euclaise/mathqa_programs huggingface dataset:
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 75 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 26 : 15 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 75 ã — 4 = 300 km ratio = 520 / 300 = 26 : 15 a"
Answer: a
Python program:
a = 65 * 8
b = 75 * 4
c = a / b
Problem: 30 ^ 10 / 90 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) 3 ^ 6 , d ) 10 ^ 5 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 90 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 10 ^ 5 e . 15 ^ 3 - > 30 ^ 10 / 90 ^ 5 = ( 30 ^ 10 ) / ( 3 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 3 ^ 5 ) = ( 3 ^ 5 ) ( 10 ^ 5 ) / ( 3 ^ 5 ) = 10 ^ 5 . thus , d is the answer ."
Answer: d
Python program:
a = 30 ** 10
b = 30 ** 5
c = a / b
Problem: the ratio of the areas of a square and rhombus whose base is same is :
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 1 , d ) 3 : 1 , e ) 2 : 3
Rationale: "solution : the square and the rhombus are equal in area if they have a common base . answer is c"
Answer: c
Python program:
a = 1/(2)
b = a * 4
c = 1/(2)
d = b / c
Problem: a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 120 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 120 km downstream = 120 / 30 hrs = 4 hrs . answer : d"
Answer: d
Python program:
a = 25 + 5 
b = 120 / a
Problem: the banker â € ™ s gain on a sum due 3 years hence at 17 % per annum is rs . 100 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 296 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 100 x 100 / 17 x 3 ) = rs . 196 . b . d = rs ( 196 + 100 ) = rs . 296 . answer c"
Answer: c
Python program:
a = 100 * 100
b = 3 * 17
c = a / b
d = c + 100
Problem: a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 8 liters of jasmine and 2 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 6.5 % , b ) 8.5 % , c ) 10.5 % , d ) 12.5 % , e ) 14.5 %
Rationale: the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 8 ) / 100 = 12.5 / 100 = 12.5 % the answer is d .
Answer: d
Python program:
a = 5 / 100
b = a * 90
c = 8 + b
Problem: if the ratio of two number is 4 : 6 and lcm of the number is 280 then what is the number .
Options: a ) 12 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: product of two no = lcm * hcf 4 x * 6 x = 280 * x x = 12 answer : a
Answer: a
Python program:
a = 4 * 6
b = 280 / a
Problem: by how much does the larger root of the equation 2 b ^ 2 + 5 b = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 b ^ 2 + 5 b = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Python program:
a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c 
e = math.sqrt(d)
f = 5 + e 
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k 
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
Problem: between 100 to 200 how many no are divisible by both 3 and 2 and 100,200 are inclusive ?
Options: a ) 77 , b ) 78 , c ) 79 , d ) 80 , e ) 81
Rationale: prime numbers are 21 so 100 - 21 = 79 answer : c
Answer: c
Python program:
a = 100 / 2
b = a / 3
c = math.floor(b)
d = 100 - c
e = d - 2
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a + b ) / 2 ?
Options: a ) 100 , b ) 110 , c ) 105 , d ) 20 , e ) 215
Rationale: "yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a + b ) / 2 = 110 + 100 = 210 / 2 = 105 ans : c"
Answer: c
Python program:
a = 20 / 2
b = 20 / 2
c = b + 1 
d = a * c
e = 19 + 1 
f = e / 2
g = 19 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: martin has to secure 80 % marks to clear his exam of class 9 th . he got 200 marks and failed by 200 marks . what is the maximum marks ?
