 80 feet , how many squares of sod does she need to buy ?
Options: a ) 1000 , b ) 1250 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: to begin , find the area of each of the two sections by multiplying the lengths of the sides : 30 feet × 40 feet = 1200 square feet 60 feet × 80 feet = 4800 square feet the total area that needs sod has an area of 1200 + 4800 = 6000 square feet . each individual square is 2 feet by 2 feet , so each has an area of 4 square feet . because all the numbers are even , there will be no waste when the squares of sod are placed . therefore , you just have to find the number of squares needed by dividing : 6000 ÷ 4 = 1500 correct answer c ) 1500
Answer: c
Python program:
a = 30 * 40
b = 2 * 2
c = a / b
d = 60 * 80
e = 2 * 2
f = d / e
g = c + f
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 32 , d ) 30 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 4 w = 120 = > w = 30 answer d"
Answer: d
Python program:
a = rectangle_area / (
Problem: this year , mbb consulting fired 7 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.3 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 7 % reduction in employees lead to 93 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 93 employees is 93 * 1100 = 102300 now the new salary is more than previous salary by x % . x = ( 102300 / 100000 ) * 100 = 102.3 % so the answer is c"
Answer: c
Python program:
a = 100 * 10
b = 100 + a 
c = 100 - 7
d = c + 4 
e = b * d
f = 100 * 10
g = e / f
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 6 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 6 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 6 is p ( 6 ) = 9.50 + 0.25 ( 6 – 1 ) = 9.50 + 0.25 * 5 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 6 ) - p ( 1 ) = 9.50 + 0.25 * 5 - 9.50 = 1.25 . answer : c ."
Answer: c
Python program:
a = 6 - 1
b = 0 * 25
c = b + 0
Problem: the sale price sarees listed for rs . 400 after successive discount is 12 % and 5 % is ?
Options: a ) 338 , b ) 277 , c ) 342 , d ) 334.4 , e ) 212
Rationale: "400 * ( 88 / 100 ) * ( 95 / 100 ) = 334.4 answer : d"
Answer: d
Python program:
a = 400 * 12
b = a / 100
c = 400 - b
d = 400 * 12
e = d / 100
f = 400 - e
g = f * 5
h = g / 100
i = c - h
Problem: if 4 b ^ 4 − 41 b ^ 2 + 100 = 0 , then what is the sum of the two greatest possible values of b ?
Options: a ) 4 , b ) 9 / 2 , c ) 7 , d ) 41 / 4 , e ) 25
Rationale: just forget about the value of b ^ 4 for the moment and let b ^ 2 = x . ( its better to work with power of 2 than 4 ) now we have equation as 4 x ^ 2 - 41 x + 100 = 0 , factoring them gives us 4 x ^ 2 - 16 x - 25 x + 100 = 0 . which can be solved as ( 4 x - 25 ) ( x - 4 ) , so x = 4 and 25 / 4 . so b ^ 2 = 4 and 25 / 4 so b = + 2 and minus 2 and + 5 / 2 and minus 5 / 2 the two greatest values are + 2 and + 5 / 2 . so their sum 2 + 5 / 2 = 9 / 2 = b
Answer: b
Python program:
a = 4 + 4 
b = a + 1 
c = b / 2
Problem: having scored 99 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: explanation : let the average score of the first 18 innings be n 18 n + 99 = 19 ( n + 4 ) = > n = 23 so , average score after 19 th innings = x + 4 = 27 . answer : b
Answer: b
Python program:
a = 19 * 4
b = 99 - a
c = b + 4
Problem: a company decreased the price of its main product by 10 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 4.3 , b ) 5.6 , c ) 6.2 , d ) 10.0 , e ) 12.0
Rationale: "for the total revenue to remain the same when the price is 1 / 10 , the number of products sold must 1 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 10 % = 10.0 answer : d"
Answer: d
Python program:
a = 100 / 10
Problem: of all the homes on gotham street , 1 / 3 are termite - ridden , and 7 / 10 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 9 , e ) 1 / 10
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 10 * 1 / 3 = 1 / 10 the answer is e ."
Answer: e
Python program:
a = 1 + 2 
b = 3 * 10
c = a / b
Problem: a train 150 meters long completely crosses a 320 meters long bridge in 40 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 42 , c ) 54 , d ) 66 , e ) 09
Rationale: "s = ( 150 + 320 ) / 40 = 470 / 40 * 18 / 5 = 42 answer : b"
Answer: b
Python program:
a = 150 + 320 
b = a / 1000
c = 40 / 3600
d = b / c
Problem: jar x is 1 / 2 full of water . jar y , which has half the capacity of jar x , is 1 / 4 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 5 / 12 , e ) 7 / 12
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 4 * p / 2 = p / 8 then the total amount in jar x is p / 2 + p / 8 = 5 p / 8 the answer is b ."
Answer: b
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 2
d = b * c
e = a + d
Problem: how much is 80 % of 40 is greater than 4 / 5 of 15 ?
Options: a ) 12 , b ) 20 , c ) 18 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 15 32 - 12 = 20 answer : b"
Answer: b
Python program:
a = 80 / 100
b = 40 * a
c = 4 / 5
d = c * 15
e = b - d
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 160 billion gallons to 200 billion gallons . if the storm increased the amount of water in the reservoirs to 50 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) 300
Rationale: "let total capacity be x we know 200 = 0.50 x x = 200 / 0.50 = 400 prior to storm , we had 160 bn gallons 400 - 160 = 240 answer : a"
Answer: a
Python program:
a = 200 * 100
b = a / 50
c = b / 2
Problem: if 6 spiders make 6 webs in 6 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 6 webs 6 : 1 1 x 6 x x = 6 x 1 x 6 = > x = 6 answer is b"
Answer: b
Python program:
a = 1 * 6
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 250 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 750 , c ) 400 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 250 then y = 750 answer : b"
Answer: b
Python program:
a = 25 - 10
b = 30 - 25
c = a / b
d = c * 250
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 3 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 2 / 1 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 300 km time taken by freddy = 3 hours average speed of freddy = 300 / 3 = 100 km / hour ratio of average speed of eddy to freddy = 200 / 100 = 2 / 1 answer a"
Answer: a
Python program:
a = 600 / 3
b = 300 / 3
c = a / b
Problem: a motorcyclist goes from nagpur to pune , a distance of 500 kms at an average of 100 kmph speed . another man starts from nagpur by car 3 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 7 , c ) 3 : 5 , d ) 1 : 5 , e ) 1 : 1
Rationale: t = 500 / 100 = 10 h t = 10 - 4 = 6 time ratio = 10 : 6 = 5 : 3 speed ratio = 3 : 5 answer : c
Answer: c
Python program:
a = 3 * 100
b = a / 500
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 287 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 178 , b ) 182 , c ) 186 , d ) 190 , e ) 194
Rationale: "j + k = 287 and so k = 287 - j j - 8 = 2 k j - 8 = 2 ( 287 - j ) 3 j = 582 j = 194 the answer is e ."
Answer: e
Python program:
a = 287 - 8
b = a / 3
c = b * 2
d = c + 8
Problem: what is the greatest positive integer q such that 3 ^ q is a factor of 9 ^ 10 ?
Options: a ) q = 5 , b ) q = 9 , c ) q = 10 , d ) q = 20 , e ) 30
Rationale: "what is the greatest positive integer q such that 3 ^ q is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Python program:
a = 9 - 10
b = a * 10