Options: a ) 500 , b ) 505 , c ) 510 , d ) 515 , e ) 525
Rationale: a 500 to pass the exam ravish needs 200 + 200 = 400 marks . = > ( 400 / 80 ) * 100 = 500
Answer: a
Python program:
a = 200 + 200 
b = 80 / 100
c = a / b
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 60 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 104.8 % , d ) 150.5 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 60 percent to make square c length of each side of square c = 1.6 * 20 = 32 area of c = 32 ^ 2 = 1024 difference in areas of c and cummulative areas of a and b = 1024 - ( 400 + 100 ) = 524 percent is the area of square c greater than the sum of the areas of squares a and b = ( 524 / 500 ) * 100 % = 104.8 % answer c"
Answer: c
Python program:
a = 100 / 100
b = 1 + a 
c = 100 / 100
d = 1 + c 
e = d * 60
f = e / 100
g = b + f 
h = square_area - (
i = h - 1
j = i / 4
k = 100 / 100
l = 1 + k 
m = 1 + square_area 
n = j * m
Problem: a pizzeria in castroville creates its own special blend of shredded cheese at a cost of $ 696.05 per kilogram . the blend includes mozzarella , at $ 504.35 per kilogram , and romano cheese , at $ 887.75 per kilogram . if the employees have already shredded 19 kilograms of mozzarella cheese , how many kilograms of romano cheese will they need to shred now ?
Options: a ) 19 kg , b ) 13 kg , c ) 10 kg , d ) 23 kg , e ) 15 kg
Rationale: 504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) solve the equation . 504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) 9 , 582.65 + 887.75 x = 13 , 224.95 + 696.05 x 9 , 582.65 + 191.7 x = 13 , 224.95 191.7 x = 3 , 642.3 x = 19 . answer is a .
Answer: a
Python program:
a = 696 - 5
b = 887 - 75
c = a / b
d = 696 - 5
e = 887 - 75
f = d / e
g = 1 - f
h = c / g
i = h * 19
Problem: product of two natural numbers is 17 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 17 ( 2 ) = 290 / 289 option a"
Answer: a
Python program:
a = 1 / 1
b = a ** 2
c = 1 / 17
d = c ** 2
e = b + d
Problem: the perimeter of an isosceles right triangle is 10 + 10 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5 , b ) 6 , c ) 7.07 , d ) 8 , e ) 9
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 10 + 10 sqrt 2 or , a . ( 2 + sqrt 2 ) = 10 ( 1 + sqrt 2 ) , a = 10 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 10 * 2.414 / 3.414 = 0.707 * 10 then hypotenuse = 7.07 c"
Answer: c
Python program:
a = math.sqrt(2)
b = 10 * a
c = b / 2
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 15 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.5 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 15 = 405 hence , new average = 405 ⁄ 10 = 40.5 answer c"
Answer: c
Python program:
a = 40 * 2
b = 13 + 15 
c = a + b 
d = c - 31
e = d / 10
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 998 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 998 y = 2 x + 2 996 = 2 x x = 498 answer : b . 498"
Answer: b
Python program:
a = 998 - 2
b = a / 2
Problem: if two - third of a bucket is filled in 2 minutes then the time taken to fill the bucket completely will be .
Options: a ) 3 minutes , b ) 70 seconds , c ) 60 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: "2 / 3 filled in 2 mint 1 / 3 filled in 1 mint then 2 / 3 + 1 / 3 = 2 + 1 = 3 minutes answer : a"
Answer: a
Python program:
a = 2 / 2
b = a * 3
Problem: marla is hanging a banner diagonally across a rectangular room . the length of the room is 3 feet shorter than its width . if the total area of the room is 130 square feet , what is the length of the banner ( in feet ) ?
Options: a ) between 16 and 17
b ) between 17 and 18
c ) between 18 and 19
d ) between 19 and 20
e ) between 20 and 21
Rationale: to solve this , we first need to set up an equation for the area of the room . if x is the width , then we have x ( x - 3 ) = 130 . by putting the equation in standard form , we get x ^ 2 - 3 x - 130 = 0 . by using the quadratic formula , we get roots of - 10 and 13 . we know that x is the width , and x - 3 is the length , so by using the roots , we get 13 as the width ( x ) , and 10 as the length ( x - 3 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 13 ^ 2 + 10 ^ 2 = 169 + 100 = 269 the square root of 269 is less than 17 , since 17 ^ 2 = 289 . going down a number , we can compute 16 ^ 2 = 256 < 269 . therefore , the length of the diagonal must be between 16 and 17 . the correct answer is a .
Answer: a
Python program:
a = 4 * 130
b = 3 ** 2
c = a + b 
d = math.sqrt(c)
e = 3 + d 
f = e / 2
g = f - 3
h = g ** 2
i = 4 * 130
j = 3 ** 2
k = i + j 
l = math.sqrt(k)
m = 3 + l 
n = m / 2
o = n ** 2
p = h + o 
q = math.sqrt(p)
Problem: if p gets 25 % more than q , then by what percent does q get less than p ?
Options: a ) 45 , b ) 34 , c ) 20 , d ) 76 , e ) 54
Rationale: let q get 1 unit . 25 % of 1 unit = 1 / 4 = 0.25 p gets ( 1 + 0.25 ) i . e . , 1.25 units . difference = ( 1.25 - 1 ) = 0.25 required percentage = 0.25 / 1.25 * 100 = 1 / 5 * 100 = 20 answer : c
Answer: c
Python program:
a = 25 / 100
b = 25 / 100
c = b + 1 
d = a / c
e = d * 100
Problem: before 5 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 58 , d ) 60 , e ) 64
Rationale: "a - 5 = 4 ( b - 5 ) - - > a - 4 b = - 15 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 23 - - > a = 3 ( 27 ) = 81 a - b = 81 - 23 = 58 answer : c"
Answer: c
Python program:
a = 4 * 4
b = a - 4
c = 4 * 5
d = c - 5
e = b + d 
f = 4 * e
g = 4 * 5
h = g - 5
i = f - h
j = 4 * 4
k = j - 4
l = 4 * 5
m = l - 5
n = k + m 
o = i - n
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people b who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , b = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000
Answer: d
Python program:
a = 500 / 2
b = 500 + a 
c = b * 2
d = c - 500
Problem: of 70 players on a football team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "37 are throwers and right handed 1 / 3 of remaining 33 , i . e 11 are left handed and remaining are right handed . basically , out of 70 , only 11 are left handed and remaining 70 - 11 = 59 are right handed . b is the answer"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 37
d = b * c
e = d + 37
Problem: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , sam ' s new income would be what fraction of quentin ' s new income ?
Options: a ) 11 / 12 , b ) 12 / 11 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 9.6 and q 8.8 so 9.6 / 8.8 = 1.2 / 1.1 ans : b"
Answer: b
Python program:
a = 40 * 100
b = 100 - 20
c = 40 * b
d = a + c 
e = 40 * 100
f = 40 + 20 
g = f * 40
h = e + g 
i = d / h
Problem: how many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 7 sets with 10 such number in each set will give 7 x 10 = 70 integers . c"
Answer: c
Python program:
a = 10 - 2
b = 10 * a
Problem: there are 200 female managers in a certain company . find the total number of female employees q in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) q = 300 , b ) q = 400 , c ) q = 500 , d ) q = 600 , e ) none of these
Rationale: { managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .
Answer: c
Python program:
a = 2 / 5
b = 200 / a
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 8,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 12000 , c ) 16160.8 , d ) 14000 , e ) 15000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 8,000 ( 1 + 0.04 / 4 ) ^ 4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 8,000 ( 1.0201 + 1 ) = 16160.8 hence answer is c ."
Answer: c
Python program:
a = 4 * 100
b = a * 100
c = 4 / 100
d = c / 4
e = 1 + d 
f = e ** 4
g = b * f
h = 4 * 100
i = h * 100
j = g - i
k = 2 / 100
l = k / 2
m = 1 + l 
n = m ** 2
o = n - 1
p = j / o
Problem: if the sum of two numbers is 24 and the sum of their squares is 404 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 86 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 24 and x 2 + y 2 = 404 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 24 ) 2 - 404 = 576 - 404 = 172 xy = 86 . answer d"
Answer: d
Python program:
a = 24 ** 2
b = a - 404
c = b / 2
Problem: product of two natural numbers is 3 . then , the sum of reciprocals of their squares is
Options: a ) 10 / 9 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 3 , as 3 is a prime number , so a = 1 , b = 3 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 3 ( 2 ) = 10 / 9 option a"
Answer: a
Python program:
a = 1 / 1
b = a ** 2
c = 1 / 3
d = c ** 2
e = b + d
Problem: if the least common multiple of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
Rationale: lcm of two prime numbers will basically be multiple of those numbers . lcm = 10 = 2 * 5 , both of which are prime . now we know x > y , so x = 5 and y = 2 . 2 x + y = 2 * 5 + 2 = 10 + 2 = 12 . answer : d
Answer: d
Python program:
a = 10 / 2
b = a * 2
c = b + 2
Problem: if the cost price is 96 % of selling price then what is the profit percentage .
Options: a ) 7.14 , b ) 7.41 , c ) 4.71 , d ) 4.17 , e ) none of them
Rationale: "selling price = rs 100 : then cost price = rs 96 : profit = rs 4 . profit = { ( 4 / 96 ) * 100 } % = 4.17 % answer is d ."
Answer: d
Python program:
a = 100 - 96
b = a / 96
c = b * 100
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 50 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 33 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 50 = > x = 11 so deepak age is = 3 ( 11 ) = 33 answer : option c"
Answer: c
Python program:
a = 50 - 6
b = a * 3
c = b / 4
Problem: if x ^ 3 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c"
Answer: c
Python program:
a = 240 / 3
b = a / 3
Problem: a man buys a cycle for rs . 1750 and sells it at a loss of 8 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1610 , c ) s . 1190 , d ) s . 1202 , e ) s . 1092
Rationale: "s . p . = 92 % of rs . 1750 = rs . 92 x 1750 / 100 = rs . 1610 answer : option b"
Answer: b
Python program:
a = 100 - 8
b = a * 1750
c = b / 100
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 12 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 66 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 12 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 12 = 4 / 9 ( t - 12 ) 10 t = 1188 - 528 = > t = 66 . answer : c"
Answer: c
Python program:
a = 6 / 5
b = a * 5
c = b - 4
d = 12 / c
e = 5 * d
f = 6 / 5
g = f * 5
h = g - 4
i = 12 / h
j = e + i 
k = j + 12
Problem: a rope of which a calf is tied is increased from 5 m to 9 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 180 , c ) 176 , d ) 200 , e ) 291
Rationale: "π ( 92 – 52 ) = 176 answer : c"
Answer: c
Python program:
a = 9 ** 2
b = 5 ** 2
c = a - b
d = 5 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: if the number of white balls in a box are 6 times the black balls , which of the below is the total number of balls , if there are 8 black balls in the box ?
Options: a ) a - 56 , b ) b - 57 , c ) c - 58 , d ) d - 59 , e ) e - 60
Rationale: let the number of black balls = x and the number of white balls = 6 x then , total number of balls in the box = x + 6 x = 7 x i . e . , the total number of balls must be a multiple of 7 from the given choices , only 56 is the multiple of 7 . hence , 56 are the number of balls in the box . answer is a .
Answer: a
Python program:
a = 6 * 8
b = a + 8
Problem: a trader marked the selling price of an article at 50 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 7.3 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 150 * 100 ] % = 7.3 % answer a"
Answer: a
Python program:
a = 2 + 3 
b = a * 2
c = b + 1 
d = 100 + 50 
e = c / d
f = 100 * e
Problem: 45 % of 750 - 25 % of 480 = ?
Options: a ) 216 , b ) 217.5 , c ) 236.5 , d ) 245 , e ) 250
Rationale: "explanation : given expression = ( 45 / 100 * 750 ) - ( 25 / 100 * 480 ) = ( 337.50 - 120 ) = 217.50 answer is b"
Answer: b
Python program:
a = 45 * 750
b = a / 25
Problem: among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 90 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 42 , c ) 56 , d ) 32 , e ) 40
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 90 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 90 = 110 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 60 = 40 . thus e is the correct answer choice"
Answer: e
Python program:
a = 15 / 100
b = 30 / a
c = b - 90
d = c / 2
Problem: 72 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 77 , b ) b ) 99 , c ) c ) 66 , d ) d ) 55 , e ) e ) 88
Rationale: "( 72 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 160 160 – 72 = 88 answer : e"
Answer: e
Python program:
a = 72 * 8
b = a / 30
c = b * 50
d = c / 6
e = d - 72
Problem: how many of the positive divisors of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120 . consider factors of 120 4 * 30 6 * 20 15 * 8 24 * 5 60 * 2 total we get 5 different ways and all are part of 4 . answer : c is correct option .
Answer: c
Python program:
a = 120 / 4
b = a / 2
c = b / 3